Spin Bose-metal phase in a spin- (1)/(2) model with ring exchange on a two-leg triangular strip

NASA Astrophysics Data System (ADS)

Sheng, D. N.; Motrunich, Olexei I.; Fisher, Matthew P. A.

2009-05-01

Recent experiments on triangular lattice organic Mott insulators have found evidence for a two-dimensional (2D) spin liquid in close proximity to the metal-insulator transition. A Gutzwiller wave function study of the triangular lattice Heisenberg model with a four-spin ring exchange term appropriate in this regime has found that the projected spinon Fermi sea state has a low variational energy. This wave function, together with a slave particle-gauge theory analysis, suggests that this putative spin liquid possesses spin correlations that are singular along surfaces in momentum space, i.e., “Bose surfaces.” Signatures of this state, which we will refer to as a “spin Bose metal” (SBM), are expected to manifest in quasi-one-dimensional (quasi-1D) ladder systems: the discrete transverse momenta cut through the 2D Bose surface leading to a distinct pattern of 1D gapless modes. Here, we search for a quasi-1D descendant of the triangular lattice SBM state by exploring the Heisenberg plus ring model on a two-leg triangular strip (zigzag chain). Using density matrix renormalization group (DMRG) supplemented by variational wave functions and a bosonization analysis, we map out the full phase diagram. In the absence of ring exchange the model is equivalent to the J1-J2 Heisenberg chain, and we find the expected Bethe-chain and dimerized phases. Remarkably, moderate ring exchange reveals a new gapless phase over a large swath of the phase diagram. Spin and dimer correlations possess singular wave vectors at particular “Bose points” (remnants of the 2D Bose surface) and allow us to identify this phase as the hoped for quasi-1D descendant of the triangular lattice SBM state. We use bosonization to derive a low-energy effective theory for the zigzag spin Bose metal and find three gapless modes and one Luttinger parameter controlling all power law correlations. Potential instabilities out of the zigzag SBM give rise to other interesting phases such as a period-3 valence bond solid or a period-4 chirality order, which we discover in the DMRG. Another interesting instability is into a spin Bose-metal phase with partial ferromagnetism (spin polarization of one spinon band), which we also find numerically using the DMRG.

Hydration of an apolar solute in a two-dimensional waterlike lattice fluid

NASA Astrophysics Data System (ADS)

Buzano, C.; de Stefanis, E.; Pretti, M.

2005-05-01

In a previous work, we investigated a two-dimensional lattice-fluid model, displaying some waterlike thermodynamic anomalies. The model, defined on a triangular lattice, is now extended to aqueous solutions with apolar species. Water molecules are of the “Mercedes Benz” type, i.e., they possess a D3 (equilateral triangle) symmetry, with three equivalent bonding arms. Bond formation depends both on orientation and local density. The insertion of inert molecules displays typical signatures of hydrophobic hydration: large positive transfer free energy, large negative transfer entropy (at low temperature), strong temperature dependence of the transfer enthalpy and entropy, i.e., large (positive) transfer heat capacity. Model properties are derived by a generalized first order approximation on a triangle cluster.

Hydration of an apolar solute in a two-dimensional waterlike lattice fluid.

PubMed

Buzano, C; De Stefanis, E; Pretti, M

2005-05-01

In a previous work, we investigated a two-dimensional lattice-fluid model, displaying some waterlike thermodynamic anomalies. The model, defined on a triangular lattice, is now extended to aqueous solutions with apolar species. Water molecules are of the "Mercedes Benz" type, i.e., they possess a D3 (equilateral triangle) symmetry, with three equivalent bonding arms. Bond formation depends both on orientation and local density. The insertion of inert molecules displays typical signatures of hydrophobic hydration: large positive transfer free energy, large negative transfer entropy (at low temperature), strong temperature dependence of the transfer enthalpy and entropy, i.e., large (positive) transfer heat capacity. Model properties are derived by a generalized first order approximation on a triangle cluster.

Spin liquid state in the disordered triangular lattice Sc 2Ga 2CuO 7 revealed by NMR

DOE PAGES

Khuntia, P.; Kumar, R.; Mahajan, A. V.; ...

2016-04-18

We present microscopic magnetic properties of a two-dimensional triangular lattice Sc 2Ga 2CuO 7, consisting of single and double triangular Cu planes. An antiferromagnetic (AFM) exchange interaction J/k B ≈ 35 K between Cu 2+ (S = 1/2) spins in the triangular biplane is obtained from the analysis of intrinsic magnetic susceptibility data. The intrinsic magnetic susceptibility, extracted from 71Ga NMR shift data, displays the presence of AFM short range spin correlations and remains finite down to 50 mK, suggesting a nonsinglet ground state. The nuclear spin-lattice relaxation rate (1/T 1) reveals a slowing down of Cu 2+ spin fluctuationsmore » with decreasing T down to 100 mK. Magnetic specific heat (C m) and 1/T 1 exhibit power law behavior at low temperatures, implying the gapless nature of the spin excitation spectrum. The absence of long range magnetic ordering down to ~J/700, nonzero spin susceptibility at low T, and the power law behavior of C m and 1/T 1 suggest a gapless quantum spin liquid (QSL) state. Our results demonstrate that persistent spin dynamics induced by frustration maintain a quantum-disordered state at T → 0 in this triangular lattice antiferromagnet. Furthermore, this suggests that the low energy modes are dominated by spinon excitations in the QSL state due to randomness engendered by disorder and frustration.« less

Ising antiferromagnet on the Archimedean lattices.

PubMed

Yu, Unjong

2015-06-01

Geometric frustration effects were studied systematically with the Ising antiferromagnet on the 11 Archimedean lattices using the Monte Carlo methods. The Wang-Landau algorithm for static properties (specific heat and residual entropy) and the Metropolis algorithm for a freezing order parameter were adopted. The exact residual entropy was also found. Based on the degree of frustration and dynamic properties, ground states of them were determined. The Shastry-Sutherland lattice and the trellis lattice are weakly frustrated and have two- and one-dimensional long-range-ordered ground states, respectively. The bounce, maple-leaf, and star lattices have the spin ice phase. The spin liquid phase appears in the triangular and kagome lattices.

Ising antiferromagnet on the Archimedean lattices

NASA Astrophysics Data System (ADS)

Yu, Unjong

2015-06-01

Geometric frustration effects were studied systematically with the Ising antiferromagnet on the 11 Archimedean lattices using the Monte Carlo methods. The Wang-Landau algorithm for static properties (specific heat and residual entropy) and the Metropolis algorithm for a freezing order parameter were adopted. The exact residual entropy was also found. Based on the degree of frustration and dynamic properties, ground states of them were determined. The Shastry-Sutherland lattice and the trellis lattice are weakly frustrated and have two- and one-dimensional long-range-ordered ground states, respectively. The bounce, maple-leaf, and star lattices have the spin ice phase. The spin liquid phase appears in the triangular and kagome lattices.

Two-dimensional lattice-fluid model with waterlike anomalies.

PubMed

Buzano, C; De Stefanis, E; Pelizzola, A; Pretti, M

2004-06-01

We investigate a lattice-fluid model defined on a two-dimensional triangular lattice, with the aim of reproducing qualitatively some anomalous properties of water. Model molecules are of the "Mercedes Benz" type, i.e., they possess a D3 (equilateral triangle) symmetry, with three bonding arms. Bond formation depends both on orientation and local density. We work out phase diagrams, response functions, and stability limits for the liquid phase, making use of a generalized first order approximation on a triangle cluster, whose accuracy is verified, in some cases, by Monte Carlo simulations. The phase diagram displays one ordered (solid) phase which is less dense than the liquid one. At fixed pressure the liquid phase response functions show the typical anomalous behavior observed in liquid water, while, in the supercooled region, a reentrant spinodal is observed.

Magnetic Interaction in the Geometrically Frustrated Triangular LatticeAntiferromagnet CuFeO2

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ye, Feng; Fernandez-Baca, Jaime A; Fishman, Randy Scott

2007-01-01

The spin wave excitations of the geometrically frustrated triangular lattice antiferromagnet (TLA) CuFeO2 have been measured using high resolution inelastic neutron scattering. Antiferromagnetic interactions up to third nearest neighbors in the ab plane (J1, J2, J3, with J2=J1 0:44 and J3=J1 0:57), as well as out-of-plane coupling (Jz, with Jz=J1 0:29) are required to describe the spin wave dispersion relations, indicating a three dimensional character of the magnetic interactions. Two energy deeps in the spin wave dispersion occur at the incommensurate wavevectors associated with multiferroic phase, and can be interpreted as dynamic precursors to the magnetoelectric behavior in this system.

Field-Induced Magnetic Phase Transitions in a Triangular Lattice Antiferromagnet CuFeO 2 up to 14.5 T

NASA Astrophysics Data System (ADS)

Mitsuda, Setsuo; Mase, Motoshi; Prokes, K.; Kitazawa, Hideaki; Katori, H.

2000-11-01

Neutron diffraction studies on a frustrated triangular lattice antiferromagnet (TLA) CuFeO2 have been performed under an applied magnetic field up to 14.5 T. The first-field-induced state was found to be not the commensurate 5-sublattice (↑↑↑↓↓) magnetic state but rather an incommensurate complex helical state reflecting the Heisenberg spin character of orbital singlet Fe3+ magnetic ions. In contrast, the second-field-induced state was found to be the 5-sublattice (↑↑↑↓↓) magnetic state predicted by the two-dimensional (2D) Ising spin TLA model with competing exchange interactions up to the 3rd neighbors.

Properties of spin-1/2 triangular-lattice antiferromagnets CuY2Ge2O8 and CuLa2Ge2O8

NASA Astrophysics Data System (ADS)

Cho, Hwanbeom; Kratochvílová, Marie; Sim, Hasung; Choi, Ki-Young; Kim, Choong Hyun; Paulsen, Carley; Avdeev, Maxim; Peets, Darren C.; Jo, Younghun; Lee, Sanghyun; Noda, Yukio; Lawler, Michael J.; Park, Je-Geun

2017-04-01

We found new two-dimensional (2D) quantum (S =1 /2 ) antiferromagnetic systems: Cu R E2G e2O8 (R E =Y and La). According to our analysis of high-resolution x-ray and neutron diffraction experiments, the Cu network of Cu R E2G e2O8 (R E =Y and La) exhibits a 2D triangular lattice linked via weak bonds along the perpendicular b axis. Our bulk characterizations from 0.08 to 400 K show that they undergo a long-range order at 0.51(1) and 1.09(4) K for the Y and La systems, respectively. Interestingly, they also exhibit field induced phase transitions. For theoretical understanding, we carried out the density functional theory (DFT) band calculations to find that they are typical charge-transfer-type insulators with a gap of Eg≅2 eV . Taken together, our observations make Cu R E2G e2O8 (R E =Y and La) additional examples of low-dimensional quantum spin triangular antiferromagnets with the low-temperature magnetic ordering.

Diophantine Approach to the Classification of Two-Dimensional Lattices: Surfaces of Face-Centered Cubic Materials.

PubMed

Jenkins, Stephen J

2018-04-03

The long-range periodic order of a crystalline surface is generally represented by means of a two-dimensional Bravais lattice, of which only five symmetrically distinct types are possible. Here, we explore the circumstances under which each type may or may not be found at the surfaces of face-centered cubic materials and provide means by which the type of lattice may be determined with reference only to the Miller indices of the surface; the approach achieves formal rigor by focusing on the number theory of integer variables rather than directly upon real geometry. We prove that the {100} and {111} surfaces are, respectively, the only exemplars of square and triangular lattices. For surfaces exhibiting a single mirror plane, we not only show that rectangular and rhombic lattices are the only two possibilities, but also capture their alternation in terms of the parity of the indices. In the case of chiral surfaces, oblique lattices predominate, but rectangular and rhombic cases are also possible and arise according to well-defined rules, here partially recounted.

Field-controlled ultrafast magnetization dynamics in two-dimensional nanoscale ferromagnetic antidot arrays

PubMed Central

De, Anulekha; Mondal, Sucheta; Sahoo, Sourav; Barman, Saswati; Otani, Yoshichika; Mitra, Rajib Kumar

2018-01-01

Ferromagnetic antidot arrays have emerged as a system of tremendous interest due to their interesting spin configuration and dynamics as well as their potential applications in magnetic storage, memory, logic, communications and sensing devices. Here, we report experimental and numerical investigation of ultrafast magnetization dynamics in a new type of antidot lattice in the form of triangular-shaped Ni80Fe20 antidots arranged in a hexagonal array. Time-resolved magneto-optical Kerr effect and micromagnetic simulations have been exploited to study the magnetization precession and spin-wave modes of the antidot lattice with varying lattice constant and in-plane orientation of the bias-magnetic field. A remarkable variation in the spin-wave modes with the orientation of in-plane bias magnetic field is found to be associated with the conversion of extended spin-wave modes to quantized ones and vice versa. The lattice constant also influences this variation in spin-wave spectra and spin-wave mode profiles. These observations are important for potential applications of the antidot lattices with triangular holes in future magnonic and spintronic devices. PMID:29719763

Two-dimensional lattice-fluid model with waterlike anomalies

NASA Astrophysics Data System (ADS)

Buzano, C.; de Stefanis, E.; Pelizzola, A.; Pretti, M.

2004-06-01

We investigate a lattice-fluid model defined on a two-dimensional triangular lattice, with the aim of reproducing qualitatively some anomalous properties of water. Model molecules are of the “Mercedes Benz” type, i.e., they possess a D3 (equilateral triangle) symmetry, with three bonding arms. Bond formation depends both on orientation and local density. We work out phase diagrams, response functions, and stability limits for the liquid phase, making use of a generalized first order approximation on a triangle cluster, whose accuracy is verified, in some cases, by Monte Carlo simulations. The phase diagram displays one ordered (solid) phase which is less dense than the liquid one. At fixed pressure the liquid phase response functions show the typical anomalous behavior observed in liquid water, while, in the supercooled region, a reentrant spinodal is observed.

An existence criterion for low-dimensional materials

NASA Astrophysics Data System (ADS)

Chen, Jiapeng; Wang, Biao; Hu, Yangfan

2017-10-01

The discovery of graphene and other two-dimensional (2-D) materials has stimulated a general interest in low-dimensional (low-D) materials. Whereas long time ago, Peierls (1935) and Landau's (1937) theoretical work demonstrated that any one- and two-dimensional materials could not exist in any finite temperature environment. Then, two basic issues became a central concern for many researchers: How can stable low-D materials exist? What kind of low-D materials are stable? Here, we establish an energy stability criterion for low-D materials, which seeks to provide a clear answer to these questions. For a certain kind of element, the stability of its specific low-D structure is determined by several derivatives of its interatomic potential. This atomistic-based approach is then applied to study any straight/planar, low-D, equal-bond-length elemental materials. We found that 1-D monatomic chains, 2-D honeycomb lattices, square lattices, and triangular lattices are the only four permissible structures, and the stability of these structures can only be understood by assuming multi-body interatomic potentials. Using this approach, the stable existence of graphene, silicene and germanene can be explained.

Critical frontier of the Potts and percolation models on triangular-type and kagome-type lattices. II. Numerical analysis

NASA Astrophysics Data System (ADS)

Ding, Chengxiang; Fu, Zhe; Guo, Wenan; Wu, F. Y.

2010-06-01

In the preceding paper, one of us (F. Y. Wu) considered the Potts model and bond and site percolation on two general classes of two-dimensional lattices, the triangular-type and kagome-type lattices, and obtained closed-form expressions for the critical frontier with applications to various lattice models. For the triangular-type lattices Wu’s result is exact, and for the kagome-type lattices Wu’s expression is under a homogeneity assumption. The purpose of the present paper is twofold: First, an essential step in Wu’s analysis is the derivation of lattice-dependent constants A,B,C for various lattice models, a process which can be tedious. We present here a derivation of these constants for subnet networks using a computer algorithm. Second, by means of a finite-size scaling analysis based on numerical transfer matrix calculations, we deduce critical properties and critical thresholds of various models and assess the accuracy of the homogeneity assumption. Specifically, we analyze the q -state Potts model and the bond percolation on the 3-12 and kagome-type subnet lattices (n×n):(n×n) , n≤4 , for which the exact solution is not known. Our numerical determination of critical properties such as conformal anomaly and magnetic correlation length verifies that the universality principle holds. To calibrate the accuracy of the finite-size procedure, we apply the same numerical analysis to models for which the exact critical frontiers are known. The comparison of numerical and exact results shows that our numerical values are correct within errors of our finite-size analysis, which correspond to 7 or 8 significant digits. This in turn infers that the homogeneity assumption determines critical frontiers with an accuracy of 5 decimal places or higher. Finally, we also obtained the exact percolation thresholds for site percolation on kagome-type subnet lattices (1×1):(n×n) for 1≤n≤6 .

Supersolid-like magnetic states in a mixed honeycomb-triangular lattice system.

NASA Astrophysics Data System (ADS)

Garlea, Ovidiu

Field-induced magnetic states that occur in layered triangular antiferromagnets have been of broad interest due to the emergence of new exotic phases, such as topologically ordered states and supersolids. Experimental realization of the supersolid states where spin components break simultaneously the translational and rotational symmetries remains scarce. In this context, the mixed vanadate -carbonate K2Mn3(VO4)2CO3 is a very promising system. This compound contains two types of two-dimensional layers alternately stacked along the crystallographic c-axis: one layer consists of a honeycomb web structure made of edge sharing MnO6 octahedra, while the other consists of MnO5 trigonal bipyramids linked by [CO3] triangles to form a triangular magnetic lattice. Magnetization and heat capacity measurements reveal a complex magnetic phase diagram that includes three phase transition associated with sequential long range magnetic ordering of the different sublattices. The lowest temperature state resembles a supersolid state that was predicted to occur in two-dimensional frustrated magnet with easy axis anisotropy. Such a supersolid phase is defined by a commensurate √3× √3 magnetic superlattice, where two thirds of the spins are canted away from the easy axis direction. Applied magnetic field destabilizes this ordered state and induces a cascade of new exotic magnetic ground states. The nature of these field-induced magnetic states is evaluated by using neutron scattering techniques. Work at the Oak Ridge National Laboratory was sponsored by the US Department of Energy, Office of Science, Basic Energy Sciences, Scientific User Facilities Division and Materials Sciences and Engineering Division.

Internal Magnetic Field on the Two-Dimensional Triangular Lattice Formed by Mo3O8 Trimers

NASA Astrophysics Data System (ADS)

Sugiyama, Jun; Nozaki, Hiroshi; Umegaki, Izumi; Haraguchi, Yuya; Michioka, Chishiro; Ueda, Hiroaki; Yoshimura, Kazuyoshi; Sassa, Yasmine; Forslund, Ola Kenji; Andreica, Daniel; Goko, Tatsuo; Amato, Alex; Månsson, Martin

In order to elucidate the magnetic ground state of the cluster magnets with a half filled triangular lattice, we have recorded zero field (ZF-) and weak transverse field (wTF-) μ+SR spectra using powder samples of Li2InMo3O8 and Li2ScMo3O8 down to 1.9 K. The ZF measurements at 1.9 K demonstrated the presence of static magnetic order in Li2InMo3O8, whereas paramagnetic nature in Li2ScMo3O8. The wTF measurements clarified that the magnetic transition occurs at around 11 K (= TN) in Li2InMo3O8. However, for Li2ScMo3O8, there is no detectable change in the ZF- and wTF-μ+SR fit-parameters in the temperature range between 60 and 1.9 K.

Multiferroicity in the generic easy-plane triangular lattice antiferromagnet RbFe(MoO4)2

NASA Astrophysics Data System (ADS)

White, J. S.; Niedermayer, Ch.; Gasparovic, G.; Broholm, C.; Park, J. M. S.; Shapiro, A. Ya.; Demianets, L. A.; Kenzelmann, M.

2013-08-01

RbFe(MoO4)2 is a quasi-two-dimensional (quasi-2D) triangular lattice antiferromagnet (TLA) that displays a zero-field magnetically driven multiferroic phase with a chiral spin structure. By inelastic neutron scattering, we determine quantitatively the spin Hamiltonian. We show that the easy-plane anisotropy is nearly 1/3 of the dominant spin exchange, making RbFe(MoO4)2 an excellent system for studying the physics of the model 2D easy-plane TLA. Our measurements demonstrate magnetic-field-induced fluctuations in this material to stabilize the generic finite-field phases of the 2D XY TLA. We further explain how Dzyaloshinskii-Moriya interactions can generate ferroelectricity only in the zero-field phase. Our conclusion is that multiferroicity in RbFe(MoO4)2, and its absence at high fields, results from the generic properties of the 2D XY TLA.

Spontaneous magnetization and anomalous Hall effect in an emergent Dice lattice

PubMed Central

Dutta, Omjyoti; Przysiężna, Anna; Zakrzewski, Jakub

2015-01-01

Ultracold atoms in optical lattices serve as a tool to model different physical phenomena appearing originally in condensed matter. To study magnetic phenomena one needs to engineer synthetic fields as atoms are neutral. Appropriately shaped optical potentials force atoms to mimic charged particles moving in a given field. We present the realization of artificial gauge fields for the observation of anomalous Hall effect. Two species of attractively interacting ultracold fermions are considered to be trapped in a shaken two dimensional triangular lattice. A combination of interaction induced tunneling and shaking can result in an emergent Dice lattice. In such a lattice the staggered synthetic magnetic flux appears and it can be controlled with external parameters. The obtained synthetic fields are non-Abelian. Depending on the tuning of the staggered flux we can obtain either anomalous Hall effect or its quantized version. Our results are reminiscent of Anomalous Hall conductivity in spin-orbit coupled ferromagnets. PMID:26057635

Spin Structures and Phase Diagrams of Extended Spatially Completely Anisotropic Triangular Lattice Antiferromagnets

NASA Astrophysics Data System (ADS)

Sakakida, Keishiro; Shimahara, Hiroshi

2017-12-01

Motivated by recently discovered organic antiferromagnets, we examine an extended triangular lattice that consists of two types of triangles of bonds with exchange coupling constants Jℓ and J'ℓ (ℓ= 1, 2, and 3), respectively. The simplified system with Jℓ = J'ℓ > 0 is the spatially completely anisotropic triangular lattice (SCATL) antiferromagnet examined previously. The extended system, which we call an extended SCATL (ESCATL), has two different spatial anisotropy parameters J3/J2 and J'3/J'2 when J1 = J'1 is assumed. We derive classical phase diagrams and spin structures. It is found that the ESCATL antiferromagnet exhibits two up-up-down-down (uudd) phases when the imbalance of the anisotropy parameters is significant, in addition to the three Néel phases that occur in the SCATL. When the model parameters vary, these collinear phases are continuously connected by the spiral-spin phase. Using the available model parameters for the organic compounds λ-(BETS)2XCl4 (X = Fe and Ga), we examine the stabilities of the spin structures of the independent π-electron system, which is considered to primarily sustain the magnetic order, where BETS represents bis(ethylenedithio)tetraselenafulvalene. It is found that one of the uudd phases has an energy close to the ground-state energy for λ-(BETS)2FeCl4. We discuss the relevance of the magnetic anion FeCl4 and the quantum fluctuation to the magnetism of these compounds. When J'3 = 0, the system is reduced to a trellis lattice antiferromagnet. The system exhibits a stripe spiral-spin phase, which comprises one-dimensional spiral-spin states stacked alternately.

Linear flavor-wave theory for fully antisymmetric SU(N ) irreducible representations

NASA Astrophysics Data System (ADS)

Kim, Francisco H.; Penc, Karlo; Nataf, Pierre; Mila, Frédéric

2017-11-01

The extension of the linear flavor-wave theory to fully antisymmetric irreducible representations (irreps) of SU (N ) is presented in order to investigate the color order of SU (N ) antiferromagnetic Heisenberg models in several two-dimensional geometries. The square, triangular, and honeycomb lattices are considered with m fermionic particles per site. We present two different methods: the first method is the generalization of the multiboson spin-wave approach to SU (N ) which consists of associating a Schwinger boson to each state on a site. The second method adopts the Read and Sachdev bosons which are an extension of the Schwinger bosons that introduces one boson for each color and each line of the Young tableau. The two methods yield the same dispersing modes, a good indication that they properly capture the semiclassical fluctuations, but the first one leads to spurious flat modes of finite frequency not present in the second one. Both methods lead to the same physical conclusions otherwise: long-range Néel-type order is likely for the square lattice for SU(4) with two particles per site, but quantum fluctuations probably destroy order for more than two particles per site, with N =2 m . By contrast, quantum fluctuations always lead to corrections larger than the classical order parameter for the tripartite triangular lattice (with N =3 m ) or the bipartite honeycomb lattice (with N =2 m ) for more than one particle per site, m >1 , making the presence of color very unlikely except maybe for m =2 on the honeycomb lattice, for which the correction is only marginally larger than the classical order parameter.

Shear localization in three-dimensional amorphous solids.

PubMed

Dasgupta, Ratul; Gendelman, Oleg; Mishra, Pankaj; Procaccia, Itamar; Shor, Carmel A B Z

2013-09-01

In this paper we extend the recent theory of shear localization in two-dimensional (2D) amorphous solids to three dimensions. In two dimensions the fundamental instability of shear localization is related to the appearance of a line of displacement quadrupoles that makes an angle of 45^{∘} with the principal stress axis. In three dimensions the fundamental plastic instability is also explained by the formation of a lattice of anisotropic elastic inclusions. In the case of pure external shear stress, we demonstrate that this is a 2D triangular lattice of similar elementary events. It is shown that this lattice is arranged on a plane that, similarly to the 2D case, makes an angle of 45^{∘} with the principal stress axis. This solution is energetically favorable only if the external strain exceeds a yield-strain value that is determined by the strain parameters of the elementary events and the Poisson ratio. The predictions of the theory are compared to numerical simulations and very good agreement is observed.

Mean-field scaling of the superfluid to Mott insulator transition in a 2D optical superlattice.

NASA Astrophysics Data System (ADS)

Okano, Masayuki; Thomas, Claire; Barter, Thomas; Leung, Tsz-Him; Jo, Gyu-Boong; Guzman, Jennie; Kimchi, Itamar; Vishwanath, Ashvin; Stamper-Kurn, Dan

2017-04-01

Quantum gases within optical lattices provide a nearly ideal experimental representation of the Bose-Hubbard model. The mean-field treatment of this model predicts properties of non-zero temperature lattice-trapped gasses to be insensitive to the specific lattice geometry once system energies are scaled by the lattice coordination number z. We examine an ultracold Bose gas of rubidium atoms prepared within a two-dimensional lattice whose geometry can be tuned between two configurations, triangular and kagome, for which z varies from six to four, respectively. Measurements of the coherent fraction of the gas thereby provide a quantitative test of the mean-field scaling prediction. We observe the suppression of superfluidity upon decreasing z, and find our results to be consistent with the predicted mean-field scaling. These optical lattice systems can offer a way to study paradigmatic solid-state phenomena in highly controlled crystal structures. This work was supported by the NSF and by the Army Research Office with funding from the DARPA OLE program.

Still states of bistable lattices, compatibility, and phase transition

NASA Astrophysics Data System (ADS)

Cherkaev, Andrej; Kouznetsov, Andrei; Panchenko, Alexander

2010-09-01

We study a two-dimensional triangular lattice made of bistable rods. Each rod has two equilibrium lengths, and thus its energy has two equal minima. A rod undergoes a phase transition when its elongation exceeds a critical value. The lattice is subject to a homogeneous strain and is periodic with a sufficiently large period. The effective strain of a periodic element is defined. After phase transitions, the lattice rods are in two different states and lattice strain is inhomogeneous, the Cauchy-Born rule is not applicable. We show that the lattice has a number of deformed still states that carry no stresses. These states densely cover a neutral region in the space of entries of effective strains. In this region, the minimal energy of the periodic lattice is asymptotically close to zero. When the period goes to infinity, the effective energy of such lattices has the “flat bottom” which we explicitly describe. The compatibility of the partially transited lattice is studied. We derive compatibility conditions for lattices and demonstrate a family of compatible lattices (strips) that densely covers the flat bottom region. Under an additional assumption of the small difference of two equilibrium lengths, we demonstrate that the still structures continuously vary with the effective strain and prove a linear dependence of the average strain on the concentration of transited rods.

Finite-temperature mechanical instability in disordered lattices.

PubMed

Zhang, Leyou; Mao, Xiaoming

2016-02-01

Mechanical instability takes different forms in various ordered and disordered systems and little is known about how thermal fluctuations affect different classes of mechanical instabilities. We develop an analytic theory involving renormalization of rigidity and coherent potential approximation that can be used to understand finite-temperature mechanical stabilities in various disordered systems. We use this theory to study two disordered lattices: a randomly diluted triangular lattice and a randomly braced square lattice. These two lattices belong to two different universality classes as they approach mechanical instability at T=0. We show that thermal fluctuations stabilize both lattices. In particular, the triangular lattice displays a critical regime in which the shear modulus scales as G∼T(1/2), whereas the square lattice shows G∼T(2/3). We discuss generic scaling laws for finite-T mechanical instabilities and relate them to experimental systems.

Numerical-Diagonalization Study of Magnetization Process of Frustrated Spin-1/2 Heisenberg Antiferromagnets in Two Dimensions: —Triangular- and Kagome-Lattice Antiferromagnets—

NASA Astrophysics Data System (ADS)

Nakano, Hiroki; Sakai, Tôru

2018-06-01

The S = 1/2 triangular- and kagome-lattice Heisenberg antiferromagnets are investigated under a magnetic field using the numerical-diagonalization method. A procedure is proposed to extract data points with very small finite-size deviations using the numerical-diagonalization results for capturing the magnetization curve. For the triangular-lattice antiferromagnet, the plateau edges at one-third the height of the saturation and the saturation field are successfully estimated. This study additionally presents results of magnetization process for a 45-site cluster of the kagome-lattice antiferromagnet; the present analysis suggests that the plateau does not open at one-ninth the height of the saturation.

Spin frustration and magnetic ordering in triangular lattice antiferromagnet Ca3CoNb2O9

NASA Astrophysics Data System (ADS)

Dai, Jia; Zhou, Ping; Wang, Peng-Shuai; Pang, Fei; Munsie, Tim J.; Luke, Graeme M.; Zhang, Jin-Shan; Yu, Wei-Qiang

2015-12-01

We synthesized a quasi-two-dimensional distorted triangular lattice antiferromagnet Ca3CoNb2O9, in which the effective spin of Co2+ is 1/2 at low temperatures, whose magnetic properties were studied by dc susceptibility and magnetization techniques. The x-ray diffraction confirms the quality of our powder samples. The large Weiss constant θCW˜ -55 K and the low Neel temperature TN˜ 1.45 K give a frustration factor f = | θCW/TN | ≈ 38, suggesting that Ca3CoNb2O9 resides in strong frustration regime. Slightly below TN, deviation between the susceptibility data under zero-field cooling (ZFC) and field cooling (FC) is observed. A new magnetic state with 1/3 of the saturate magnetization Ms is suggested in the magnetization curve at 0.46 K. Our study indicates that Ca3CoNb2O9 is an interesting material to investigate magnetism in triangular lattice antiferromagnets with weak anisotropy. Project supported by the National Natural Science Foundation of China (Grant Nos. 11374364 and 11222433), the National Basic Research Program of China (Grant No. 2011CBA00112). Research at McMaster University supported by the Natural Sciences and Engineering Research Council. Work at North China Electric Power University supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.

Infinite lattices of vortex molecules in Rabi-coupled condensates

NASA Astrophysics Data System (ADS)

Mencia Uranga, B.; Lamacraft, Austen

2018-04-01

Vortex molecules can form in a two-component superfluid when a Rabi field drives transitions between the two components. We study the ground state of an infinite system of vortex molecules in two dimensions, using a numerical scheme which makes no use of the lowest Landau level approximation. We find the ground state lattice geometry for different values of intercomponent interactions and strength of the Rabi field. In the limit of large field when molecules are tightly bound, we develop a complementary analytical description. The energy governing the alignment of molecules on a triangular lattice is found to correspond to that of an infinite system of two-dimensional quadrupoles, which may be written in terms of an elliptic function Q (zi j;ω1,ω2) . This allows for a numerical evaluation of the energy which enables us to find the ground state configuration of the molecules.

Magnetic Correlations in the Triangular Antiferromagnet TbInO3

NASA Astrophysics Data System (ADS)

Sala, Gabriele; Clark, Lucy; Maharaj, Dalini; Stone, Matthew B.; Knight, Kevin S.; Cheong, Sang-Wook; Gaulin, Bruce D.

TbInO3 crystallizes with a hexagonal P63 cm structure in which layers of edge-sharing triangles of magnetic Tb3+ ions are separated by non-magnetic [InO5]7- units. TbInO3, therefore, realizes an excellent opportunity to explore the behavior of a two-dimensional magnetic triangular lattice, a canonical model of geometric frustration. Here we present our study of a polycrystalline sample of TbInO3. Our high resolution powder neutron diffraction data (HRPD, ISIS) of TbInO3 confirm that the triangular layers of Tb3+ remain undistorted to at least 0 . 46 K. Magnetic susceptibility data follow Curie-Weiss behavior over a wide range of T with θ = - 17 . 19 (3) K indicating the dominance of antiferromagnetic correlations. The susceptibility data also show an absence of conventional long-range spin order down to at least 0 . 55 K, reflecting the frustrated nature of TbInO3. Elastic magnetic diffuse neutron scattering (SEQUOIA, SNS) is observed below ~ 15 K, due to the presence of static two-dimensional spin correlations. The spectrum of crystal field excitations in TbInO3 appears to have an exotic form due to the existence of two crystallographically distinct Tb3+ sites and leads to a strong Ising anisotropy of the spin symmetry.

The triangular kagomé lattices revisited

NASA Astrophysics Data System (ADS)

Liu, Xiaoyun; Yan, Weigen

2013-11-01

The dimer problem, Ising spins and bond percolation on the triangular kagomé lattice have been studied extensively by physicists. In this paper, based on the fact the triangular kagomé lattice with toroidal boundary condition can be regarded as the line graph of 3.12.12 lattice with toroidal boundary condition, we derive the formulae of the number of spanning trees, the energy, and the Kirchhoff index of the triangular kagomé lattice with toroidal boundary condition.

A novel analytical model for scattering limited electron transport in nano-dimensional InAlAs/InGaAs heterostructure for cryogenic applications

NASA Astrophysics Data System (ADS)

Sharma, Neetika; Verma, Neha; Jogi, Jyotika

2017-11-01

This paper models the scattering limited electron transport in a nano-dimensional In0.52Al0.48As/In0.53Ga0.47As/InP heterostructure. An analytical model for temperature dependent sheet carrier concentration and carrier mobility in a two dimensional electron gas, confined in a triangular potential well has been developed. The model accounts for all the major scattering process including ionized impurity scattering and lattice scattering. Quantum mechanical variational technique is employed for studying the intrasubband scattering mechanism in the two dimensional electron gas. Results of various scattering limited structural parameters such as energy band-gap and functional parameters such as sheet carrier concentration, scattering rate and mobility are presented. The model corroborates the dominance of ionized impurity scattering mechanism at low temperatures and that of lattice scattering at high temperatures, both in turn limiting the carrier mobility. Net mobility obtained taking various scattering mechanisms into account has been found in agreement with earlier reported results, thus validating the model.

Emergent properties of magnetic materials

NASA Astrophysics Data System (ADS)

Ratcliff, William Davis, II

In Tolstoy's War and Peace, history is presented as a tapestry spun from the daily interactions of large numbers of individuals. Even if one understands individuals, it is very difficult to predict history. Similarly, the interactions of large numbers of electrons give rise to properties that one would not initially guess from their microscopic interactions. During the course of my dissertation, I have explored emergent phenomena in a number of contexts. In ZnCr2O4, geometric frustration gives rise to a plethora of equivalent ground states. From these, a lower dimensional set of collinear spins on hexagons are selected to form the building blocks of the lattice. In MgTi2O4, quantum spins dimerize and form a unique chiral ordering pattern on the spinel lattice. Descending into two dimensions, differences in size and charge give rise to an ordering between triangular layers of magnetic and nonmagnetic ions. This triangular lattice allows for the possibility of observing the RVB spin liquid state, or perhaps a valence bond crystal and initial measurements are promising. Also, on the spinel lattice, ionic ordering gives rise to one dimensional chains with their own interesting physics. Finally, in the SrCoxTi1-x O3, system we find that upon reduction, tiny clusters of Co metal precipitate out and chemical inhomogeneity on the microscale may determine much of the physics. This has relevance to a number of recent claims of room temperature ferromagnism in dilute magnetic systems. In all of these systems, complex behavior emerges from well understood microscopic behavior. For me, this is the fascination of strongly correlated electronic systems.

Magnetoelectric control of spin-chiral ferroelectric domains in a triangular lattice antiferromagnet

NASA Astrophysics Data System (ADS)

Kimura, Kenta; Nakamura, Hiroyuki; Ohgushi, Kenya; Kimura, Tsuyoshi

2008-10-01

We have grown single crystals of a triangular lattice antiferromagnet (TLA), CuCrO2 , and investigated the correlation between magnetic and dielectric properties. Two magnetic phase transitions are observed at TN2≈24.2K and TN1≈23.6K . It was found that ferroelectric polarization along the triangular lattice plane develops at TN1 , suggesting that the system undergoes a transition into an out-of-plane 120° spin-chiral phase at TN1 . The TLA provides an opportunity for unique magnetoelectric control of spin-chiral ferroelectric domain structures by means of electric and/or magnetic fields.

Two-dimensional Magnetism in Arrays of Superconducting Rings

NASA Astrophysics Data System (ADS)

Reich, Daniel H.

1996-03-01

An array of superconducting rings in an applied field corresponding to a flux of Φ0 /2 per ring behaves like a 2D Ising antiferromagnet. Each ring has two energetically equivalent states with equal and opposite magnetic moments due to fluxoid quantization, and the dipolar coupling between rings favors antiparallel alignment of the moments. Using SQUID magnetometry and scanning Hall probe microscopy, we have studied the dynamics and magnetic configurations of micron-size aluminum rings on square, triangular, honeycomb, and kagomé lattices. We have found that there are significant antiferromagnetic correlations between rings, and that effects of geometrical frustration can be observed on the triangular and kagomé lattices. Long range correlations on the other lattices are suppressed by the analog of spin freezing that locks the rings in metastable states at low temperatures, and by quenched disorder due to imperfections in the fabrication. This disorder produces a roughly 1% variation in the rings' areas, which translates into an effective random field on the spins. The ring arrays are thus an extremely good realization of the 2D random-field Ising model. (Performed in collaboration with D. Davidović, S. Kumar, J. Siegel, S. B. Field, R. C. Tiberio, R. Hey, and K. Ploog.) (Supported by NSF grants DMR-9222541, and DMR-9357518, and by the David and Lucile Packard Foundation.)

Ordering of two-dimensional crystals confined in strips of finite width

NASA Astrophysics Data System (ADS)

Ricci, A.; Nielaba, P.; Sengupta, S.; Binder, K.

2007-01-01

Monte Carlo simulations are used to study the effect of confinement on a crystal of point particles interacting with an inverse power law potential ∝r-12 in d=2 dimensions. This system can describe colloidal particles at the air-water interface, a model system for experimental study of two-dimensional melting. It is shown that the state of the system (a strip of width D ) depends very sensitively on the precise boundary conditions at the two “walls” providing the confinement. If one uses a corrugated boundary commensurate with the order of the bulk triangular crystalline structure, both orientational order and positional order is enhanced, and such surface-induced order persists near the boundaries also at temperatures where the system in the bulk is in its fluid state. However, using smooth repulsive boundaries as walls providing the confinement, only the orientational order is enhanced, but positional (quasi-)long range order is destroyed: The mean-square displacement of two particles n lattice parameters apart in the y direction along the walls then crosses over from the logarithmic increase (characteristic for d=2 ) to a linear increase with n (characteristic for d=1 ). The strip then exhibits a vanishing shear modulus. These results are interpreted in terms of a phenomenological harmonic theory. Also the effect of incommensurability of the strip width D with the triangular lattice structure is discussed, and a comparison with surface effects on phase transitions in simple Ising and XY models is made.

Thermodynamics of Ising spins on the triangular kagome lattice: Exact analytical method and Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Loh, Y. L.; Yao, D. X.; Carlson, E. W.

2008-04-01

A new class of two-dimensional magnetic materials Cu9X2(cpa)6ṡxH2O ( cpa=2 -carboxypentonic acid; X=F,Cl,Br ) was recently fabricated in which Cu sites form a triangular kagome lattice (TKL). As the simplest model of geometric frustration in such a system, we study the thermodynamics of Ising spins on the TKL using exact analytic method as well as Monte Carlo simulations. We present the free energy, internal energy, specific heat, entropy, sublattice magnetizations, and susceptibility. We describe the rich phase diagram of the model as a function of coupling constants, temperature, and applied magnetic field. For frustrated interactions in the absence of applied field, the ground state is a spin liquid phase with residual entropy per spin s0/kB=(1)/(9)ln72≈0.4752… . In weak applied field, the system maps to the dimer model on a honeycomb lattice, with residual entropy 0.0359 per spin and quasi-long-range order with power-law spin-spin correlations that should be detectable by neutron scattering. The power-law correlations become exponential at finite temperatures, but the correlation length may still be long.

Graphical Representations and Cluster Algorithms for Ice Rule Vertex Models.

NASA Astrophysics Data System (ADS)

Shtengel, Kirill; Chayes, L.

2002-03-01

We introduce a new class of polymer models which is closely related to loop models, recently a topic of intensive studies. These particular models arise as graphical representations for ice-rule vertex models. The associated cluster algorithms provide a unification and generalisation of most of the existing algorithms. For many lattices, percolation in the polymer models evidently indicates first order phase transitions in the vertex models. Critical phases can be understood as being susceptible to colour symmetry breaking in the polymer models. The analysis includes, but is certainly not limited to the square lattice six-vertex model. In particular, analytic criteria can be found for low temperature phases in other even coordinated 2D lattices such as the triangular lattice, or higher dimensional lattices such as the hyper-cubic lattices of arbitrary dimensionality. Finally, our approach can be generalised to the vertex models that do not obey the ice rule, such as the eight-vertex model.

Comparison of different models of motion in a crowded environment: a Monte Carlo study.

PubMed

Polanowski, P; Sikorski, A

2017-02-22

In this paper we investigate the motion of molecules in crowded environments for two dramatically different types of molecular transport. The first type is realized by the dynamic lattice liquid model, which is based on a cooperative movement concept and thus, the motion of molecules is highly correlated. The second one corresponds to a so-called motion of a single agent where the motion of molecules is considered as a random walk without any correlation with other moving elements. The crowded environments are modeled as a two-dimensional triangular lattice with fixed impenetrable obstacles. Our simulation results indicate that the type of transport has an impact on the dynamics of the system, the percolation threshold, critical exponents, and on molecules' trajectories.

Response properties in the adsorption-desorption model on a triangular lattice

NASA Astrophysics Data System (ADS)

Šćepanović, J. R.; Stojiljković, D.; Jakšić, Z. M.; Budinski-Petković, Lj.; Vrhovac, S. B.

2016-06-01

The out-of-equilibrium dynamical processes during the reversible random sequential adsorption (RSA) of objects of various shapes on a two-dimensional triangular lattice are studied numerically by means of Monte Carlo simulations. We focused on the influence of the order of symmetry axis of the shape on the response of the reversible RSA model to sudden perturbations of the desorption probability Pd. We provide a detailed discussion of the significance of collective events for governing the time coverage behavior of shapes with different rotational symmetries. We calculate the two-time density-density correlation function C(t ,tw) for various waiting times tw and show that longer memory of the initial state persists for the more symmetrical shapes. Our model displays nonequilibrium dynamical effects such as aging. We find that the correlation function C(t ,tw) for all objects scales as a function of single variable ln(tw) / ln(t) . We also study the short-term memory effects in two-component mixtures of extended objects and give a detailed analysis of the contribution to the densification kinetics coming from each mixture component. We observe the weakening of correlation features for the deposition processes in multicomponent systems.

Mechanism of Superconductivity in Quasi-Two-Dimensional Organic Conductor β-(BDA-TTP) Salts

NASA Astrophysics Data System (ADS)

Nonoyama, Yoshito; Maekawa, Yukiko; Kobayashi, Akito; Suzumura, Yoshikazu; Ito, Hiroshi

2008-09-01

We investigate theoretically the superconductivity of two-dimensional organic conductors, β-(BDA-TTP)2SbF6 and β-(BDA-TTP)2AsF6, to understand the role of the spin and charge fluctuations. The transition temperature is estimated by applying random phase approximation to an extended Hubbard model wherein realistic transfer energies are estimated by extended Hückel calculation. We find a gapless superconducting state with a dxy-like symmetry, which is consistent with the experimental results obtained by specific heat and scanning tunneling microscope. In the present model with an effectively half-filled triangular lattice, spin fluctuation competes with charge fluctuation as a mechanism of pairing interaction since both fluctuations have the same characteristic momentum q=(π,0) for V being smaller than U. This is in contrast to a model with a quarter-filled square lattice, wherein both fluctuations contribute cooperatively to pairing interaction due to fluctuations having different characteristic momenta. The resultant difference in the superconductivity of these two materials is also discussed.

Finite element method analysis of band gap and transmission of two-dimensional metallic photonic crystals at terahertz frequencies.

PubMed

Degirmenci, Elif; Landais, Pascal

2013-10-20

Photonic band gap and transmission characteristics of 2D metallic photonic crystals at THz frequencies have been investigated using finite element method (FEM). Photonic crystals composed of metallic rods in air, in square and triangular lattice arrangements, are considered for transverse electric and transverse magnetic polarizations. The modes and band gap characteristics of metallic photonic crystal structure are investigated by solving the eigenvalue problem over a unit cell of the lattice using periodic boundary conditions. A photonic band gap diagram of dielectric photonic crystal in square lattice array is also considered and compared with well-known plane wave expansion results verifying our FEM approach. The photonic band gap designs for both dielectric and metallic photonic crystals are consistent with previous studies obtained by different methods. Perfect match is obtained between photonic band gap diagrams and transmission spectra of corresponding lattice structure.

Phase Transitions in a Model of Y-Molecules Abstract

NASA Astrophysics Data System (ADS)

Holz, Danielle; Ruth, Donovan; Toral, Raul; Gunton, James

Immunoglobulin is a Y-shaped molecule that functions as an antibody to neutralize pathogens. In special cases where there is a high concentration of immunoglobulin molecules, self-aggregation can occur and the molecules undergo phase transitions. This prevents the molecules from completing their function. We used a simplified model of 2-Dimensional Y-molecules with three identical arms on a triangular lattice with 2-dimensional Grand Canonical Ensemble. The molecules were permitted to be placed, removed, rotated or moved on the lattice. Once phase coexistence was found, we used histogram reweighting and multicanonical sampling to calculate our phase diagram.

2-D modeling of dual-mode acoustic phonon excitation of a triangular nanoplate

NASA Astrophysics Data System (ADS)

Tai, Po-Tse; Yu, Pyng; Tang, Jau

2010-08-01

In this theoretical work, we investigated coherent phonon excitation of a triangular nanoplate based on 2-D Fermi-Pasta-Ulam lattice model. Based on the two-temperature model commonly used in description of laser heating of metals, we considered two kinds of forces related to electronic and lattice stresses. Based on extensive simulation and analysis, we identified two major planar phonon modes, namely, a standing wave mode related to the triangle bisector and another mode corresponding to half of the side length. This work elucidates the roles of laser-induced electronic stress and lattice stress in controlling the initial phase and the amplitude ratio between these two phonon modes.

Computing arbitrary defect structures on arbitrary lattices on arbitrary geometries from arbitrary energies

NASA Astrophysics Data System (ADS)

Allen, Brian; Travesset, Alex

2004-03-01

Dislocations and disclinations play a fundamental role in the properties of two dimensional crystals. In this talk, it will be shown that a general computational framework can be developed by combining previous work of Seung and Nelson* and modern advances in objected oriented design. This allows separating the problem into independent classes such as: geometry (sphere, plane, torus..), lattice (triangular, square, etc..), type of defect (dislocation, disclinations, etc..), boundary conditions, type of order (crystalline, hexatic) or energy functional. As applications, the ground state of crystals in several geometries will be discussed. Experimental examples with colloidal particles will be shown. *S. Seung and D. Nelson, Phys. Rev. A 38, 1005 (1988)

Disorder-induced losses in photonic crystal waveguides with line defects.

PubMed

Gerace, Dario; Andreani, Lucio Claudio

2004-08-15

A numerical analysis of extrinsic diffraction losses in two-dimensional photonic crystal slabs with line defects is reported. To model disorder, a Gaussian distribution of hole radii in the triangular lattice of airholes is assumed. The extrinsic losses below the light line increase quadratically with the disorder parameter, decrease slightly with increasing core thickness, and depend weakly on the hole radius. For typical values of the disorder parameter the calculated loss values of guided modes below the light line compare favorably with available experimental results.

Effect of background dielectric on TE-polarized photonic bandgap of metallodielectric photonic crystals using Dirichlet-to-Neumann map method.

PubMed

Sedghi, Aliasghar; Rezaei, Behrooz

2016-11-20

Using the Dirichlet-to-Neumann map method, we have calculated the photonic band structure of two-dimensional metallodielectric photonic crystals having the square and triangular lattices of circular metal rods in a dielectric background. We have selected the transverse electric mode of electromagnetic waves, and the resulting band structures showed the existence of photonic bandgap in these structures. We theoretically study the effect of background dielectric on the photonic bandgap.

Ashkin-Teller criticality and weak first-order behavior of the phase transition to a fourfold degenerate state in two-dimensional frustrated Ising antiferromagnets

NASA Astrophysics Data System (ADS)

Liu, R. M.; Zhuo, W. Z.; Chen, J.; Qin, M. H.; Zeng, M.; Lu, X. B.; Gao, X. S.; Liu, J.-M.

2017-07-01

We study the thermal phase transition of the fourfold degenerate phases (the plaquette and single-stripe states) in the two-dimensional frustrated Ising model on the Shastry-Sutherland lattice using Monte Carlo simulations. The critical Ashkin-Teller-like behavior is identified both in the plaquette phase region and the single-stripe phase region. The four-state Potts critical end points differentiating the continuous transitions from the first-order ones are estimated based on finite-size-scaling analyses. Furthermore, a similar behavior of the transition to the fourfold single-stripe phase is also observed in the anisotropic triangular Ising model. Thus, this work clearly demonstrates that the transitions to the fourfold degenerate states of two-dimensional Ising antiferromagnets exhibit similar transition behavior.

Frustrated spin- 1 2 molecular magnetism in the mixed-valence antiferromagnets Ba 3 M Ru 2 O 9 ( M = In , Y, Lu)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ziat, D.; Aczel, Adam A.; Sinclair, R.

We have performed magnetic susceptibility, heat capacity, muon spin relaxation, and neutron-scattering measurements on three members of the family Ba 3MRu 2O 9, where M=In, Y, and Lu. These systems consist of mixed-valence Ru dimers on a triangular lattice with antiferromagnetic interdimer exchange. Although previous work has argued that charge order within the dimers or intradimer double exchange plays an important role in determining the magnetic properties, our results suggest that the dimers are better described as molecular units due to significant orbital hybridization, resulting in one spin-1/2 moment distributed equally over the two Ru sites. These molecular building blocksmore » form a frustrated, quasi-two-dimensional triangular lattice. Our zero- and longitudinal-field μSR results indicate that the molecular moments develop a collective, static magnetic ground state, with oscillations of the zero-field muon spin polarization indicative of long-range magnetic order in the Lu sample. In conclusion, the static magnetism is much more disordered in the Y and In samples, but they do not appear to be conventional spin glasses.« less

Frustrated spin- 1 2 molecular magnetism in the mixed-valence antiferromagnets Ba 3 M Ru 2 O 9 ( M = In , Y, Lu)

DOE PAGES

Ziat, D.; Aczel, Adam A.; Sinclair, R.; ...

2017-05-22

We have performed magnetic susceptibility, heat capacity, muon spin relaxation, and neutron-scattering measurements on three members of the family Ba 3MRu 2O 9, where M=In, Y, and Lu. These systems consist of mixed-valence Ru dimers on a triangular lattice with antiferromagnetic interdimer exchange. Although previous work has argued that charge order within the dimers or intradimer double exchange plays an important role in determining the magnetic properties, our results suggest that the dimers are better described as molecular units due to significant orbital hybridization, resulting in one spin-1/2 moment distributed equally over the two Ru sites. These molecular building blocksmore » form a frustrated, quasi-two-dimensional triangular lattice. Our zero- and longitudinal-field μSR results indicate that the molecular moments develop a collective, static magnetic ground state, with oscillations of the zero-field muon spin polarization indicative of long-range magnetic order in the Lu sample. In conclusion, the static magnetism is much more disordered in the Y and In samples, but they do not appear to be conventional spin glasses.« less

Strong and weak second-order topological insulators with hexagonal symmetry and ℤ3 index

NASA Astrophysics Data System (ADS)

Ezawa, Motohiko

2018-06-01

We propose second-order topological insulators (SOTIs) whose lattice structure has a hexagonal symmetry C6. We start with a three-dimensional weak topological insulator constructed on a stacked triangular lattice, which has only side topological surface states. We then introduce an additional mass term which gaps out the side surface states but preserves the hinge states. The resultant system is a three-dimensional SOTI. The bulk topological quantum number is shown to be the Z3 index protected by inversion time-reversal symmetry I T and rotoinversion symmetry I C6 . We obtain three phases: trivial, strong, and weak SOTI phases. We argue the origin of these two types of SOTIs. A hexagonal prism is a typical structure respecting these symmetries, where six topological hinge states emerge at the side. The building block is a hexagon in two dimensions, where topological corner states emerge at the six corners in the SOTI phase. Strong and weak SOTIs are obtained when the interlayer hopping interaction is strong and weak, respectively.

Phase diagram of the quantum Ising model with long-range interactions on an infinite-cylinder triangular lattice

NASA Astrophysics Data System (ADS)

Saadatmand, S. N.; Bartlett, S. D.; McCulloch, I. P.

2018-04-01

Obtaining quantitative ground-state behavior for geometrically-frustrated quantum magnets with long-range interactions is challenging for numerical methods. Here, we demonstrate that the ground states of these systems on two-dimensional lattices can be efficiently obtained using state-of-the-art translation-invariant variants of matrix product states and density-matrix renormalization-group algorithms. We use these methods to calculate the fully-quantitative ground-state phase diagram of the long-range interacting triangular Ising model with a transverse field on six-leg infinite-length cylinders and scrutinize the properties of the detected phases. We compare these results with those of the corresponding nearest neighbor model. Our results suggest that, for such long-range Hamiltonians, the long-range quantum fluctuations always lead to long-range correlations, where correlators exhibit power-law decays instead of the conventional exponential drops observed for short-range correlated gapped phases. Our results are relevant for comparisons with recent ion-trap quantum simulator experiments that demonstrate highly-controllable long-range spin couplings for several hundred ions.

Experimental realization of two-dimensional boron sheets

NASA Astrophysics Data System (ADS)

Feng, Baojie; Zhang, Jin; Zhong, Qing; Li, Wenbin; Li, Shuai; Li, Hui; Cheng, Peng; Meng, Sheng; Chen, Lan; Wu, Kehui

2016-06-01

A variety of two-dimensional materials have been reported in recent years, yet single-element systems such as graphene and black phosphorus have remained rare. Boron analogues have been predicted, as boron atoms possess a short covalent radius and the flexibility to adopt sp2 hybridization, features that favour the formation of two-dimensional allotropes, and one example of such a borophene material has been reported recently. Here, we present a parallel experimental work showing that two-dimensional boron sheets can be grown epitaxially on a Ag(111) substrate. Two types of boron sheet, a β12 sheet and a χ3 sheet, both exhibiting a triangular lattice but with different arrangements of periodic holes, are observed by scanning tunnelling microscopy. Density functional theory simulations agree well with experiments, and indicate that both sheets are planar without obvious vertical undulations. The boron sheets are quite inert to oxidization and interact only weakly with their substrate. We envisage that such boron sheets may find applications in electronic devices in the future.

Thermal algebraic-decay charge liquid driven by competing short-range Coulomb repulsion

NASA Astrophysics Data System (ADS)

Kaneko, Ryui; Nonomura, Yoshihiko; Kohno, Masanori

2018-05-01

We explore the possibility of a Berezinskii-Kosterlitz-Thouless-like critical phase for the charge degrees of freedom in the intermediate-temperature regime between the charge-ordered and disordered phases in two-dimensional systems with competing short-range Coulomb repulsion. As the simplest example, we investigate the extended Hubbard model with on-site and nearest-neighbor Coulomb interactions on a triangular lattice at half filling in the atomic limit by using a classical Monte Carlo method, and find a critical phase, characterized by algebraic decay of the charge correlation function, belonging to the universality class of the two-dimensional XY model with a Z6 anisotropy. Based on the results, we discuss possible conditions for the critical phase in materials.

On the estimation of sound speed in two-dimensional Yukawa fluids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Semenov, I. L., E-mail: Igor.Semenov@dlr.de; Thomas, H. M.; Khrapak, S. A.

2015-11-15

The longitudinal sound speed in two-dimensional Yukawa fluids is estimated using the conventional hydrodynamic expression supplemented by appropriate thermodynamic functions proposed recently by Khrapak et al. [Phys. Plasmas 22, 083706 (2015)]. In contrast to the existing approaches, such as quasi-localized charge approximation (QLCA) and molecular dynamics simulations, our model provides a relatively simple estimate for the sound speed over a wide range of parameters of interest. At strong coupling, our results are shown to be in good agreement with the results obtained using the QLCA approach and those derived from the phonon spectrum for the triangular lattice. On the othermore » hand, our model is also expected to remain accurate at moderate values of the coupling strength. In addition, the obtained results are used to discuss the influence of the strong coupling effects on the adiabatic index of two-dimensional Yukawa fluids.« less

Structure and Reversibility of 2D von Neumann Cellular Automata Over Triangular Lattice

NASA Astrophysics Data System (ADS)

Uguz, Selman; Redjepov, Shovkat; Acar, Ecem; Akin, Hasan

2017-06-01

Even though the fundamental main structure of cellular automata (CA) is a discrete special model, the global behaviors at many iterative times and on big scales could be a close, nearly a continuous, model system. CA theory is a very rich and useful phenomena of dynamical model that focuses on the local information being relayed to the neighboring cells to produce CA global behaviors. The mathematical points of the basic model imply the computable values of the mathematical structure of CA. After modeling the CA structure, an important problem is to be able to move forwards and backwards on CA to understand their behaviors in more elegant ways. A possible case is when CA is to be a reversible one. In this paper, we investigate the structure and the reversibility of two-dimensional (2D) finite, linear, triangular von Neumann CA with null boundary case. It is considered on ternary field ℤ3 (i.e. 3-state). We obtain their transition rule matrices for each special case. For given special triangular information (transition) rule matrices, we prove which triangular linear 2D von Neumann CAs are reversible or not. It is known that the reversibility cases of 2D CA are generally a much challenged problem. In the present study, the reversibility problem of 2D triangular, linear von Neumann CA with null boundary is resolved completely over ternary field. As far as we know, there is no structure and reversibility study of von Neumann 2D linear CA on triangular lattice in the literature. Due to the main CA structures being sufficiently simple to investigate in mathematical ways, and also very complex to obtain in chaotic systems, it is believed that the present construction can be applied to many areas related to these CA using any other transition rules.

Effective Hubbard model for Helium atoms adsorbed on a graphite

NASA Astrophysics Data System (ADS)

Motoyama, Yuichi; Masaki-Kato, Akiko; Kawashima, Naoki

Helium atoms adsorbed on a graphite is a two-dimensional strongly correlated quantum system and it has been an attractive subject of research for a long time. A helium atom feels Lennard-Jones like potential (Aziz potential) from another one and corrugated potential from the graphite. Therefore, this system may be described by a hardcore Bose Hubbard model with the nearest neighbor repulsion on the triangular lattice, which is the dual lattice of the honeycomb lattice formed by carbons. A Hubbard model is easier to simulate than the original problem in continuous space, but we need to know the model parameters of the effective model, hopping constant t and interaction V. In this presentation, we will present an estimation of the model parameters from ab initio quantum Monte Carlo calculation in continuous space in addition to results of quantum Monte Carlo simulation for an obtained discrete model.

Three-dimensional periodic dielectric structures having photonic Dirac points

DOEpatents

Bravo-Abad, Jorge; Joannopoulos, John D.; Soljacic, Marin

2015-06-02

The dielectric, three-dimensional photonic materials disclosed herein feature Dirac-like dispersion in quasi-two-dimensional systems. Embodiments include a face-centered cubic (fcc) structure formed by alternating layers of dielectric rods and dielectric slabs patterned with holes on respective triangular lattices. This fcc structure also includes a defect layer, which may comprise either dielectric rods or a dielectric slab with patterned with holes. This defect layer introduces Dirac cone dispersion into the fcc structure's photonic band structure. Examples of these fcc structures enable enhancement of the spontaneous emission coupling efficiency (the .beta.-factor) over large areas, contrary to the conventional wisdom that the .beta.-factor degrades as the system's size increases. These results enable large-area, low-threshold lasers; single-photon sources; quantum information processing devices; and energy harvesting systems.

Charge-patterning phase transition on a surface lattice of titratable sites adjacent to an electrolyte solution

NASA Astrophysics Data System (ADS)

Shore, Joel; Thurston, George

We discuss a model for a charge-patterning phase transition on a two-dimensional square lattice of titratable sites, here regarded as protonation sites, placed on a square lattice in a dielectric medium just below the planar interface between this medium and an aqueous salt solution. Within Debye-Huckel theory, the analytical form of the electrostatic repulsion between protonated sites exhibits an approximate inverse cubic power-law decrease beyond short distances. The problem can thus be mapped onto the two-dimensional antiferromagnetic Ising model with this longer-range interaction, which we study with Monte Carlo simulations. As we increase pH, the occupation probability of a site decreases from 1 at low pH to 0 at high pH. For sufficiently-strong interaction strengths, a phase transition occurs as the occupation probability of 1/2 is approached: the charges arrange themselves into a checkerboard pattern. This ordered phase persists over a range of pH until a transition occurs back to a disordered state. This state is the analogue of the Neel state in the antiferromagnetic Ising spin model. More complicated ordered phases are expected for sufficiently strong interactions (with occupation probabilities of 1/4 and 3/4) and if the lattice is triangular rather than square. This work was supported by NIH EY018249 (GMT).

Two-dimensional liquid crystalline growth within a phase-field-crystal model.

PubMed

Tang, Sai; Praetorius, Simon; Backofen, Rainer; Voigt, Axel; Yu, Yan-Mei; Wang, Jincheng

2015-07-01

By using a two-dimensional phase-field-crystal (PFC) model, the liquid crystalline growth of the plastic triangular phase is simulated with emphasis on crystal shape and topological defect formation. The equilibrium shape of a plastic triangular crystal (PTC) grown from an isotropic phase is compared with that grown from a columnar or smectic-A (CSA) phase. While the shape of a PTC nucleus in the isotropic phase is almost identical to that of the classical PFC model, the shape of a PTC nucleus in CSA is affected by the orientation of stripes in the CSA phase, and irregular hexagonal, elliptical, octagonal, and rectangular shapes are obtained. Concerning the dynamics of the growth process, we analyze the topological structure of the nematic order, which starts from nucleation of +1/2 and -1/2 disclination pairs at the PTC growth front and evolves into hexagonal cells consisting of +1 vortices surrounded by six satellite -1/2 disclinations. It is found that the orientational and the positional order do not evolve simultaneously; the orientational order evolves behind the positional order, leading to a large transition zone, which can span over several lattice spacings.

Frustrated quantum magnetism in the Kondo lattice on the zigzag ladder

NASA Astrophysics Data System (ADS)

Peschke, Matthias; Rausch, Roman; Potthoff, Michael

2018-03-01

The interplay between the Kondo effect, indirect magnetic interaction, and geometrical frustration is studied in the Kondo lattice on the one-dimensional zigzag ladder. Using the density-matrix renormalization group, the ground-state and various short- and long-range spin- and density-correlation functions are calculated for the model at half filling as a function of the antiferromagnetic Kondo interaction down to J =0.3 t , where t is the nearest-neighbor hopping on the zigzag ladder. Geometrical frustration is shown to lead to at least two critical points: Starting from the strong-J limit, where almost local Kondo screening dominates and where the system is a nonmagnetic Kondo insulator, antiferromagnetic correlations between nearest-neighbor and next-nearest-neighbor local spins become stronger and stronger, until at Jcdim≈0.89 t frustration is alleviated by a spontaneous breaking of translational symmetry and a corresponding transition to a dimerized state. This is characterized by antiferromagnetic correlations along the legs and by alternating antiferro- and ferromagnetic correlations on the rungs of the ladder. A mechanism of partial Kondo screening that has been suggested for the Kondo lattice on the two-dimensional triangular lattice is not realized in the one-dimensional case. Furthermore, within the symmetry-broken dimerized state, there is a magnetic transition to a 90∘ quantum spin spiral with quasi-long-range order at Jcmag≈0.84 t . The quantum-critical point is characterized by a closure of the spin gap (with decreasing J ) and a divergence of the spin-correlation length and of the spin-structure factor S (q ) at wave vector q =π /2 . This is opposed to the model on the one-dimensional bipartite chain, which is known to have a finite spin gap for all J >0 at half filling.

Solutions for correlations along the coexistence curve and at the critical point of a kagomé lattice gas with three-particle interactions

NASA Astrophysics Data System (ADS)

Barry, J. H.; Muttalib, K. A.; Tanaka, T.

2008-01-01

We consider a two-dimensional (d=2) kagomé lattice gas model with attractive three-particle interactions around each triangular face of the kagomé lattice. Exact solutions are obtained for multiparticle correlations along the liquid and vapor branches of the coexistence curve and at criticality. The correlation solutions are also determined along the continuation of the curvilinear diameter of the coexistence region into the disordered fluid region. The method generates a linear algebraic system of correlation identities with coefficients dependent only upon the interaction parameter. Using a priori knowledge of pertinent solutions for the density and elementary triplet correlation, one finds a closed and linearly independent set of correlation identities defined upon a spatially compact nine-site cluster of the kagomé lattice. Resulting exact solution curves of the correlations are plotted and discussed as functions of the temperature and are compared with corresponding results in a traditional kagomé lattice gas having nearest-neighbor pair interactions. An example of application for the multiparticle correlations is demonstrated in cavitation theory.

Static and dynamical properties of the spin-1/2 equilateral triangular-lattice antiferromagnet Ba 3CoSb 2O 9

DOE PAGES

Ma, Jie; Kamiya, Yoshitomo; Hong, Tao; ...

2016-02-24

We present single-crystal neutron scattering measurements of the spin-1/2 equilateral triangular-lattice antiferromagnet Ba 3CoSb 2O 9. Besides confirming that the Co 2+ magnetic moments lie in the ab plane for zero magnetic field and then determining all the exchange parameters of the minimal quasi-2D spin Hamiltonian, we provide conclusive experimental evidence of magnon decay through observation of intrinsic line broadening. Through detailed comparisons with the linear and nonlinear spin-wave theories, we also point out that the large-S approximation, which is conventionally employed to predict magnon decay in noncollinear magnets, is inadequate to explain our experimental observation. Hence, our results callmore » for a new theoretical framework for describing excitation spectra in low-dimensional frustrated magnets under strong quantum effects.« less

Mean-Field Scaling of the Superfluid to Mott Insulator Transition in a 2D Optical Superlattice.

PubMed

Thomas, Claire K; Barter, Thomas H; Leung, Tsz-Him; Okano, Masayuki; Jo, Gyu-Boong; Guzman, Jennie; Kimchi, Itamar; Vishwanath, Ashvin; Stamper-Kurn, Dan M

2017-09-08

The mean-field treatment of the Bose-Hubbard model predicts properties of lattice-trapped gases to be insensitive to the specific lattice geometry once system energies are scaled by the lattice coordination number z. We test this scaling directly by comparing coherence properties of ^{87}Rb gases that are driven across the superfluid to Mott insulator transition within optical lattices of either the kagome (z=4) or the triangular (z=6) geometries. The coherent fraction measured for atoms in the kagome lattice is lower than for those in a triangular lattice with the same interaction and tunneling energies. A comparison of measurements from both lattices agrees quantitatively with the scaling prediction. We also study the response of the gas to a change in lattice geometry, and observe the dynamics as a strongly interacting kagome-lattice gas is suddenly "hole doped" by introducing the additional sites of the triangular lattice.

Application of the DMRG in two dimensions: a parallel tempering algorithm

NASA Astrophysics Data System (ADS)

Hu, Shijie; Zhao, Jize; Zhang, Xuefeng; Eggert, Sebastian

The Density Matrix Renormalization Group (DMRG) is known to be a powerful algorithm for treating one-dimensional systems. When the DMRG is applied in two dimensions, however, the convergence becomes much less reliable and typically ''metastable states'' may appear, which are unfortunately quite robust even when keeping a very high number of DMRG states. To overcome this problem we have now successfully developed a parallel tempering DMRG algorithm. Similar to parallel tempering in quantum Monte Carlo, this algorithm allows the systematic switching of DMRG states between different model parameters, which is very efficient for solving convergence problems. Using this method we have figured out the phase diagram of the xxz model on the anisotropic triangular lattice which can be realized by hardcore bosons in optical lattices. SFB Transregio 49 of the Deutsche Forschungsgemeinschaft (DFG) and the Allianz fur Hochleistungsrechnen Rheinland-Pfalz (AHRP).

Thermodynamics of dilute 3He-4He solid solutions with hcp structure

NASA Astrophysics Data System (ADS)

Chishko, K. A.

2018-02-01

To interpret the anomalies in heat capacity CV(T) and temperature-dependent pressure P(T) of solid hexagonal close-packed (hcp) 4He we exploit the model of hcp crystalline polytype with specific lattice degrees of freedom and describe the thermodynamics of impurity-free 4He solid as superposition of phononic and polytypic contributions. The hcp-based polytype is a stack of 2D basal atomic monolayers on triangular lattice packed with arbitrary long (up to infinity) spatial period along the hexagonal c axis perpendicular to the basal planes. It is a crystal with perfect ordering along the layers, but without microscopic translational symmetry in perpendicular direction (which remains, nevertheless, the rotational crystallographic axis of third order, so that the polytype can be considered as semidisordered system). Each atom of the hcp polytype has twelve crystallographic neighbors in both first and second coordination spheres at any arbitrary packing order. It is shown that the crystal of such structure behaves as anisotropic elastic medium with specific dispersion law of phonon excitations along c axis. The free energy and the heat capacity consist of two terms: one of them is a normal contribution [with CV(T) ˜ T3] from phonon excitations in an anisotropic lattice of hexagonal symmetry, and another term (an "excessive" heat) is a contribution resulted by packing entropy from quasi-one-dimensional system of 2D basal planes on triangular lattice stacked randomly along c axis without braking the closest pack between neighboring atomic layers. The excessive part of the free energy has been treated within 1D quasi-Ising (lattice gas) model using the transfer matrix approach. This model makes us possible to interpret successfully the thermodynamic anomaly (heat capacity peak in hcp 4He) observed experimentally.

Ultrasmall multi-channel resonant-tunneling filter using mode gap of width-tuned photonic-crystal waveguide.

PubMed

Shinya, Akihiko; Mitsugi, Satoshi; Kuramochi, Eiichi; Notomi, Masaya

2005-05-30

We have devised an ultra-small multi-channel drop filter based on a two-port resonant tunneling system in a two-dimensional photonic crystal with a triangular air-hole lattice. This filter does not require careful consideration of the interference process to achieve a high dropping efficiency. First we develop three-port systems based on a two-port resonant tunneling filter. Next we devise a multi-port channel drop filter by cascading these three-port systems. In this paper, we demonstrate a ten-channel drop filter with an 18 mum device size by 2D-FDTD calculation, and a three-port resonant tunneling filter with 65+/- 20 % dropping efficiency by experiment.

Competition between dynamic and structural disorder in a doped triangular antiferromagnet RbFe(MoO4)2

NASA Astrophysics Data System (ADS)

Smirnov, A. I.; Soldatov, T. A.; Petrenko, O. A.; Takata, A.; Kida, T.; Hagiwara, M.; Zhitomirsky, M. E.; Shapiro, A. Ya

2018-03-01

Magnetisation measurements and electron spin resonance (ESR) spectra of a doped quasi two dimensional (2D) antiferromagnet on a triangular lattice Rb1 ‑ x K x Fe(MoO4)2 reveal a crucial change of the ground state spin configuration and a disappearance of a characteristic 1/3-magnetisation plateau at x = 0.15. According to theory for triangular antiferromagnets with a weak random modulation of the exchange bonds, this is a result of the competition between the structural and dynamic disorders. The dynamic zero-point or thermal fluctuations are known to lift the degeneracy of the mean field ground state of a triangular antiferromagnet and cause the spin configuration to be the most collinear, while the static disorder provides another selection of the ground state, with the least collinear structure. Low-level doping (x ≤ 0.15) was found to decrease the Néel temperature and saturation field by only few percent, while the magnetisation plateau disappears completely and the spin configuration is drastically changed. ESR spectra confirm an impurity-induced change of the so-called Y-type structure to an inverted Y-structure for x = 0.15. For x = 0.075 the intermediate regime with the decrease of width and weakening of flattening of 1/3-plateau was found.

Dynamic hysteresis behaviors in the kinetic Ising system on triangular lattice

NASA Astrophysics Data System (ADS)

Kantar, Ersin; Ertaş, Mehmet

2018-04-01

We studied dynamic hysteresis behaviors of the spin-1 Blume-Capel (BC) model in a triangular lattice by means of the effective-field theory (EFT) with correlations and using Glauber-type stochastic dynamics. The effects of the exchange interaction (J), crystal field (D), temperature (T) and oscillating frequency (w) on the hysteresis behaviors of the BC model in a triangular lattice are investigated in detail. Results are compared with some other dynamic studies and quantitatively good agreement is found.

Effective elastic moduli of triangular lattice material with defects

NASA Astrophysics Data System (ADS)

Liu, Xiaoyu; Liang, Naigang

2012-10-01

This paper presents an attempt to extend homogenization analysis for the effective elastic moduli of triangular lattice materials with microstructural defects. The proposed homogenization method adopts a process based on homogeneous strain boundary conditions, the micro-scale constitutive law and the micro-to-macro static operator to establish the relationship between the macroscopic properties of a given lattice material to its micro-discrete behaviors and structures. Further, the idea behind Eshelby's equivalent eigenstrain principle is introduced to replace a defect distribution by an imagining displacement field (eigendisplacement) with the equivalent mechanical effect, and the triangular lattice Green's function technique is developed to solve the eigendisplacement field. The proposed method therefore allows handling of different types of microstructural defects as well as its arbitrary spatial distribution within a general and compact framework. Analytical closed-form estimations are derived, in the case of the dilute limit, for all the effective elastic moduli of stretch-dominated triangular lattices containing fractured cell walls and missing cells, respectively. Comparison with numerical results, the Hashin-Shtrikman upper bounds and uniform strain upper bounds are also presented to illustrate the predictive capability of the proposed method for lattice materials. Based on this work, we propose that not only the effective Young's and shear moduli but also the effective Poisson's ratio of triangular lattice materials depend on the number density of fractured cell walls and their spatial arrangements.

Simulation of Molecular Transport in Systems Containing Mobile Obstacles.

PubMed

Polanowski, Piotr; Sikorski, Andrzej

2016-08-04

In this paper, we investigate the movement of molecules in crowded environments with obstacles undergoing Brownian motion by means of extensive Monte Carlo simulations. Our investigations were performed using the dynamic lattice liquid model, which was based on the cooperative movement concept and allowed to mimic systems at high densities where the motion of all elements (obstacles as well as moving particles) were highly correlated. The crowded environments are modeled on a two-dimensional triangular lattice containing obstacles (particles whose mobility was significantly reduced) moving by a Brownian motion. The subdiffusive motion of both elements in the system was analyzed. It was shown that the percolation transition does not exist in such systems in spite of the cooperative character of the particles' motion. The reduction of the obstacle mobility leads to the longer caging of liquid particles by mobile obstacles.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kishino, Katsumi, E-mail: kishino@sophia.ac.jp; Sophia Nanotechnology Research Center, Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo 102-8554; Ishizawa, Shunsuke

Bottom-up grown structurally graded InGaN-based nanocolumn photonic crystals, in which nanocolumns were arranged in triangular lattice and the nanocolumn diameter changed one-dimensionally from 93 to 213 nm with a fixed lattice constant of 250 nm, were fabricated. The spatial distribution of the diameter resulted in random-laser-like operation under optical excitation. A broad multi-wavelength lasing spectrum with more than 10 peaks was obtained with a full width at half maximum of 27 nm at 505 nm wavelength as well as lowering of the polarization degree, which is expected to be suitable for speckle contrast reduction in laser projection display applications.

Reconfigurable all-optical NOT, XOR, and NOR logic gates based on two dimensional photonic crystals

NASA Astrophysics Data System (ADS)

Parandin, Fariborz; Malmir, M. Reza; Naseri, Mosayeb; Zahedi, Abdulhamid

2018-01-01

Photonic crystals can be considered as one of the most important basis for designing optical devices. In this research, using two-dimensional photonic crystals with triangular lattices, ultra-compact logic gates are designed and simulated. The intended structure has the capability to be used as three logical gates (NOT, XOR, and NOR). The designed structures not only have characteristics of small dimensions which make them suitable for integrated optical circuits, but also exhibit very low power transfer delay which makes it possible to design high speed gates. On comparison with the previous works, our simulations show that at a wavelength of 1.55 μm , the gates indicate a time delay of about 0.1 ps and the contrast ratio for the XOR gate is about 30 dB, i.e., the proposed structures are more applicable in designing low error optical logic gates.

Simultaneous breaking of lattice symmetry and spin frustration in triangular lattice antiferromagnet CuFeO2

NASA Astrophysics Data System (ADS)

Ren, Y.; Ye, F.; Huang, Q.; Fernandez-Baca, J. A.; Dai, Pengcheng; Lynn, J. W.; Kimura, T.

2006-03-01

We use high resolution synchrotron X-ray and neutron diffraction to study the geometrically frustrated triangular lattice antiferromagnet (TLA) CuFeO2. We show that the occurrence of the two magnetic transitions, at 14 K and 11 K, respectively is accompanied simultaneously by a second-and first- order structural phase transitions from a hexagonal structure to a monoclinic form. This is the first observation of two successive spin-driven structural transitions directly coupled with incommensurate and commensurate magnetic orderings in frustrated TLA systems. This work is supported by the U. S. NSF DMR-0453804 and DOE Nos. DE-FG02-05ER46202 and DE-AC05-00OR22725 with UT/Battelle LLC. Use of the Advanced Photon Source was supported by the U. S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. W-31-109-Eng-38.

Anomalous critical behavior in the polymer collapse transition of three-dimensional lattice trails.

PubMed

Bedini, Andrea; Owczarek, Aleksander L; Prellberg, Thomas

2012-07-01

Trails (bond-avoiding walks) provide an alternative lattice model of polymers to self-avoiding walks, and adding self-interaction at multiply visited sites gives a model of polymer collapse. Recently a two-dimensional model (triangular lattice) where doubly and triply visited sites are given different weights was shown to display a rich phase diagram with first- and second-order collapse separated by a multicritical point. A kinetic growth process of trails (KGTs) was conjectured to map precisely to this multicritical point. Two types of low-temperature phases, a globule phase and a maximally dense phase, were encountered. Here we investigate the collapse properties of a similar extended model of interacting lattice trails on the simple cubic lattice with separate weights for doubly and triply visited sites. Again we find first- and second-order collapse transitions dependent on the relative sizes of the doubly and triply visited energies. However, we find no evidence of a low-temperature maximally dense phase with only the globular phase in existence. Intriguingly, when the ratio of the energies is precisely that which separates the first-order from the second-order regions anomalous finite-size scaling appears. At the finite-size location of the rounded transition clear evidence exists for a first-order transition that persists in the thermodynamic limit. This location moves as the length increases, with its limit apparently at the point that maps to a KGT. However, if one fixes the temperature to sit at exactly this KGT point, then only a critical point can be deduced from the data. The resolution of this apparent contradiction lies in the breaking of crossover scaling and the difference in the shift and transition width (crossover) exponents.

Multiorbital kinetic effects on charge ordering of frustrated electrons on the triangular lattice

NASA Astrophysics Data System (ADS)

Février, C.; Fratini, S.; Ralko, A.

2015-06-01

The role of the multiorbital effects on the emergence of frustrated electronic orders on the triangular lattice at half filling is investigated through an extended spinless fermion Hubbard model. By using two complementary approaches, unrestricted Hartree-Fock and exact diagonalizations, we unravel a very rich phase diagram controlled by the strength of both local and off-site Coulomb interactions and by the interorbital hopping anisotropy ratio t'/t . Three robust unconventional electronic phases, a pinball liquid, an inverse pinball liquid, and a large-unit-cell √{12 }×√{12 } droplet phase, are found to be generic in the triangular geometry, being controlled by the band structure parameters. The latter are also stabilized in the isotropic limit of our microscopic model, which recovers the standard SU(2) spinful extended single-band Hubbard model.

Dimer covering and percolation frustration.

PubMed

Haji-Akbari, Amir; Haji-Akbari, Nasim; Ziff, Robert M

2015-09-01

Covering a graph or a lattice with nonoverlapping dimers is a problem that has received considerable interest in areas, such as discrete mathematics, statistical physics, chemistry, and materials science. Yet, the problem of percolation on dimer-covered lattices has received little attention. In particular, percolation on lattices that are fully covered by nonoverlapping dimers has not evidently been considered. Here, we propose a procedure for generating random dimer coverings of a given lattice. We then compute the bond percolation threshold on random and ordered coverings of the square and the triangular lattices on the remaining bonds connecting the dimers. We obtain p_{c}=0.367713(2) and p_{c}=0.235340(1) for random coverings of the square and the triangular lattices, respectively. We observe that the percolation frustration induced as a result of dimer covering is larger in the low-coordination-number square lattice. There is also no relationship between the existence of long-range order in a covering of the square lattice and its percolation threshold. In particular, an ordered covering of the square lattice, denoted by shifted covering in this paper, has an unusually low percolation threshold and is topologically identical to the triangular lattice. This is in contrast to the other ordered dimer coverings considered in this paper, which have higher percolation thresholds than the random covering. In the case of the triangular lattice, the percolation thresholds of the ordered and random coverings are very close, suggesting the lack of sensitivity of the percolation threshold to microscopic details of the covering in highly coordinated networks.

The Position Control of the Surface Motor with the Poles Distribution of Triangular Lattice

NASA Astrophysics Data System (ADS)

Watada, Masaya; Katsuyama, Norikazu; Ebihara, Daiki

Recently, as for the machine tools or industrial robots, high performance, accuracy, etc. are demanded. Generally, when drive of many degrees of freedom is required in the machine tools or industrial robots, it has realized by using two or more motors. For example, two-dimensional positioning stages such as the X-Y plotter or the X-Y stage are enabling the two-dimensional drive by using each one motor in the direction of x, y. In order to use plural motors, these, however, have problems that equipment becomes large and complicate control system. From such problems, the Surface Motor (SFM) that can drive two directions by only one motor is researched. Authors have proposed SFM that considered wide range movement and the application to a curved surface. In this paper, the characteristics of the micro step drive by the open loop control are showed. Introduction of closed loop control for highly accurate positioning, moreover, is examined. The drive characteristics by each control are compared.

Quantum Information Processing in the Wall of Cytoskeletal Microtubules

PubMed Central

Qiu, Xijun; Wu, Tongcheng; Li, Ruxin

2006-01-01

Microtubules (MT) are composed of 13 protofilaments, each of which is a series of two-state tubulin dimers. In the MT wall, these dimers can be pictured as “lattice” sites similar to crystal lattices. Based on the pseudo-spin model, two different location states of the mobile electron in each dimer are proposed. Accordingly, the MT wall is described as an anisotropic two-dimensional (2D) pseudo-spin system considering a periodic triangular “lattice”. Because three different “spin-spin” interactions in each cell exist periodically in the whole MT wall, the system may be shown to be an array of three types of two-pseudo-spin-state dimers. For the above-mentioned condition, the processing of quantum information is presented by using the scheme developed by Lloyd. PMID:19669447

Critical anisotropies of a geometrically frustrated triangular-lattice antiferromagnet

NASA Astrophysics Data System (ADS)

Swanson, M.; Haraldsen, J. T.; Fishman, R. S.

2009-05-01

This work examines the critical anisotropy required for the local stability of the collinear ground states of a geometrically frustrated triangular-lattice antiferromagnet (TLA). Using a Holstein-Primakoff expansion, we calculate the spin-wave frequencies for the one-, two-, three-, four-, and eight-sublattice (SL) ground states of a TLA with up to third neighbor interactions. Local stability requires that all spin-wave frequencies are real and positive. The two-, four-, and eight-SL phases break up into several regions where the critical anisotropy is a different function of the exchange parameters. We find that the critical anisotropy is a continuous function everywhere except across the two-SL/three-SL and three-SL/four-SL phase boundaries, where the three-SL phase has the higher critical anisotropy.

Topological magnon bands and unconventional thermal Hall effect on the frustrated honeycomb and bilayer triangular lattice.

PubMed

Owerre, S A

2017-09-27

In the conventional ferromagnetic systems, topological magnon bands and thermal Hall effect are due to the Dzyaloshinskii-Moriya interaction (DMI). In principle, however, the DMI is either negligible or it is not allowed by symmetry in some quantum magnets. Therefore, we expect that topological magnon features will not be present in those systems. In addition, quantum magnets on the triangular-lattice are not expected to possess topological features as the DMI or spin-chirality cancels out due to equal and opposite contributions from adjacent triangles. Here, however, we predict that the isomorphic frustrated honeycomb-lattice and bilayer triangular-lattice antiferromagnetic system will exhibit topological magnon bands and topological thermal Hall effect in the absence of an intrinsic DMI. These unconventional topological magnon features are present as a result of magnetic-field-induced non-coplanar spin configurations with nonzero scalar spin chirality. The relevance of the results to realistic bilayer triangular antiferromagnetic materials are discussed.

Ising antiferromagnet on a finite triangular lattice with free boundary conditions

NASA Astrophysics Data System (ADS)

Kim, Seung-Yeon

2015-11-01

The exact integer values for the density of states of the Ising model on an equilateral triangular lattice with free boundary conditions are evaluated up to L = 24 spins on a side for the first time by using the microcanonical transfer matrix. The total number of states is 2 N s = 2300 ≈ 2.037 × 1090 for L = 24, where N s = L( L+1)/2 is the number of spins. Classifying all 2300 spin states according to their energy values is an enormous work. From the density of states, the exact partition function zeros in the complex temperature plane of the triangular-lattice Ising model are evaluated. Using the density of states and the partition function zeros, we investigate the properties of the triangularlattice Ising antiferromagnet. The scaling behavior of the ground-state entropy and the form of the correlation length at T = 0 are studied for the triangular-lattice Ising antiferromagnet with free boundary conditions. Also, the scaling behavior of the Fisher edge singularity is investigated.

High magnetic field magnetization of a new triangular lattice antiferromagnet

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou, H. D.; Stritzinger, Laurel Elaine Winter; Harrison, Neil

2017-03-23

In CsV(MoO 4) 2, the magnetic V 3+ ions with octahedral oxygen-coordination form a geometrically frustrated triangular lattice. So fare, there is no magnetic properties reported on it. Recently, we successfully grew single crystals of CsV(MoO 4) 2 by using flux method. The susceptibility shows a sharp drop around 24 K, representing a long range magnetic ordering. To understand the physical properties of this new triangular lattice antiferromagnet (TLAF), we pursued high field magnetization measurements to answer two questions: (i) what is the saturation field, which will be very useful to calculate the exchange interaction of the system? (ii) Willmore » it exhibit spin state transition, such as the up up down phase with 1/3-saturation moment as other TLAFs? Recently, we performed VSM measurements in Cell 8, Tallahassee, NHMFL, the results show that the magnetization reaches 0.38 MuB at 34 T, which is just 19% of the full moment of 2 MuB for V 3+ (3d 2) ions. Apparently we need higher field to reach 1/3 value or full moment.« less

Yu-Shiba-Rusinov states of impurities in a triangular lattice of NbSe2 with spin-orbit coupling

NASA Astrophysics Data System (ADS)

Ptok, Andrzej; Głodzik, Szczepan; Domański, Tadeusz

2017-11-01

We study the topography of the spin-polarized bound states of magnetic impurities embedded in a triangular lattice of a superconducting host. Such states have been observed experimentally in 2 H -NbSe2 crystal [G. C. Ménard et al., Nat. Phys. 11, 1013 (2015), 10.1038/nphys3508], and they revealed oscillating particle-hole asymmetry extending to tens of nanometers. Using the Bogoliubov-de Gennes approach, we explore the Yu-Shiba-Rusinov states in the presence of spin-orbit interaction. We also study the bound states of double impurities for several relative positions in a triangular lattice.

2d affine XY-spin model/4d gauge theory duality and deconfinement

NASA Astrophysics Data System (ADS)

Anber, Mohamed M.; Poppitz, Erich; Ünsal, Mithat

2012-04-01

We introduce a duality between two-dimensional XY-spin models with symmetry-breaking perturbations and certain four-dimensional SU(2) and SU(2)/ {{Z}_2} gauge theories, compactified on a small spatial circle {{R}^{{^{{{1},{2}}}}}} × {{S}^{{^{{1}}}}} , and considered at temperatures near the deconfinement transition. In a Euclidean set up, the theory is defined on {{R}^{{^{{2}}}}} × {{T}^{{^{{2}}}}} . Similarly, thermal gauge theories of higher rank are dual to new families of "affine" XY-spin models with perturbations. For rank two, these are related to models used to describe the melting of a 2d crystal with a triangular lattice. The connection is made through a multi-component electric-magnetic Coulomb gas representation for both systems. Perturbations in the spin system map to topological defects in the gauge theory, such as monopole-instantons or magnetic bions, and the vortices in the spin system map to the electrically charged W-bosons in field theory (or vice versa, depending on the duality frame). The duality permits one to use the two-dimensional technology of spin systems to study the thermal deconfinement and discrete chiral transitions in four-dimensional SU( N c ) gauge theories with n f ≥1 adjoint Weyl fermions.

Quantum fluctuations in anisotropic triangular lattices with ferromagnetic and antiferromagnetic exchange

NASA Astrophysics Data System (ADS)

Schmidt, Burkhard; Thalmeier, Peter

2014-05-01

The Heisenberg model on a triangular lattice is a prime example of a geometrically frustrated spin system. However most experimentally accessible compounds have spatially anisotropic exchange interactions. As a function of this anisotropy, ground states with different magnetic properties can be realized. Motivated by recent experimental findings on Cs2CuCl4-xBrx, we discuss the full phase diagram of the anisotropic model with two exchange constants J1 and J2, including possible ferromagnetic exchange. Furthermore a comparison with the related square lattice model is carried out. We discuss the zero-temperature phase diagram, ordering vector, ground-state energy, and ordered moment on a classical level and investigate the effect of quantum fluctuations within the framework of spin-wave theory. The field dependence of the ordered moment is shown to be nonmonotonic with field and control parameter.

Quantum Phase Transition and Local Entanglement in Extended Hubbard Model on Anisotropic Triangular Lattices

NASA Astrophysics Data System (ADS)

Gao, Ji-Ming; Tang, Rong-An; Zhang, Zheng-Mei; Xue, Ju-Kui

2016-11-01

Using a mean-field theory based upon Hartree—Fock approximation, we theoretically investigate the competition between the metallic conductivity, spin order and charge order phases in a two-dimensional half-filled extended Hubbard model on anisotropic triangular lattice. Bond order, double occupancy, spin and charge structure factor are calculated, and the phase diagram of the extended Hubbard model is presented. It is found that the interplay of strong interaction and geometric frustration leads to exotic phases, the charge fluctuation is enhanced and three kinds of charge orders appear with the introduction of the nearest-neighbor interaction. Moreover, for different frustrations, it is also found that the antiferromagnetic insulating phase and nonmagnetic insulating phase are rapidly suppressed, and eventually disappeared as the ratio between the nearest-neighbor interaction and on-site interaction increases. This indicates that spin order is also sensitive to the nearest-neighbor interaction. Finally, the single-site entanglement is calculated and it is found that a clear discontinuous of the single-site entanglement appears at the critical points of the phase transition. Supported by National Natural Science Foundation of China under Grant Nos.11274255, 11475027 and 11305132, Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20136203110001, and Technology of Northwest Normal University, China under Grants No. NWNU-LKQN-11-26

Mermin-Wagner physics, (H ,T ) phase diagram, and candidate quantum spin-liquid phase in the spin-1/2 triangular-lattice antiferromagnet Ba8CoNb6O24

NASA Astrophysics Data System (ADS)

Cui, Y.; Dai, J.; Zhou, P.; Wang, P. S.; Li, T. R.; Song, W. H.; Wang, J. C.; Ma, L.; Zhang, Z.; Li, S. Y.; Luke, G. M.; Normand, B.; Xiang, T.; Yu, W.

2018-04-01

Ba8CoNb6O24 presents a system whose Co2 + ions have an effective spin 1/2 and construct a regular triangular-lattice antiferromagnet (TLAFM) with a very large interlayer spacing, ensuring purely two-dimensional character. We exploit this ideal realization to perform a detailed experimental analysis of the S =1 /2 TLAFM, which is one of the keystone models in frustrated quantum magnetism. We find strong low-energy spin fluctuations and no magnetic ordering, but a diverging correlation length down to 0.1 K, indicating a Mermin-Wagner trend toward zero-temperature order. Below 0.1 K, however, our low-field measurements show an unexpected magnetically disordered state, which is a candidate quantum spin liquid. We establish the (H ,T ) phase diagram, mapping in detail the quantum fluctuation corrections to the available theoretical analysis. These include a strong upshift in field of the maximum ordering temperature, qualitative changes to both low- and high-field phase boundaries, and an ordered regime apparently dominated by the collinear "up-up-down" state. Ba8CoNb6O24 , therefore, offers fresh input for the development of theoretical approaches to the field-induced quantum phase transitions of the S =1 /2 Heisenberg TLAFM.

Optical fabrication of large area photonic microstructures by spliced lens

NASA Astrophysics Data System (ADS)

Jin, Wentao; Song, Meng; Zhang, Xuehua; Yin, Li; Li, Hong; Li, Lin

2018-05-01

We experimentally demonstrate a convenient approach to fabricate large area photorefractive photonic microstructures by a spliced lens device. Large area two-dimensional photonic microstructures are optically induced inside an iron-doped lithium niobate crystal. The experimental setups of our method are relatively compact and stable without complex alignment devices. It can be operated in almost any optical laboratories. We analyze the induced triangular lattice microstructures by plane wave guiding, far-field diffraction pattern imaging and Brillouin-zone spectroscopy. By designing the spliced lens appropriately, the method can be easily extended to fabricate other complex large area photonic microstructures, such as quasicrystal microstructures. Induced photonic microstructures can be fixed or erased and re-recorded in the photorefractive crystal.

Direct writing of tunable multi-wavelength polymer lasers on a flexible substrate.

PubMed

Zhai, Tianrui; Wang, Yonglu; Chen, Li; Zhang, Xinping

2015-08-07

Tunable multi-wavelength polymer lasers based on two-dimensional distributed feedback structures are fabricated on a transparent flexible substrate using interference ablation. A scalene triangular lattice structure was designed to support stable tri-wavelength lasing emission and was achieved through multiple exposure processes. Three wavelengths were controlled by three periods of the compound cavity. Mode competition among different cavity modes was observed by changing the pump fluence. Both a redshift and blueshift of the laser wavelength could be achieved by bending the soft substrate. These results not only provide insight into the physical mechanisms behind co-cavity polymer lasers but also introduce new laser sources and laser designs for white light lasers.

Ising lattices with +/-J second-nearest-neighbor interactions

NASA Astrophysics Data System (ADS)

Ramírez-Pastor, A. J.; Nieto, F.; Vogel, E. E.

1997-06-01

Second-nearest-neighbor interactions are added to the usual nearest-neighbor Ising Hamiltonian for square lattices in different ways. The starting point is a square lattice where half the nearest-neighbor interactions are ferromagnetic and the other half of the bonds are antiferromagnetic. Then, second-nearest-neighbor interactions can also be assigned randomly or in a variety of causal manners determined by the nearest-neighbor interactions. In the present paper we consider three causal and three random ways of assigning second-nearest-neighbor exchange interactions. Several ground-state properties are then calculated for each of these lattices:energy per bond ɛg, site correlation parameter pg, maximal magnetization μg, and fraction of unfrustrated bonds hg. A set of 500 samples is considered for each size N (number of spins) and array (way of distributing the N spins). The properties of the original lattices with only nearest-neighbor interactions are already known, which allows realizing the effect of the additional interactions. We also include cubic lattices to discuss the distinction between coordination number and dimensionality. Comparison with results for triangular and honeycomb lattices is done at specific points.

Why square lattices are not seen on curved ionic membranes

NASA Astrophysics Data System (ADS)

Thomas, Creighton; Olvera de La Cruz, Monica

2013-03-01

Ionic crystalline membranes on curved surfaces are ubiquitous in nature, appearing for example on the membranes of halophilic organisms. Even when these membranes buckle into polyhedra with square or rectangular sides, the crystalline structure is seen to have hexagonal symmetry. Here, we theoretically and numerically investigate the effects of curvature on square lattices. Our model system consists of both positive and negative ions with a 1:1 charge ratio adsorbed onto the surface of a sphere. In flat space, the lowest-energy configuration of this system can be a square lattice. This bipartite arrangement is favored because there are two types of ions. It leads to a fundamentally different defect structure than what has been seen when triangular lattices are favored. We classify these defects and find that curvature disrupts long-range square symmetry in a crystal. Through numerical simulations, we see that small square regions are possible in some cases, but this phase coexists with other structures, limiting the scale of these square-lattice microstructures. Thus, at large length scales, curvature leads to triangular structures.

Supersymmetrical bounding of asymmetric states and quantum phase transitions by anti-crossing of symmetric states

PubMed Central

Afzal, Muhammad Imran; Lee, Yong Tak

2016-01-01

Von Neumann and Wigner theorized the bounding and anti-crossing of eigenstates. Experiments have demonstrated that owing to anti-crossing and similar radiation rates, the graphene-like resonance of inhomogeneously strained photonic eigenstates can generate a pseudomagnetic field, bandgaps and Landau levels, whereas exponential or dissimilar rates induce non-Hermicity. Here, we experimentally demonstrate higher-order supersymmetry and quantum phase transitions by resonance between similar one-dimensional lattices. The lattices consisted of inhomogeneous strain-like phases of triangular solitons. The resonance created two-dimensional, inhomogeneously deformed photonic graphene. All parent eigenstates were annihilated. Eigenstates of mildly strained solitons were annihilated at similar rates through one tail and generated Hermitian bounded eigenstates. The strongly strained solitons with positive phase defects were annihilated at exponential rates through one tail, which bounded eigenstates through non-Hermitianally generated exceptional points. Supersymmetry was evident, with preservation of the shapes and relative phase differences of the parent solitons. Localizations of energies generated from annihilations of mildly and strongly strained soliton eigenstates were responsible for geometrical (Berry) and topological phase transitions, respectively. Both contributed to generating a quantum Zeno phase, whereas only strong twists generated topological (Anderson) localization. Anti-bunching-like condensation was also observed. PMID:27966596

Classical Magnetic Frustration

NASA Astrophysics Data System (ADS)

Tsao, Eugene; Henriksen, Erik

We report on studies of classical magnetic frustration, inspired by Mellado et al., by studying an ensemble of freely rotating magnets, made of 1'' rare-earth bar magnets press-fit into polypropylene spheres floating on air bearings. The magnets can be arranged in any configuration to study frustration in 1, 2, or 3 dimensions. For instance, arranged in a Kagome lattice the magnets show an absence of high-energy in-in-in and out-out-out states; the presence of multiple ground states is indicative of macroscopic frustration. We also observe classical ``magnon'' transport in a one-dimensional chain. We will report on progress made in exploring the behavior of these magnets in triangular, Kagome, and honeycomb lattice configurations.

Strain-induced intervortex interaction and vortex lattices in tetragonal superconductors

DOE PAGES

Lin, Shi -Zeng; Kogan, Vladimir G.

2017-02-22

In superconductors with strong coupling between superconductivity and elasticity manifested in a strong dependence of transition temperature on pressure, there is an additional contribution to intervortex interactions due to the strain field generated by vortices. When vortex lines are along the c axis of a tetragonal crystal, a square vortex lattice (VL) is favored at low vortex densities, because the vortex-induced strains contribution to the intervortex interactions is long range. At intermediate magnetic fields, the triangular lattice is stabilized. Furthermore, the triangular lattice evolves to the square lattice upon increasing magnetic field, and eventually the system locks to the squaremore » structure. We argue, however, that as magnetic field approaches the upper critical field H c2 the elastic intervortex interactions disappear faster than the standard London interactions, so that VL should return to the triangular structure. Our results are compared to VLs observed in the heavy fermion superconductor CeCoIn 5.« less

Gapless spin excitations in the S = 1 / 2 Kagome- and triangular-lattice Heisenberg antiferromagnets

NASA Astrophysics Data System (ADS)

Sakai, Tôru; Nakano, Hiroki

2018-05-01

The S = 1 / 2 kagome- and triangular-lattice Heisenberg antiferromagnets are investigated using the numerical exact diagonalization and the finite-size scaling analysis. The behaviour of the field derivative at zero magnetization is examined for both systems. The present result indicates that the spin excitation is gapless for each system.

Triangular lattice atomic layer of Sn(1 × 1) at graphene/SiC(0001) interface

NASA Astrophysics Data System (ADS)

Hayashi, Shingo; Visikovskiy, Anton; Kajiwara, Takashi; Iimori, Takushi; Shirasawa, Tetsuroh; Nakastuji, Kan; Miyamachi, Toshio; Nakashima, Shuhei; Yaji, Koichiro; Mase, Kazuhiko; Komori, Fumio; Tanaka, Satoru

2018-01-01

Sn atomic layers attract considerable interest owing to their spin-related physical properties caused by their strong spin-orbit interactions. We performed Sn intercalation into the graphene/SiC(0001) interface and found a new type of Sn atomic layer. Sn atoms occupy on-top sites of Si-terminated SiC(0001) with in-plane Sn-Sn bondings, resulting in a triangular lattice. Angle-resolved photoemission spectroscopy revealed characteristic dispersions at \\bar{\\text{K}} and \\bar{\\text{M}} points, which agreed well with density functional theory calculations. The Sn triangular lattice atomic layer at the interface showed no oxidation upon exposure to air, which is useful for characterization and device fabrication ex situ.

Tunable two-dimensional photonic crystals using liquid crystal infiltration

NASA Astrophysics Data System (ADS)

Leonard, S. W.; Mondia, J. P.; van Driel, H. M.; Toader, O.; John, S.; Busch, K.; Birner, A.; Gösele, U.; Lehmann, V.

2000-01-01

The photonic band gap of a two-dimensional photonic crystal is continuously tuned using the temperature dependent refractive index of a liquid crystal. Liquid crystal E7 was infiltrated into the air pores of a macroporous silicon photonic crystal with a triangular lattice pitch of 1.58 μm and a band gap wavelength range of 3.3-5.7 μm. After infiltration, the band gap for the H polarized field shifted dramatically to 4.4-6.0 μm while that of the E-polarized field collapsed. As the sample was heated to the nematic-isotropic phase transition temperature of the liquid crystal (59 °C), the short-wavelength band edge of the H gap shifted by as much as 70 nm while the long-wavelength edge was constant within experimental error. Band structure calculations incorporating the temperature dependence of the liquid crystal birefringence can account for our results and also point to an escaped-radial alignment of the liquid crystal in the nematic phase.

Evidence for intertwined superfluid and density wave order in two dimensional 4He

NASA Astrophysics Data System (ADS)

Saunders, John

2015-03-01

We report the identification of a new state of quantum matter with intertwined superfluid and density wave order in a system of two dimensional bosons subject to a triangular lattice potential. Using a torsional oscillator we have measured the response of the second atomic layer of 4He adsorbed on the surface of graphite over a wide temperature range down to 2 mK. Superfluidity is observed over a narrow range of film densities, emerging suddenly and collapsing towards a quantum critical point, near to layer completion where a Mott insulating phase is predicted to form. The unusual temperature dependence of the superfluid density in the T --> 0 limit and the absence of a clear superfluid onset temperature are explained, self-consistently, by an ansatz for the excitation spectrum, reflecting density wave order, and a quasi-condensate wavefunction breaking both gauge and translational symmetry. In collaboration with Jan Nyeki, Anastasia Phillis, Andrew Ho, Derek Lee, Piers Coleman, Jeevak Parpia, Brian Cowan. Supported by EPSRC (U.K) EP/H048375/1.

Triangular Quantum Loop Topography for Machine Learning

NASA Astrophysics Data System (ADS)

Zhang, Yi; Kim, Eun-Ah

Despite rapidly growing interest in harnessing machine learning in the study of quantum many-body systems there has been little success in training neural networks to identify topological phases. The key challenge is in efficiently extracting essential information from the many-body Hamiltonian or wave function and turning the information into an image that can be fed into a neural network. When targeting topological phases, this task becomes particularly challenging as topological phases are defined in terms of non-local properties. Here we introduce triangular quantum loop (TQL) topography: a procedure of constructing a multi-dimensional image from the ''sample'' Hamiltonian or wave function using two-point functions that form triangles. Feeding the TQL topography to a fully-connected neural network with a single hidden layer, we demonstrate that the architecture can be effectively trained to distinguish Chern insulator and fractional Chern insulator from trivial insulators with high fidelity. Given the versatility of the TQL topography procedure that can handle different lattice geometries, disorder, interaction and even degeneracy our work paves the route towards powerful applications of machine learning in the study of topological quantum matters.

Magnetic structure of the swedenborgite CaBa (Co3Fe ) O7 derived by unpolarized neutron diffraction and spherical neutron polarimetry

NASA Astrophysics Data System (ADS)

Qureshi, N.; Díaz, M. T. Fernández; Chapon, L. C.; Senyshyn, A.; Schweika, W.; Valldor, M.

2018-02-01

We present a study that combines polarized and unpolarized neutrons to derive the magnetic structure of the swedenborgite compound CaBa (Co3Fe ) O7. Integrated intensities from a standard neutron diffraction experiment and polarization matrices from spherical neutron polarimetry have been simultaneously analyzed revealing a complex order, which differs from the usual spin configurations on a kagome lattice. We find that the magnetic structure is well described by a combination of two one-dimensional representations corresponding to the magnetic superspace symmetry P 21' , and it consists of spins rotating around an axis close to the [110] direction. Due to the propagation vector q =(1/3 00 ) , this modulation has cycloidal and helicoidal character rendering this system a potential multiferroic. The resulting spin configuration can be mapped onto the classical √{3 }×√{3 } structure of a kagome lattice, and it indicates an important interplay between the kagome and the triangular layers of the crystal structure.

Statistical transmutation in doped quantum dimer models.

PubMed

Lamas, C A; Ralko, A; Cabra, D C; Poilblanc, D; Pujol, P

2012-07-06

We prove a "statistical transmutation" symmetry of doped quantum dimer models on the square, triangular, and kagome lattices: the energy spectrum is invariant under a simultaneous change of statistics (i.e., bosonic into fermionic or vice versa) of the holes and of the signs of all the dimer resonance loops. This exact transformation enables us to define the duality equivalence between doped quantum dimer Hamiltonians and provides the analytic framework to analyze dynamical statistical transmutations. We investigate numerically the doping of the triangular quantum dimer model with special focus on the topological Z(2) dimer liquid. Doping leads to four (instead of two for the square lattice) inequivalent families of Hamiltonians. Competition between phase separation, superfluidity, supersolidity, and fermionic phases is investigated in the four families.

Topological color codes on Union Jack lattices: a stable implementation of the whole Clifford group

DOE Office of Scientific and Technical Information (OSTI.GOV)

Katzgraber, Helmut G.; Theoretische Physik, ETH Zurich, CH-8093 Zurich; Bombin, H.

We study the error threshold of topological color codes on Union Jack lattices that allow for the full implementation of the whole Clifford group of quantum gates. After mapping the error-correction process onto a statistical mechanical random three-body Ising model on a Union Jack lattice, we compute its phase diagram in the temperature-disorder plane using Monte Carlo simulations. Surprisingly, topological color codes on Union Jack lattices have a similar error stability to color codes on triangular lattices, as well as to the Kitaev toric code. The enhanced computational capabilities of the topological color codes on Union Jack lattices with respectmore » to triangular lattices and the toric code combined with the inherent robustness of this implementation show good prospects for future stable quantum computer implementations.« less

The Rényi entanglement entropy of a general quantum dimer model at the RK point: a highly efficient algorithm.

PubMed

Pei, Jiquan; Han, Steve; Liao, Haijun; Li, Tao

2014-01-22

A highly efficient and simple-to-implement Monte Carlo algorithm is proposed for the evaluation of the Rényi entanglement entropy (REE) of the quantum dimer model (QDM) at the Rokhsar-Kivelson (RK) point. It makes possible the evaluation of REE at the RK point to the thermodynamic limit for a general QDM. We apply the algorithm to a QDM defined on the triangular and the square lattice in two dimensions and the simple and the face centered cubic (fcc) lattice in three dimensions. We find the REE on all these lattices follows perfect linear scaling in the thermodynamic limit, apart from an even-odd oscillation in the case of the square lattice. We also evaluate the topological entanglement entropy (TEE) with both a subtraction and an extrapolation procedure. We find the QDMs on both the triangular and the fcc lattice exhibit robust Z2 topological order. The expected TEE of ln2 is clearly demonstrated in both cases. Our large scale simulation also proves the recently proposed extrapolation procedure in cylindrical geometry to be a highly reliable way to extract the TEE of a topologically ordered system.

Two-dimensional triangular lattice and its application to lithium-intercalated layered compounds

NASA Astrophysics Data System (ADS)

Decerqueira, R. O.

1982-08-01

Good rechargeable batteries are being searched for use in electric vehicles and in energy storage during off-peak consumption periods and from solar sources. The interest in lithium intercalation compounds has been recently enhanced by the search for such batteries. The process of intercalation of lithium in several transition metal dichalcogenides can provide an emf of several volts. The progress achieved in the last decade in the investigation of these intercalates has been facilitated by the availability of the dichalcogenides as single crystals and by their chemical stability. The transition-metal dichalcogenides and their Li-intercalates are studied, with emphasis on the Li/su xTa/sub yTi/sub l-y/S2 series. The interactions between the Li atoms and the applicability of a lattice gas model to the problem of ordering of these atoms is discussed. A formulation is presented of the cluster-variation aproximation to the lattice gas problem. The single-site and the nearest-neighbor triangle basic clusters are considered as models for Li/sub x TiS2. Also a theory is presented for the effects of a random distribution of different species of host atoms, as in Ta/sub y/Ti/sub l-y/S2.

Complete band gaps of phononic crystal plates with square rods.

PubMed

El-Naggar, Sahar A; Mostafa, Samia I; Rafat, Nadia H

2012-04-01

Much of previous work has been devoted in studying complete band gaps for bulk phononic crystal (PC). In this paper, we theoretically investigate the existence and widths of these gaps for PC plates. We focus our attention on steel rods of square cross sectional area embedded in epoxy matrix. The equations for calculating the dispersion relation for square rods in a square or a triangular lattice have been derived. Our analysis is based on super cell plane wave expansion (SC-PWE) method. The influence of inclusions filling factor and plate thickness on the existence and width of the phononic band gaps has been discussed. Our calculations show that there is a certain filling factor (f=0.55) below which arrangement of square rods in a triangular lattice is superior to the arrangement in a square lattice. A comparison between square and circular cross sectional rods reveals that the former has superior normalized gap width than the latter in case of a square lattice. This situation is switched in case of a triangular lattice. Moreover, a maximum normalized gap width of 0.7 can be achieved for PC plate of square rods embedded in a square lattice and having height 90% of the lattice constant. Copyright © 2011 Elsevier B.V. All rights reserved.

The modified semi-discrete two-dimensional Toda lattice with self-consistent sources

NASA Astrophysics Data System (ADS)

Gegenhasi

2017-07-01

In this paper, we derive the Grammian determinant solutions to the modified semi-discrete two-dimensional Toda lattice equation, and then construct the semi-discrete two-dimensional Toda lattice equation with self-consistent sources via source generation procedure. The algebraic structure of the resulting coupled modified differential-difference equation is clarified by presenting its Grammian determinant solutions and Casorati determinant solutions. As an application of the Grammian determinant and Casorati determinant solution, the explicit one-soliton and two-soliton solution of the modified semi-discrete two-dimensional Toda lattice equation with self-consistent sources are given. We also construct another form of the modified semi-discrete two-dimensional Toda lattice equation with self-consistent sources which is the Bäcklund transformation for the semi-discrete two-dimensional Toda lattice equation with self-consistent sources.

a Triangular Deformation of the Two-Dimensional POINCARÉ Algebra

NASA Astrophysics Data System (ADS)

Khorrami, M.; Shariati, A.; Abolhassani, M. R.; Aghamohammadi, A.

Contracting the h-deformation of SL(2, ℝ), we construct a new deformation of two-dimensional Poincaré's algebra, the algebra of functions on its group and its differential structure. It is seen that these dual Hopf algebras are isomorphic to each other. It is also shown that the Hopf algebra is triangular, and its universal R-matrix is also constructed explicitly. We then find a deformation map for the universal enveloping algebra, and at the end, give the deformed mass shells and Lorentz transformation.

Coprimeness-preserving non-integrable extension to the two-dimensional discrete Toda lattice equation

NASA Astrophysics Data System (ADS)

Kamiya, Ryo; Kanki, Masataka; Mase, Takafumi; Tokihiro, Tetsuji

2017-01-01

We introduce a so-called coprimeness-preserving non-integrable extension to the two-dimensional Toda lattice equation. We believe that this equation is the first example of such discrete equations defined over a three-dimensional lattice. We prove that all the iterates of the equation are irreducible Laurent polynomials of the initial data and that every pair of two iterates is co-prime, which indicate confined singularities of the equation. By reducing the equation to two- or one-dimensional lattices, we obtain coprimeness-preserving non-integrable extensions to the one-dimensional Toda lattice equation and the Somos-4 recurrence.

Spin-Chirality-Driven Ferroelectricity on a Perfect Triangular Lattice Antiferromagnet

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mitamura, H.; Watanuki, R.; Kaneko, Koji

Magnetic field (B) variation of the electrical polarization P c ( ∥c) of the perfect triangular lattice antiferromagnet RbFe(MoO 4) 2 is examined up to the saturation point of the magnetization for B⊥c. P c is observed only in phases for which chirality is predicted in the in-plane magnetic structures. No strong anomaly is observed in P c at the field at which the spin modulation along the c axis, and hence the spin helicity, exhibits a discontinuity to the commensurate state. These results indicate that the ferroelectricity in this compound originates predominantly from the spin chirality, the explanation ofmore » which would require a new mechanism for magnetoferroelectricity. Lastly, the obtained field-temperature phase diagrams of ferroelectricity well agree with those theoretically predicted for the spin chirality of a Heisenberg spin triangular lattice antiferromagnet.« less

Spin-Chirality-Driven Ferroelectricity on a Perfect Triangular Lattice Antiferromagnet

DOE PAGES

Mitamura, H.; Watanuki, R.; Kaneko, Koji; ...

2014-10-01

Magnetic field (B) variation of the electrical polarization P c ( ∥c) of the perfect triangular lattice antiferromagnet RbFe(MoO 4) 2 is examined up to the saturation point of the magnetization for B⊥c. P c is observed only in phases for which chirality is predicted in the in-plane magnetic structures. No strong anomaly is observed in P c at the field at which the spin modulation along the c axis, and hence the spin helicity, exhibits a discontinuity to the commensurate state. These results indicate that the ferroelectricity in this compound originates predominantly from the spin chirality, the explanation ofmore » which would require a new mechanism for magnetoferroelectricity. Lastly, the obtained field-temperature phase diagrams of ferroelectricity well agree with those theoretically predicted for the spin chirality of a Heisenberg spin triangular lattice antiferromagnet.« less

Towards the simplest hydrodynamic lattice-gas model.

PubMed

Boghosian, Bruce M; Love, Peter J; Meyer, David A

2002-03-15

It has been known since 1986 that it is possible to construct simple lattice-gas cellular automata whose hydrodynamics are governed by the Navier-Stokes equations in two dimensions. The simplest such model heretofore known has six bits of state per site on a triangular lattice. In this work, we demonstrate that it is possible to construct a model with only five bits of state per site on a Kagome lattice. Moreover, the model has a simple, deterministic set of collision rules and is easily implemented on a computer. In this work, we derive the equilibrium distribution function for this lattice-gas automaton and carry out the Chapman-Enskog analysis to determine the form of the Navier-Stokes equations.

Monte Carlo study of the honeycomb structure of anthraquinone molecules on Cu(111)

NASA Astrophysics Data System (ADS)

Kim, Kwangmoo; Einstein, T. L.

2011-06-01

Using Monte Carlo calculations of the two-dimensional (2D) triangular lattice gas model, we demonstrate a mechanism for the spontaneous formation of honeycomb structure of anthraquinone (AQ) molecules on a Cu(111) plane. In our model long-range attractions play an important role, in addition to the long-range repulsions and short-range attractions proposed by Pawin, Wong, Kwon, and Bartels [ScienceSCIEAS0036-807510.1126/science.1129309 313, 961 (2006)]. We provide a global account of the possible combinations of long-range attractive coupling constants which lead to a honeycomb superstructure. We also provide the critical temperature of disruption of the honeycomb structure and compare the critical local coverage rate of AQ’s where the honeycomb structure starts to form with the experimental observations.

Anisotropic magnetic properties of the triangular plane lattice material TmMgGaO 4

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cevallos, F. Alex; Stolze, Karoline; Kong, Tai

Here, the crystal growth, structure, and basic magnetic properties of TmMgGaO 4 are reported. The Tm ions are located in a planar triangular lattice consisting of distorted TmO6 octahedra, while the Mg and Ga atoms randomly occupy intermediary bilayers of M-O triangular bipyramids. The Tm ions are positionally disordered. The material displays an antiferromagnetic Curie Weiss theta of ~ -20 -25 K, with no clear ordering visible in the magnetic susceptibility down to 1.8 K; the structure and magnetic properties suggest that ordering of the magnetic moments is frustrated by both structural disorder and the triangular magnetic motif. Single crystalmore » magnetization measurements indicate that the magnetic properties are highly anisotropic, with large moments measured perpendicular to the triangular planes. At 2 K, a broad step-like feature is seen in the field-dependent magnetization perpendicular to the plane on applied field near 2 Tesla.« less

Anisotropic magnetic properties of the triangular plane lattice material TmMgGaO 4

DOE PAGES

Cevallos, F. Alex; Stolze, Karoline; Kong, Tai; ...

2018-04-30

Here, the crystal growth, structure, and basic magnetic properties of TmMgGaO 4 are reported. The Tm ions are located in a planar triangular lattice consisting of distorted TmO6 octahedra, while the Mg and Ga atoms randomly occupy intermediary bilayers of M-O triangular bipyramids. The Tm ions are positionally disordered. The material displays an antiferromagnetic Curie Weiss theta of ~ -20 -25 K, with no clear ordering visible in the magnetic susceptibility down to 1.8 K; the structure and magnetic properties suggest that ordering of the magnetic moments is frustrated by both structural disorder and the triangular magnetic motif. Single crystalmore » magnetization measurements indicate that the magnetic properties are highly anisotropic, with large moments measured perpendicular to the triangular planes. At 2 K, a broad step-like feature is seen in the field-dependent magnetization perpendicular to the plane on applied field near 2 Tesla.« less

Limitation of optical properties through porous silicon photonic crystals influenced by porosity and lattice dynamic

NASA Astrophysics Data System (ADS)

Amedome Min-Dianey, Kossi Aniya; Zhang, Hao-Chun; M'Bouana, Noé Landry Privace; Kougblenou, Komi; Xia, Xinlin

2018-01-01

Finite differential time domain (FDTD) tools were applied to simulate the optical properties characteristics' through square and triangular lattices of porous silicon (pSi) photonic crystals (PhCs); which consisted of periodical patterns of circular air holes built into the pSi material. This was used to investigate the influence of porosity and lattice dynamic on the reflection, transmission and absorption characteristics through unit cell pSi PhC in the visible wavelength domain (400 nm - 700 nm). The numerical simulation was achieved using FDTD Lumerical solutions with periodic boundary conditions (PBC) and perfectly matched layers (PML) as the appropriate boundary conditions. The results revealed that the limitation of optical properties is dependent on porosity and the lattice dynamic in pSi PhC. This was presented by the trend; the higher the reflection the higher the porosity and a decrease in porosity led to an increase in absorption in both lattice considerations. It was discovered that attaining optimum properties for triangular lattice will entail considering porosities less than 50% and hole radius r to the lattice constant a ratio (r / a) above 0.3 for the absorption characteristic and below 0.3 for the transmission characteristic. Triangular lattice can be adapted to improve the optical pattern through the PhC. In addition, the optimisation of these properties through pSi PhCs was achieved by controlling porosity and the ratio r / a .

Light propagation in two-dimensional photonic crystals based on uniaxial polar materials: results on polaritonic spectrum

NASA Astrophysics Data System (ADS)

Gómez-Urrea, H. A.; Duque, C. A.; Pérez-Quintana, I. V.; Mora-Ramos, M. E.

2017-03-01

The dispersion relations of two-dimensional photonic crystals made of uniaxial polaritonic cylinders arranged in triangular lattice are calculated. The particular case of the transverse magnetic polarization is taken into account. Three different uniaxial materials showing transverse phonon-polariton excitations are considered: aluminum nitride, gallium nitride, and indium nitride. The study is carried out by means of the finite-difference time-domain technique for the solution of Maxwell equations, together with the method of the auxiliary differential equation. It is shown that changing the filling fraction can result in the modification of both the photonic and polaritonic bandgaps in the optical dispersion relations. Wider gaps appear for smaller filling fraction values, whereas a larger number of photonic bandgaps will occur within the frequency range considered when a larger filling fraction is used. The effect of including the distinct wurtzite III-V nitride semiconductors as core materials in the cylinders embedded in the air on the photonic properties is discussed as well, highlighting the effect of the dielectric anisotropy on the properties of the polaritonic part of the photonic spectrum.

Accidental degeneracy in photonic bands and topological phase transitions in two-dimensional core-shell dielectric photonic crystals.

PubMed

Xu, Lin; Wang, Hai-Xiao; Xu, Ya-Dong; Chen, Huan-Yang; Jiang, Jian-Hua

2016-08-08

A simple core-shell two-dimensional photonic crystal is studied where the triangular lattice symmetry and the C₆ point group symmetry give rich physics in accidental touching points of photonic bands. We systematically evaluate different types of accidental nodal points at the Brillouin zone center for transverse-magnetic harmonic modes when the geometry and permittivity of the core-shell material are continuously tuned. The accidental nodal points can have different dispersions and topological properties (i.e., Berry phases). These accidental nodal points can be the critical states lying between a topological phase and a normal phase of the photonic crystal. They are thus very important for the study of topological photonic states. We show that, without breaking time-reversal symmetry, by tuning the geometry of the core-shell material, a phase transition into the photonic quantum spin Hall insulator can be achieved. Here the "spin" is defined as the orbital angular momentum of a photon. We study the topological phase transition as well as the properties of the edge and bulk states and their application potentials in optics.

Self-assembly and electrostriction of arrays and chains of hopfion particles in chiral liquid crystals

PubMed Central

Ackerman, Paul J.; van de Lagemaat, Jao; Smalyukh, Ivan I.

2015-01-01

Some of the most exotic condensed matter phases, such as twist grain boundary and blue phases in liquid crystals and Abrikosov phases in superconductors, contain arrays of topological defects in their ground state. Comprised of a triangular lattice of double-twist tubes of magnetization, the so-called ‘A-phase’ in chiral magnets is an example of a thermodynamically stable phase with topologically nontrivial solitonic field configurations referred to as two-dimensional skyrmions, or baby-skyrmions. Here we report that three-dimensional skyrmions in the form of double-twist tori called ‘hopfions’, or ‘torons’ when accompanied by additional self-compensating defects, self-assemble into periodic arrays and linear chains that exhibit electrostriction. In confined chiral nematic liquid crystals, this self-assembly is similar to that of liquid crystal colloids and originates from long-range elastic interactions between particle-like skyrmionic torus knots of molecular alignment field, which can be tuned from isotropic repulsive to weakly or highly anisotropic attractive by low-voltage electric fields. PMID:25607778

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ackerman, P. J.; van de Lagemaat, J.; Smalyukh, I. I.

Some of the most exotic condensed matter phases, such as twist grain boundary and blue phases in liquid crystals and Abrikosov phases in superconductors, contain arrays of topological defects in their ground state. Comprised of a triangular lattice of double-twist tubes of magnetization, the so-called ‘A-phase’ in chiral magnets is an example of a thermodynamically stable phase with topologically nontrivial solitonic field configurations referred to as two-dimensional skyrmions, or baby-skyrmions. Here we report that three-dimensional skyrmions in the form of double-twist tori called ‘hopfions’, or ‘torons’ when accompanied by additional self-compensating defects, self-assemble into periodic arrays and linear chains thatmore » exhibit electrostriction. In confined chiral nematic liquid crystals, this self-assembly is similar to that of liquid crystal colloids and originates from long-range elastic interactions between particle-like skyrmionic torus knots of molecular alignment field, which can be tuned from isotropic repulsive to weakly or highly anisotropic attractive by low-voltage electric fields.« less

Bursting at the Seams: Rippled Monolayer Bismuth on NbSe 2

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fang, Alan; Adamo, Carolina; Jia, Shuang

Bismuth, one of the heaviest semimetals in nature, ignited the interest of the materials-physics community for its potential impact on topological quantum-material systems that utilize its strong spin-orbit coupling (SOC) and unique orbital hybridization. In particular, recent theoretical predictions of unique topological and superconducting properties of thin bismuth films and interfaces prompted intense research on the growth of sub- to a few monolayers of bismuth on different substrates. Similar to bulk rhombohedral bismuth, the initial growth of bismuth films on most substrates results in buckled bilayers that either grow in the (111) or (110) directions, with a lattice constant closemore » to that of bulk Bi. By contrast, in this paper we show a new growth pattern for bismuth monolayers on NbSe 2. We find that the initial growth of Bi can form a strongly bonded commensurate layer, resulting in a compressively strained two-dimensional triangular lattice. A unique pattern of 1D ripples and domain walls is observed. The single layer of bismuth also introduces strong marks on the electronic properties at the surface.« less

Magnetic phase diagram of Ba3CoSb2O9 as determined by ultrasound velocity measurements

NASA Astrophysics Data System (ADS)

Quirion, G.; Lapointe-Major, M.; Poirier, M.; Quilliam, J. A.; Dun, Z. L.; Zhou, H. D.

2015-07-01

Using high-resolution sound velocity measurements we have obtained a very precise magnetic phase diagram of Ba3CoSb2O9 , a material that is considered to be an archetype of the spin-1/2 triangular-lattice antiferromagnet. Results obtained for the field parallel to the basal plane (up to 18 T) show three phase transitions, consistent with predictions based on simple two-dimensional isotropic Heisenberg models and previous experimental investigations. The phase diagram obtained for the field perpendicular to the basal plane clearly reveals an easy-plane character of this compound and, in particular, our measurements show a single first-order phase transition at Hc 1=12.0 T which can be attributed to a spin flop between an umbrella-type configuration and a coplanar V -type order where spins lie in a plane perpendicular to the a b plane. At low temperatures, softening of the lattice within some of the ordered phases is also observed and may be a result of residual spin fluctuations.

Electrodynamics of quantum spin liquids

NASA Astrophysics Data System (ADS)

Dressel, Martin; Pustogow, Andrej

2018-05-01

Quantum spin liquids attract great interest due to their exceptional magnetic properties characterized by the absence of long-range order down to low temperatures despite the strong magnetic interaction. Commonly, these compounds are strongly correlated electron systems, and their electrodynamic response is governed by the Mott gap in the excitation spectrum. Here we summarize and discuss the optical properties of several two-dimensional quantum spin liquid candidates. First we consider the inorganic material herbertsmithite ZnCu3(OH)6Cl2 and related compounds, which crystallize in a kagome lattice. Then we turn to the organic compounds -EtMe3Sb[Pd(dmit)2]2, κ-(BEDT-TTF)2Ag2(CN)3 and κ-(BEDT-TTF)2Cu2(CN)3, where the spins are arranged in an almost perfect triangular lattice, leading to strong frustration. Due to differences in bandwidth, the effective correlation strength varies over a wide range, leading to a rather distinct behavior as far as the electrodynamic properties are concerned. We discuss the spinon contributions to the optical conductivity in comparison to metallic quantum fluctuations in the vicinity of the Mott transition.

Bursting at the Seams: Rippled Monolayer Bismuth on NbSe 2

DOE PAGES

Fang, Alan; Adamo, Carolina; Jia, Shuang; ...

2018-04-13

Bismuth, one of the heaviest semimetals in nature, ignited the interest of the materials-physics community for its potential impact on topological quantum-material systems that utilize its strong spin-orbit coupling (SOC) and unique orbital hybridization. In particular, recent theoretical predictions of unique topological and superconducting properties of thin bismuth films and interfaces prompted intense research on the growth of sub- to a few monolayers of bismuth on different substrates. Similar to bulk rhombohedral bismuth, the initial growth of bismuth films on most substrates results in buckled bilayers that either grow in the (111) or (110) directions, with a lattice constant closemore » to that of bulk Bi. By contrast, in this paper we show a new growth pattern for bismuth monolayers on NbSe 2. We find that the initial growth of Bi can form a strongly bonded commensurate layer, resulting in a compressively strained two-dimensional triangular lattice. A unique pattern of 1D ripples and domain walls is observed. The single layer of bismuth also introduces strong marks on the electronic properties at the surface.« less

A Well-Balanced Central-Upwind Scheme for the 2D Shallow Water Equations on Triangular Meshes

NASA Technical Reports Server (NTRS)

Bryson, Steve; Levy, Doron

2004-01-01

We are interested in approximating solutions of the two-dimensional shallow water equations with a bottom topography on triangular meshes. We show that there is a certain flexibility in choosing the numerical fluxes in the design of semi-discrete Godunov-type central schemes. We take advantage of this fact to generate a new second-order, central-upwind method for the two-dimensional shallow water equations that is well-balanced. We demonstrate the accuracy of our method as well as its balance properties in a variety of examples.

Instability of a triangular Abrikosov lattice at values of the Ginzburg–Landau parameter κ close to unity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ovchinnikov, Yu. N., E-mail: ovc@itp.ac.ru; Sigal, I. M.

2016-07-15

The “soft” transverse mode of gapless excitations related to the deformation of a triangular Abrikosov lattice with a single flux quantum per unit cell at an arbitrary value of the Ginzburg–Landau parameter κ is investigated. An Abrikosov lattice with the angle φ = π/3 between the unit cell vectors is shown to be unstable in a narrow range of values, 1 < κ < 1.000634. The excitation spectrum of the mode under consideration at low values of the momentum k (in the k{sup 2} approximation) is isotropic at k lying in a plane perpendicular to the magnetic field.

Fault-tolerance in Two-dimensional Topological Systems

NASA Astrophysics Data System (ADS)

Anderson, Jonas T.

This thesis is a collection of ideas with the general goal of building, at least in the abstract, a local fault-tolerant quantum computer. The connection between quantum information and topology has proven to be an active area of research in several fields. The introduction of the toric code by Alexei Kitaev demonstrated the usefulness of topology for quantum memory and quantum computation. Many quantum codes used for quantum memory are modeled by spin systems on a lattice, with operators that extract syndrome information placed on vertices or faces of the lattice. It is natural to wonder whether the useful codes in such systems can be classified. This thesis presents work that leverages ideas from topology and graph theory to explore the space of such codes. Homological stabilizer codes are introduced and it is shown that, under a set of reasonable assumptions, any qubit homological stabilizer code is equivalent to either a toric code or a color code. Additionally, the toric code and the color code correspond to distinct classes of graphs. Many systems have been proposed as candidate quantum computers. It is very desirable to design quantum computing architectures with two-dimensional layouts and low complexity in parity-checking circuitry. Kitaev's surface codes provided the first example of codes satisfying this property. They provided a new route to fault tolerance with more modest overheads and thresholds approaching 1%. The recently discovered color codes share many properties with the surface codes, such as the ability to perform syndrome extraction locally in two dimensions. Some families of color codes admit a transversal implementation of the entire Clifford group. This work investigates color codes on the 4.8.8 lattice known as triangular codes. I develop a fault-tolerant error-correction strategy for these codes in which repeated syndrome measurements on this lattice generate a three-dimensional space-time combinatorial structure. I then develop an integer program that analyzes this structure and determines the most likely set of errors consistent with the observed syndrome values. I implement this integer program to find the threshold for depolarizing noise on small versions of these triangular codes. Because the threshold for magic-state distillation is likely to be higher than this value and because logical CNOT gates can be performed by code deformation in a single block instead of between pairs of blocks, the threshold for fault-tolerant quantum memory for these codes is also the threshold for fault-tolerant quantum computation with them. Since the advent of a threshold theorem for quantum computers much has been improved upon. Thresholds have increased, architectures have become more local, and gate sets have been simplified. The overhead for magic-state distillation has been studied, but not nearly to the extent of the aforementioned topics. A method for greatly reducing this overhead, known as reusable magic states, is studied here. While examples of reusable magic states exist for Clifford gates, I give strong reasons to believe they do not exist for non-Clifford gates.

Strings on plane-waves and spin chains on orbifolds

NASA Astrophysics Data System (ADS)

Sadri, Darius

This thesis covers a number of topics in string theory focusing on various aspects of the AdS/CFT duality in various guises and regimes. In the first chapter we present a self-contained review of the Plane-wave/super-Yang-Mills duality. This duality is a specification of the usual AdS/CFT correspondence in the "Penrose limit". In chapter two we study the most general parallelizable pp-wave backgrounds which are non-dilatonic solutions in the NS-NS sector of type IIA and IIB string theories. We demonstrate that parallelizable pp-wave backgrounds are necessarily homogeneous plane-waves, and that a large class of homogeneous plane-waves are parallelizable, stating the necessary conditions. Quantization of string modes, their compactification and behaviour under T-duality are also studied, as are BPS Dp-branes on such backgrounds. In chapter three we consider giant gravitons on the maximally supersymmetric plane-wave background. We deduce the low energy effective light-cone Hamiltonian of the three-sphere giant graviton, and place sources in this effective gauge theory. Although non-vanishing net electric charge configurations are disallowed by Gauss' law, electric dipoles can be formed. From the string theory point of view these dipoles can be understood as open strings piercing the three-sphere, giving a two dimensional (worldsheet) description of giant gravitons. Chapter four presents some new ideas regarding the relation between super-conformal gauge theories and string theories with three-dimensional target spaces, possible relations of these systems to Hamiltonian lattice gauge theories, and integrable spin chains. We consider N = 1, D = 4 superconformal SU( N)px q Yang-Mills theories dual to AdS5 x S5/Zp x Zq orbifolds. We show that a specific sector of this dilatation operator can be thought of as the transfer matrix for a three-dimensional statistical mechanical system, which in turn is equivalent to a 2 + 1-dimensional string theory where the spatial slices are discretized on a triangular lattice, and comment on the integrability of this N = 1 gauge theory, its connection to three-dimensional lattice gauge theories, extensions to six-dimensional string theories, AdS/CFT type dualities and finally their construction via orbifolds and brane-box models. In the process we discover a new class of almost-BPS BMN type operators with large engineering dimensions but controllably small anomalous corrections.

Cascaded chirped narrow bandpass filter with flat-top based on two-dimensional photonic crystals.

PubMed

Zhuang, Yuyang; Chen, Heming; Ji, Ke

2017-05-10

We propose a structure of a cascaded chirped narrow bandpass filter with a flat-top based on two-dimensional (2D) photonic crystals (PhCs). The filter discussed here consists of three filter units, each with a resonator and two reflectors. Coupled mode theory and transfer matrix method are methodologies applied in the analysis of the features. The calculations show that the bandwidth of the filter can be adjusted by changing the distances between resonators and reflectors, and based on this, a flat-top response can be achieved by chirped-cascading the filter units. According to the theoretical model, we design a narrow bandpass filter based on 2D PhCs with a triangular lattice of air holes, the parameters of which are calculated using the finite element method. The simulation results show that the filter has a center frequency of 193.40 THz, an insertion loss of 0.18 dB, a flat bandwidth of 40 GHz, and ripples of about 0.2 dB in the passband. The filter is suitable for dense-wavelength-division-multiplexed optical communication systems with 100 GHz channel spacing.

Carbon kagome lattice and orbital-frustration-induced metal-insulator transition for optoelectronics.

PubMed

Chen, Yuanping; Sun, Y Y; Wang, H; West, D; Xie, Yuee; Zhong, J; Meunier, V; Cohen, Marvin L; Zhang, S B

2014-08-22

A three-dimensional elemental carbon kagome lattice, made of only fourfold-coordinated carbon atoms, is proposed based on first-principles calculations. Despite the existence of 60° bond angles in the triangle rings, widely perceived to be energetically unfavorable, the carbon kagome lattice is found to display exceptional stability comparable to that of C(60). The system allows us to study the effects of triangular frustration on the electronic properties of realistic solids, and it demonstrates a metal-insulator transition from that of graphene to a direct gap semiconductor in the visible blue region. By minimizing s-p orbital hybridization, which is an intrinsic property of carbon, not only the band edge states become nearly purely frustrated p states, but also the band structure is qualitatively different from any known bulk elemental semiconductors. For example, the optical properties are similar to those of direct-gap semiconductors GaN and ZnO, whereas the effective masses are comparable to or smaller than those of Si.

Pythagoras's theorem on a two-dimensional lattice from a `natural' Dirac operator and Connes's distance formula

NASA Astrophysics Data System (ADS)

Dai, Jian; Song, Xing-Chang

2001-07-01

One of the key ingredients of Connes's noncommutative geometry is a generalized Dirac operator which induces a metric (Connes's distance) on the pure state space. We generalize such a Dirac operator devised by Dimakis et al, whose Connes distance recovers the linear distance on an one-dimensional lattice, to the two-dimensional case. This Dirac operator has the local eigenvalue property and induces a Euclidean distance on this two-dimensional lattice, which is referred to as `natural'. This kind of Dirac operator can be easily generalized into any higher-dimensional lattices.

Discrete-to-continuum modelling of weakly interacting incommensurate two-dimensional lattices.

PubMed

Español, Malena I; Golovaty, Dmitry; Wilber, J Patrick

2018-01-01

In this paper, we derive a continuum variational model for a two-dimensional deformable lattice of atoms interacting with a two-dimensional rigid lattice. The starting point is a discrete atomistic model for the two lattices which are assumed to have slightly different lattice parameters and, possibly, a small relative rotation. This is a prototypical example of a three-dimensional system consisting of a graphene sheet suspended over a substrate. We use a discrete-to-continuum procedure to obtain the continuum model which recovers both qualitatively and quantitatively the behaviour observed in the corresponding discrete model. The continuum model predicts that the deformable lattice develops a network of domain walls characterized by large shearing, stretching and bending deformation that accommodates the misalignment and/or mismatch between the deformable and rigid lattices. Two integer-valued parameters, which can be identified with the components of a Burgers vector, describe the mismatch between the lattices and determine the geometry and the details of the deformation associated with the domain walls.

Development of an unstructured solution adaptive method for the quasi-three-dimensional Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Jiang, Yi-Tsann

1993-01-01

A general solution adaptive scheme-based on a remeshing technique is developed for solving the two-dimensional and quasi-three-dimensional Euler and Favre-averaged Navier-Stokes equations. The numerical scheme is formulated on an unstructured triangular mesh utilizing an edge-based pointer system which defines the edge connectivity of the mesh structure. Jameson's four-stage hybrid Runge-Kutta scheme is used to march the solution in time. The convergence rate is enhanced through the use of local time stepping and implicit residual averaging. As the solution evolves, the mesh is regenerated adaptively using flow field information. Mesh adaptation parameters are evaluated such that an estimated local numerical error is equally distributed over the whole domain. For inviscid flows, the present approach generates a complete unstructured triangular mesh using the advancing front method. For turbulent flows, the approach combines a local highly stretched structured triangular mesh in the boundary layer region with an unstructured mesh in the remaining regions to efficiently resolve the important flow features. One-equation and two-equation turbulence models are incorporated into the present unstructured approach. Results are presented for a wide range of flow problems including two-dimensional multi-element airfoils, two-dimensional cascades, and quasi-three-dimensional cascades. This approach is shown to gain flow resolution in the refined regions while achieving a great reduction in the computational effort and storage requirements since solution points are not wasted in regions where they are not required.

Development of an unstructured solution adaptive method for the quasi-three-dimensional Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Jiang, Yi-Tsann; Usab, William J., Jr.

1993-01-01

A general solution adaptive scheme based on a remeshing technique is developed for solving the two-dimensional and quasi-three-dimensional Euler and Favre-averaged Navier-Stokes equations. The numerical scheme is formulated on an unstructured triangular mesh utilizing an edge-based pointer system which defines the edge connectivity of the mesh structure. Jameson's four-stage hybrid Runge-Kutta scheme is used to march the solution in time. The convergence rate is enhanced through the use of local time stepping and implicit residual averaging. As the solution evolves, the mesh is regenerated adaptively using flow field information. Mesh adaptation parameters are evaluated such that an estimated local numerical error is equally distributed over the whole domain. For inviscid flows, the present approach generates a complete unstructured triangular mesh using the advancing front method. For turbulent flows, the approach combines a local highly stretched structured triangular mesh in the boundary layer region with an unstructured mesh in the remaining regions to efficiently resolve the important flow features. One-equation and two-equation turbulence models are incorporated into the present unstructured approach. Results are presented for a wide range of flow problems including two-dimensional multi-element airfoils, two-dimensional cascades, and quasi-three-dimensional cascades. This approach is shown to gain flow resolution in the refined regions while achieving a great reduction in the computational effort and storage requirements since solution points are not wasted in regions where they are not required.

Phase transitions and critical properties in the antiferromagnetic Ising model on a layered triangular lattice with allowance for intralayer next-nearest-neighbor interactions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Badiev, M. K., E-mail: m-zagir@mail.ru; Murtazaev, A. K.; Ramazanov, M. K.

2016-10-15

The phase transitions (PTs) and critical properties of the antiferromagnetic Ising model on a layered (stacked) triangular lattice have been studied by the Monte Carlo method using a replica algorithm with allowance for the next-nearest-neighbor interactions. The character of PTs is analyzed using the histogram technique and the method of Binder cumulants. It is established that the transition from the disordered to paramagnetic phase in the adopted model is a second-order PT. Static critical exponents of the heat capacity (α), susceptibility (γ), order parameter (β), and correlation radius (ν) and the Fischer exponent η are calculated using the finite-size scalingmore » theory. It is shown that (i) the antiferromagnetic Ising model on a layered triangular lattice belongs to the XY universality class of critical behavior and (ii) allowance for the intralayer interactions of next-nearest neighbors in the adopted model leads to a change in the universality class of critical behavior.« less

A photonic crystal waveguide with silicon on insulator in the near-infrared band

NASA Astrophysics Data System (ADS)

Tang, Hai-Xia; Zuo, Yu-Hua; Yu, Jin-Zhong; Wang, Qi-Ming

2007-07-01

A two-dimensional (2D) photonic crystal waveguide in the Γ-K direction with triangular lattice on a silicon-on-insulator (SOI) substrate in the near-infrared band is fabricated by the combination of electron beam lithography and inductively coupled plasma etching. Its transmission characteristics are analysed from the stimulated band diagram by the effective index and the 2D plane wave expansion (PWE) methods. In the experiment, the transmission band edge in a longer wavelength of the photonic crystal waveguide is about 1590 nm, which is in good qualitative agreement with the simulated value. However, there is a disagreement between the experimental and the simulated results when the wavelength ranges from 1607 to 1630 nm, which can be considered as due to the unpolarized source used in the transmission measurement.

WOLF: a computer code package for the calculation of ion beam trajectories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vogel, D.L.

1985-10-01

The WOLF code solves POISSON'S equation within a user-defined problem boundary of arbitrary shape. The code is compatible with ANSI FORTRAN and uses a two-dimensional Cartesian coordinate geometry represented on a triangular lattice. The vacuum electric fields and equipotential lines are calculated for the input problem. The use may then introduce a series of emitters from which particles of different charge-to-mass ratios and initial energies can originate. These non-relativistic particles will then be traced by WOLF through the user-defined region. Effects of ion and electron space charge are included in the calculation. A subprogram PISA forms part of this codemore » and enables optimization of various aspects of the problem. The WOLF package also allows detailed graphics analysis of the computed results to be performed.« less

A two-dimensional lattice equation as an extension of the Heideman-Hogan recurrence

NASA Astrophysics Data System (ADS)

Kamiya, Ryo; Kanki, Masataka; Mase, Takafumi; Tokihiro, Tetsuji

2018-03-01

We consider a two dimensional extension of the so-called linearizable mappings. In particular, we start from the Heideman-Hogan recurrence, which is known as one of the linearizable Somos-like recurrences, and introduce one of its two dimensional extensions. The two dimensional lattice equation we present is linearizable in both directions, and has the Laurent and the coprimeness properties. Moreover, its reduction produces a generalized family of the Heideman-Hogan recurrence. Higher order examples of two dimensional linearizable lattice equations related to the Dana Scott recurrence are also discussed.

Bold Diagrammatic Monte Carlo Method Applied to Fermionized Frustrated Spins

NASA Astrophysics Data System (ADS)

Kulagin, S. A.; Prokof'ev, N.; Starykh, O. A.; Svistunov, B.; Varney, C. N.

2013-02-01

We demonstrate, by considering the triangular lattice spin-1/2 Heisenberg model, that Monte Carlo sampling of skeleton Feynman diagrams within the fermionization framework offers a universal first-principles tool for strongly correlated lattice quantum systems. We observe the fermionic sign blessing—cancellation of higher order diagrams leading to a finite convergence radius of the series. We calculate the magnetic susceptibility of the triangular-lattice quantum antiferromagnet in the correlated paramagnet regime and reveal a surprisingly accurate microscopic correspondence with its classical counterpart at all accessible temperatures. The extrapolation of the observed relation to zero temperature suggests the absence of the magnetic order in the ground state. We critically examine the implications of this unusual scenario.

Statistical thermodynamics of long straight rigid rods on triangular lattices: nematic order and adsorption thermodynamic functions.

PubMed

Matoz-Fernandez, D A; Linares, D H; Ramirez-Pastor, A J

2012-09-04

The statistical thermodynamics of straight rigid rods of length k on triangular lattices was developed on a generalization in the spirit of the lattice-gas model and the classical Guggenheim-DiMarzio approximation. In this scheme, the Helmholtz free energy and its derivatives were written in terms of the order parameter, δ, which characterizes the nematic phase occurring in the system at intermediate densities. Then, using the principle of minimum free energy with δ as a parameter, the main adsorption properties were calculated. Comparisons with Monte Carlo simulations and experimental data were performed in order to evaluate the outcome and limitations of the theoretical model.

Structural transitions in vortex systems with anisotropic interactions

DOE PAGES

Olszewski, Maciej W.; Eskildsen, M. R.; Reichhardt, Charles; ...

2017-12-29

We introduce a model of vortices in type-II superconductors with a four-fold anisotropy in the vortex–vortex interaction potential. Using numerical simulations we show that the vortex lattice undergoes structural transitions as the anisotropy is increased, with a triangular lattice at low anisotropy, a rhombic intermediate state, and a square lattice for high anisotropy. In some cases we observe a multi-q state consisting of an Archimedean tiling that combines square and triangular local ordering. At very high anisotropy, domains of vortex chain states appear. We discuss how this model can be generalized to higher order anisotropy as well as its applicabilitymore » to other particle-based systems with anisotropic particle–particle interactions.« less

Optimal design for crosstalk analysis in 12-core 5-LP mode homogeneous multicore fiber for different lattice structure

NASA Astrophysics Data System (ADS)

Kumar, Dablu; Ranjan, Rakesh

2018-03-01

12-Core 5-LP mode homogeneous multicore fibers have been proposed for analysis of inter-core crosstalk and dispersion, with four different lattice structures (circular, 2-ring, square lattice, and triangular lattice) having cladding diameter of 200 μm and a fixed cladding thickness of 35 μm. The core-to-core crosstalk impact has been studied numerically with respect to bending radius, core pitch, transmission distance, wavelength, and core diameter for all 5-LP modes. In anticipation of further reduction in crosstalk levels, the trench-assisted cores have been incorporated for all respective designs. Ultra-low crosstalk (-138 dB/100 km) has been achieved through the triangular lattice arrangement, with trench depth Δ2 = -1.40% for fundamental (LP01) mode. It has been noted that the impact of mode polarization on crosstalk behavior is minor, with difference in crosstalk levels between two polarized spatial modes as ≤0.2 dB. Moreover, the optimized cladding diameter has been obtained for all 5-LP modes for a target value of crosstalk of -50 dB/100 km, with all the core arrangements. The dispersion characteristic has also been analyzed with respect to wavelength, which is nearly 2.5 ps/nm km at operating wavelength 1550 nm. The relative core multiplicity factor (RCMF) for the proposed design is obtained as 64.

Simulations of water nano-confined between corrugated planes

NASA Astrophysics Data System (ADS)

Zubeltzu, Jon; Artacho, Emilio

2017-11-01

Water confined to nanoscale widths in two dimensions between ideal planar walls has been the subject of ample study, aiming at understanding the intrinsic response of water to confinement, avoiding the consideration of the chemistry of actual confining materials. In this work, we study the response of such nanoconfined water to the imposition of a periodicity in the confinement by means of computer simulations, both using empirical potentials and from first-principles. For that we propose a periodic confining potential emulating the atomistic oscillation of the confining walls, which allows varying the lattice parameter and amplitude of the oscillation. We do it for a triangular lattice, with several values of the lattice parameter: one which is ideal for commensuration with layers of Ih ice and other values that would correspond to more realistic substrates. For the former, the phase diagram shows an overall rise of the melting temperature. The liquid maintains a bi-layer triangular structure, however, despite the fact that it is not favoured by the external periodicity. The first-principles liquid is significantly affected by the modulation in its layering and stacking even at relatively small amplitudes of the confinement modulation. Beyond some critical modulation amplitude, the hexatic phase present in flat confinement is replaced by a trilayer crystalline phase unlike any of the phases encountered for flat confinement. For more realistic lattice parameters, the liquid does not display higher tendency to freeze, but it clearly shows inhomogeneous behaviour as the strength of the rugosity increases. In spite of this expected inhomogeneity, the structural and dynamical response of the liquid is surprisingly insensitive to the external modulation. Although the first-principles calculations give a more triangular liquid than the one observed with empirical potentials (TIP4P/2005), both agree remarkably well for the main conclusions of the study.

A nonlinear mechanics model of bio-inspired hierarchical lattice materials consisting of horseshoe microstructures

PubMed Central

Ma, Qiang; Cheng, Huanyu; Jang, Kyung-In; Luan, Haiwen; Hwang, Keh-Chih; Rogers, John A.; Huang, Yonggang; Zhang, Yihui

2016-01-01

Development of advanced synthetic materials that can mimic the mechanical properties of non-mineralized soft biological materials has important implications in a wide range of technologies. Hierarchical lattice materials constructed with horseshoe microstructures belong to this class of bio-inspired synthetic materials, where the mechanical responses can be tailored to match the nonlinear J-shaped stress-strain curves of human skins. The underlying relations between the J-shaped stress-strain curves and their microstructure geometry are essential in designing such systems for targeted applications. Here, a theoretical model of this type of hierarchical lattice material is developed by combining a finite deformation constitutive relation of the building block (i.e., horseshoe microstructure), with the analyses of equilibrium and deformation compatibility in the periodical lattices. The nonlinear J-shaped stress-strain curves and Poisson ratios predicted by this model agree very well with results of finite element analyses (FEA) and experiment. Based on this model, analytic solutions were obtained for some key mechanical quantities, e.g., elastic modulus, Poisson ratio, peak modulus, and critical strain around which the tangent modulus increases rapidly. A negative Poisson effect is revealed in the hierarchical lattice with triangular topology, as opposed to a positive Poisson effect in hierarchical lattices with Kagome and honeycomb topologies. The lattice topology is also found to have a strong influence on the stress-strain curve. For the three isotropic lattice topologies (triangular, Kagome and honeycomb), the hierarchical triangular lattice material renders the sharpest transition in the stress-strain curve and relative high stretchability, given the same porosity and arc angle of horseshoe microstructure. Furthermore, a demonstrative example illustrates the utility of the developed model in the rapid optimization of hierarchical lattice materials for reproducing the desired stress-strain curves of human skins. This study provides theoretical guidelines for future designs of soft bio-mimetic materials with hierarchical lattice constructions. PMID:27087704

A nonlinear mechanics model of bio-inspired hierarchical lattice materials consisting of horseshoe microstructures

NASA Astrophysics Data System (ADS)

Ma, Qiang; Cheng, Huanyu; Jang, Kyung-In; Luan, Haiwen; Hwang, Keh-Chih; Rogers, John A.; Huang, Yonggang; Zhang, Yihui

2016-05-01

Development of advanced synthetic materials that can mimic the mechanical properties of non-mineralized soft biological materials has important implications in a wide range of technologies. Hierarchical lattice materials constructed with horseshoe microstructures belong to this class of bio-inspired synthetic materials, where the mechanical responses can be tailored to match the nonlinear J-shaped stress-strain curves of human skins. The underlying relations between the J-shaped stress-strain curves and their microstructure geometry are essential in designing such systems for targeted applications. Here, a theoretical model of this type of hierarchical lattice material is developed by combining a finite deformation constitutive relation of the building block (i.e., horseshoe microstructure), with the analyses of equilibrium and deformation compatibility in the periodical lattices. The nonlinear J-shaped stress-strain curves and Poisson ratios predicted by this model agree very well with results of finite element analyses (FEA) and experiment. Based on this model, analytic solutions were obtained for some key mechanical quantities, e.g., elastic modulus, Poisson ratio, peak modulus, and critical strain around which the tangent modulus increases rapidly. A negative Poisson effect is revealed in the hierarchical lattice with triangular topology, as opposed to a positive Poisson effect in hierarchical lattices with Kagome and honeycomb topologies. The lattice topology is also found to have a strong influence on the stress-strain curve. For the three isotropic lattice topologies (triangular, Kagome and honeycomb), the hierarchical triangular lattice material renders the sharpest transition in the stress-strain curve and relative high stretchability, given the same porosity and arc angle of horseshoe microstructure. Furthermore, a demonstrative example illustrates the utility of the developed model in the rapid optimization of hierarchical lattice materials for reproducing the desired stress-strain curves of human skins. This study provides theoretical guidelines for future designs of soft bio-mimetic materials with hierarchical lattice constructions.

A nonlinear mechanics model of bio-inspired hierarchical lattice materials consisting of horseshoe microstructures.

PubMed

Ma, Qiang; Cheng, Huanyu; Jang, Kyung-In; Luan, Haiwen; Hwang, Keh-Chih; Rogers, John A; Huang, Yonggang; Zhang, Yihui

2016-05-01

Development of advanced synthetic materials that can mimic the mechanical properties of non-mineralized soft biological materials has important implications in a wide range of technologies. Hierarchical lattice materials constructed with horseshoe microstructures belong to this class of bio-inspired synthetic materials, where the mechanical responses can be tailored to match the nonlinear J-shaped stress-strain curves of human skins. The underlying relations between the J-shaped stress-strain curves and their microstructure geometry are essential in designing such systems for targeted applications. Here, a theoretical model of this type of hierarchical lattice material is developed by combining a finite deformation constitutive relation of the building block (i.e., horseshoe microstructure), with the analyses of equilibrium and deformation compatibility in the periodical lattices. The nonlinear J-shaped stress-strain curves and Poisson ratios predicted by this model agree very well with results of finite element analyses (FEA) and experiment. Based on this model, analytic solutions were obtained for some key mechanical quantities, e.g., elastic modulus, Poisson ratio, peak modulus, and critical strain around which the tangent modulus increases rapidly. A negative Poisson effect is revealed in the hierarchical lattice with triangular topology, as opposed to a positive Poisson effect in hierarchical lattices with Kagome and honeycomb topologies. The lattice topology is also found to have a strong influence on the stress-strain curve. For the three isotropic lattice topologies (triangular, Kagome and honeycomb), the hierarchical triangular lattice material renders the sharpest transition in the stress-strain curve and relative high stretchability, given the same porosity and arc angle of horseshoe microstructure. Furthermore, a demonstrative example illustrates the utility of the developed model in the rapid optimization of hierarchical lattice materials for reproducing the desired stress-strain curves of human skins. This study provides theoretical guidelines for future designs of soft bio-mimetic materials with hierarchical lattice constructions.

Exact ground states for the nearest neighbor quantum XXZ model on the kagome and other lattices with triangular motifs at Jz /Jxy = - 1 / 2

NASA Astrophysics Data System (ADS)

Changlani, Hitesh; Kumar, Krishna; Kochkov, Dmitrii; Fradkin, Eduardo; Clark, Bryan

We report the existence of a quantum macroscopically degenerate ground state manifold on the nearest neighbor XXZ model on the kagome lattice at the point Jz /Jxy = - 1 / 2 . On many lattices with triangular motifs (including the kagome, sawtooth, icosidodecahedron and Shastry-Sutherland lattice for a certain choice of couplings) this Hamiltonian is found to be frustration-free with exact ground states which correspond to three-colorings of these lattices. Several results also generalize to the case of variable couplings and to other motifs (albeit with possibly more complex Hamiltonians). The degenerate manifold on the kagome lattice corresponds to a ''many-body flat band'' of interacting hard-core bosons; and for the one boson case our results also explain the well-known non-interacting flat band. On adding realistic perturbations, state selection in this manifold of quantum many-body states is discussed along with the implications for the phase diagram of the kagome lattice antiferromagnet. supported by DE-FG02-12ER46875, DMR 1408713, DE-FG02-08ER46544.

Discrete cosine and sine transforms generalized to honeycomb lattice

NASA Astrophysics Data System (ADS)

Hrivnák, Jiří; Motlochová, Lenka

2018-06-01

The discrete cosine and sine transforms are generalized to a triangular fragment of the honeycomb lattice. The honeycomb point sets are constructed by subtracting the root lattice from the weight lattice points of the crystallographic root system A2. The two-variable orbit functions of the Weyl group of A2, discretized simultaneously on the weight and root lattices, induce a novel parametric family of extended Weyl orbit functions. The periodicity and von Neumann and Dirichlet boundary properties of the extended Weyl orbit functions are detailed. Three types of discrete complex Fourier-Weyl transforms and real-valued Hartley-Weyl transforms are described. Unitary transform matrices and interpolating behavior of the discrete transforms are exemplified. Consequences of the developed discrete transforms for transversal eigenvibrations of the mechanical graphene model are discussed.

Frustration and correlations in stacked triangular-lattice Ising antiferromagnets

NASA Astrophysics Data System (ADS)

Burnell, F. J.; Chalker, J. T.

2015-12-01

We study multilayer triangular-lattice Ising antiferromagnets with interlayer interactions that are weak and frustrated in an abc stacking. By analyzing a coupled height model description of these systems, we show that they exhibit a classical spin liquid regime at low temperature, in which both intralayer and interlayer correlations are strong but there is no long-range order. Diffuse scattering in this regime is concentrated on a helix in reciprocal space, as observed for charge ordering in the materials LuFe2O4 and YbFe2O4 .

S/sub n/ analysis of the TRX metal lattices with ENDF/B version III data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wheeler, F.J.; Pearlstein, S.

1975-03-01

Two critical assemblies, designated as thermal-reactor benchmarks TRX-1 and TRX-2 for ENDF/B data testing, were analyzed using the one-dimensional S/sub n/-theory code SCAMP. The two assemblies were simple lattices of aluminum-clad, uranium-metal fuel rods in triangular arrays with D$sub 2$O as moderator and reflector. The fuel was low-enriched (1.3 percent $sup 235$U), 0.387-inch in diameter and had an active height of 48 inches. The volume ratio of water to uranium was 2.35 for the TRX-1 lattice and 4.02 for TRX-2. Full-core S/sub n/ calculations based on Version III data were performed for these assemblies and the results obtained were comparedmore » with the measured values of the multiplication factors, the ratio of epithermal-to-thermal neutron capture in $sup 238$U, the ratio of epithermal-to-thermal fission in $sup 235$U, the ratio of $sup 238$U fission to $sup 235$U fission, and the ratio of capture in $sup 238$U to fission in $sup 235$U. Reaction rates were obtained from a central region of the full- core problems. Multigroup cross sections for the reactor calculation were obtained from S/sub n/ cell calculations with resonance self-shielding calculated using the RABBLE treatment. The results of the analyses are generally consistent with results obtained by other investigators. (auth)« less

Two-dimensional lattice Boltzmann model for magnetohydrodynamics.

PubMed

Schaffenberger, Werner; Hanslmeier, Arnold

2002-10-01

We present a lattice Boltzmann model for the simulation of two-dimensional magnetohydro dynamic (MHD) flows. The model is an extension of a hydrodynamic lattice Boltzman model with 9 velocities on a square lattice resulting in a model with 17 velocities. Earlier lattice Boltzmann models for two-dimensional MHD used a bidirectional streaming rule. However, the use of such a bidirectional streaming rule is not necessary. In our model, the standard streaming rule is used, allowing smaller viscosities. To control the viscosity and the resistivity independently, a matrix collision operator is used. The model is then applied to the Hartmann flow, giving reasonable results.

Spin-1/2 Heisenberg antiferromagnet on an anisotropic triangular lattice

NASA Astrophysics Data System (ADS)

Starykh, Oleg

2007-03-01

The Triangular lattice spin-1/2 Heisenberg AntiFerromagnet (TAF) is a prototypical model of frustrated quantum magnetism. While it is believed to exhibit long-range order in the isotropic limit, changes such as spatial anisotropy can alter the delicate balance amongst competing ground states. I will describe the static and dynamic properties of the spatially anisotropic TAF, with inter-chain diagonal exchange J' much weaker than the intrachain exchange J. Treating J' as a perturbation of decoupled Heisenberg spin-1/2 chains, I find that the ground state is spontaneously dimerized in a four-fold degenerate zig-zag pattern. This dimerization instability is driven by quantum fluctuations, which are dramatically enhanced here by the frustrated nature of inter-chain exchange. A magnetic field partially relieves frustration, by canting the spins along the field direction, and causes a quantum phase transition into a magnetically-ordered spin-density-wave phase. This is followed by cone and, finally, fully polarized (saturated) phases, as a function of increasing magnetic field. I show that many of these features are in fact observed in experiments on the celebrated material Cs2CuCl4 (J'/J =1/3). I will also discuss the significant modification of the phase diagram by symmetry-breaking anisotropic Dzyaloshinskii-Moriya (DM) interactions, present in this interesting magnet. In addition to static and thermodynamic properties, the proposed ``one-dimensional'' approach offers a compelling explanation of the unusual experimentally measured dynamical structure factor of Cs2CuCl4 in terms of descendants of one-dimensional spinons. Quite generally, I find characteristic features of a momentum-dependent spinon bound state and a dispersing incoherent excitation in the structure factor, in agreement with experiments.

Fluctuation in the Intermediate Magnetic Phase of Triangular Ising Antiferromagnet (CeS)1.16[Fe0.33(NbS2)2

NASA Astrophysics Data System (ADS)

Michioka, Chishiro; Suzuki, Kazuya; Mibu, Ko

2002-10-01

We applied 57Fe Mössbauer spectroscopy for investigating the Ising spin triangular lattice antiferromagnet (TLA) (CeS)1.16[Fe0.33(NbS2)2] between 2 and 300 K. The spectra revealed that the relaxation time of the hyperfine field markedly changes in the intermediate phase between TN1=22 K and TN2=15 K due to strong spin fluctuation. The relaxation of the hyperfine field is not sufficiently fast as a paramagnet even at 77 K, which is much higher than TN1, and the inverse susceptibility of (LaS)1.14[Fe0.33(NbS2)2] deviates from the Curie-Weiss law below 100 K. These results indicate that an unusual short-range order exists above TN1. The temperature dependence of the Mössbauer spectra can be explained by phase transition of the three-dimensional TLA model with weak interlayer exchange interactions.

Universal quantum computing using (Zd) 3 symmetry-protected topologically ordered states

NASA Astrophysics Data System (ADS)

Chen, Yanzhu; Prakash, Abhishodh; Wei, Tzu-Chieh

2018-02-01

Measurement-based quantum computation describes a scheme where entanglement of resource states is utilized to simulate arbitrary quantum gates via local measurements. Recent works suggest that symmetry-protected topologically nontrivial, short-ranged entangled states are promising candidates for such a resource. Miller and Miyake [npj Quantum Inf. 2, 16036 (2016), 10.1038/npjqi.2016.36] recently constructed a particular Z2×Z2×Z2 symmetry-protected topological state on the Union Jack lattice and established its quantum-computational universality. However, they suggested that the same construction on the triangular lattice might not lead to a universal resource. Instead of qubits, we generalize the construction to qudits and show that the resulting (d -1 ) qudit nontrivial Zd×Zd×Zd symmetry-protected topological states are universal on the triangular lattice, for d being a prime number greater than 2. The same construction also holds for other 3-colorable lattices, including the Union Jack lattice.

Self-Assembly and Electrostriction of Arrays and Chains of Hopfion Particles in Chiral Liquid Crystals

DOE PAGES

Ackerman, P. J.; van de Lagemaat, J.; Smalyukh, I. I.

2015-01-21

Some of the most exotic condensed matter phases, such as twist grain boundary and blue phases in liquid crystals and Abrikosov phases in superconductors, contain arrays of topological defects in their ground state. Comprised of a triangular lattice of double-twist tubes of magnetization, the so-called ‘A-phase’ in chiral magnets is an example of a thermodynamically stable phase with topologically nontrivial solitonic field configurations referred to as two-dimensional skyrmions, or baby-skyrmions. Here we report that three-dimensional skyrmions in the form of double-twist tori called ‘hopfions’, or ‘torons’ when accompanied by additional self-compensating defects, self-assemble into periodic arrays and linear chains thatmore » exhibit electrostriction. In confined chiral nematic liquid crystals, this self-assembly is similar to that of liquid crystal colloids and originates from long-range elastic interactions between particle-like skyrmionic torus knots of molecular alignment field, which can be tuned from isotropic repulsive to weakly or highly anisotropic attractive by low-voltage electric fields.« less

Face Centered Cubic and Hexagonal Close Packed Skyrmion Crystals in Centrosymmetric Magnets

NASA Astrophysics Data System (ADS)

Lin, Shi-Zeng; Batista, Cristian D.

2018-02-01

Skyrmions are disklike objects that typically form triangular crystals in two-dimensional systems. This situation is analogous to the so-called pancake vortices of quasi-two-dimensional superconductors. The way in which Skyrmion disks or "pancake Skyrmions" pile up in layered centrosymmetric materials is dictated by the interlayer exchange. Unbiased Monte Carlo simulations and simple stabilization arguments reveal face centered cubic and hexagonal close packed Skyrmion crystals for different choices of the interlayer exchange, in addition to the conventional triangular crystal of Skyrmion lines. Moreover, an inhomogeneous current induces a sliding motion of pancake Skyrmions, indicating that they behave as effective mesoscale particles.

Continuous excitations of the triangular-lattice quantum spin liquid YbMgGaO 4

DOE PAGES

Paddison, Joseph A. M.; Daum, Marcus; Dun, Zhiling; ...

2016-12-05

A quantum spin liquid (QSL) is an exotic state of matter in which electrons’ spins are quantum entangled over long distances, but do not show magnetic order in the zero-temperature limit. The observation of QSL states is a central aim of experimental physics, because they host collective excitations that transcend our knowledge of quantum matter; however, examples in real materials are scarce. We report neutron-scattering experiments on YbMgGaO 4, a QSL candidate in which Yb 3+ ions with effective spin-1/2 occupy a triangular lattice. Furthermore, our measurements reveal a continuum of magnetic excitations—the essential experimental hallmark of a QSL7—at verymore » low temperature (0.06 K). The origin of this peculiar excitation spectrum is a crucial question, because isotropic nearest-neighbour interactions do not yield a QSL ground state on the triangular lattice. In using measurements the field-polarized state, we identify antiferromagnetic next-nearest-neighbour interactions spin-space anisotropies and chemical disorder between the magnetic layers as key ingredients in YbMgGaO 4.« less

Engineered long-range interactions on a 2D array of trapped ions

NASA Astrophysics Data System (ADS)

Britton, Joseph W.; Sawyer, Brian C.; Bollinger, John J.; Freericks, James K.

2014-03-01

Ising interactions are one paradigm used to model quantum magnetism in condensed matter systems. At NIST Boulder we confine and Doppler laser cool hundreds of 9Be+ ions in a Penning trap. The valence electron of each ion behaves as an ideal spin-1/2 particle and, in the limit of weak radial confinement relative to axial confinement, the ions naturally form a two-dimensional triangular lattice. A variable-range anti-ferromagnetic Ising interaction is engineered with a spin-dependent optical dipole force (ODF) through spin-dependent excitation of collective modes of ion motion. We have also exploited this spin-dependent force to perform spectroscopy and thermometry of the normal modes of the trapped ion crystal. The high spin-count and long-range spin-spin couplings achievable in the NIST Penning trap brings within reach simulation of computationally intractable problems in quantum magnetism. Examples include modeling quantum magnetic phase transitions and propagation of spin correlations resulting from a quantum quench. The Penning system may also be amenable to observation of spin-liquid behavior thought to arise in systems where the underlying lattice structure can frustrate long-range ordering. Supported by DARPA OLE and NIST.

Experimental observation of wave localization at the Dirac frequency in a two-dimensional photonic crystal microcavity.

PubMed

Hu, Lei; Xie, Kang; Hu, Zhijia; Mao, Qiuping; Xia, Jiangying; Jiang, Haiming; Zhang, Junxi; Wen, Jianxiang; Chen, Jingjing

2018-04-02

Trapping light within cavities or waveguides in photonic crystals is an effective technology in modern integrated optics. Traditionally, cavities rely on total internal reflection or a photonic bandgap to achieve field confinement. Recent investigations have examined new localized modes that occur at a Dirac frequency that is beyond any complete photonic bandgap. We design Al 2 O 3 dielectric cylinders placed on a triangular lattice in air, and change the central rod size to form a photonic crystal microcavity. It is predicted that waves can be localized at the Dirac frequency in this device without photonic bandgaps or total internal reflections. We perform a theoretical analysis of this new wave localization and verify it experimentally. This work paves the way for exploring localized defect modes at the Dirac point in the visible and infrared bands, with potential applicability to new optical devices.

Reconfigurable lattice mesh designs for programmable photonic processors.

PubMed

Pérez, Daniel; Gasulla, Ivana; Capmany, José; Soref, Richard A

2016-05-30

We propose and analyse two novel mesh design geometries for the implementation of tunable optical cores in programmable photonic processors. These geometries are the hexagonal and the triangular lattice. They are compared here to a previously proposed square mesh topology in terms of a series of figures of merit that account for metrics that are relevant to on-chip integration of the mesh. We find that that the hexagonal mesh is the most suitable option of the three considered for the implementation of the reconfigurable optical core in the programmable processor.

Berezinskii-Kosterlitz-Thouless phase transition for the dilute planar rotator model on a triangular lattice

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sun Yunzhou; Yi Lin; Wysin, G. M.

2008-10-15

The Berezinskii-Kosterlitz-Thouless (BKT) phase transition for the dilute planar rotator model on a triangular lattice is studied by using a hybrid Monte Carlo method. The phase-transition temperatures for different nonmagnetic impurity densities are obtained by three approaches: finite-size scaling of plane magnetic susceptibility, helicity modulus, and Binder's fourth cumulant. It is found that the phase-transition temperature decreases with increasing impurity density {rho} and the BKT phase transition vanishes when the magnetic occupancy falls to the site percolation threshold: 1-{rho}{sub c}=p{sub c}=0.5.

Thermodynamic and critical properties of an antiferromagnetically stacked triangular Ising antiferromagnet in a field

NASA Astrophysics Data System (ADS)

Žukovič, M.; Borovský, M.; Bobák, A.

2018-05-01

We study a stacked triangular lattice Ising model with both intra- and inter-plane antiferromagnetic interactions in a field, by Monte Carlo simulation. We find only one phase transition from a paramagnetic to a partially disordered phase, which is of second order and 3D XY universality class. At low temperatures we identify two highly degenerate phases: at smaller (larger) fields the system shows long-range ordering in the stacking direction (within planes) but not in the planes (stacking direction). Nevertheless, crossovers to these phases do not have a character of conventional phase transitions but rather linear-chain-like excitations.

SPECIAL ISSUE DEVOTED TO THE 80TH BIRTHDAY OF S.A. AKHMANOV: Excitation of coherent polaritons in a two-dimensional atomic lattice

NASA Astrophysics Data System (ADS)

Barinov, I. O.; Alodzhants, A. P.; Arakelyan, Sergei M.

2009-07-01

We describe a new type of spatially periodic structure (lattice models): a polaritonic crystal formed by a two-dimensional lattice of trapped two-level atoms interacting with the electromagnetic field in a cavity (or in a one-dimensional array of tunnelling-coupled microcavities), which allows polaritons to be fully localised. Using a one-dimensional polaritonic crystal as an example, we analyse conditions for quantum degeneracy of a lower-polariton gas and those for quantum optical information recording and storage.

Deconfined quantum critical point on the triangular lattice

NASA Astrophysics Data System (ADS)

Jian, Chao-Ming; Thomson, Alex; Rasmussen, Alex; Bi, Zhen; Xu, Cenke

2018-05-01

In this work we propose a theory for the deconfined quantum critical point (DQCP) for spin-1/2 systems on a triangular lattice, which is a direct unfine-tuned quantum phase transition between the standard "√{3 }×√{3 } " noncollinear antiferromagnetic order (or the so-called 120∘ state) and the "√{12 }×√{12 } " valence solid bond (VBS) order, both of which are very standard ordered phases often observed in numerical simulations. This transition is beyond the standard Landau-Ginzburg paradigm and is also fundamentally different from the original DQCP theory on the square lattice due to the very different structures of both the magnetic and VBS order on frustrated lattices. We first propose a topological term in the effective-field theory that captures the "intertwinement" between the √{3 }×√{3 } antiferromagnetic order and the √{12 }×√{12 } VBS order. Then using a controlled renormalization-group calculation, we demonstrate that an unfine-tuned direct continuous DQCP exists between the two ordered phases mentioned above. This DQCP is described by the Nf=4 quantum electrodynamics (QED) with an emergent PSU(4)=SU(4)/Z4 symmetry only at the critical point. The aforementioned topological term is also naturally derived from the Nf=4 QED. We also point out that physics around this DQCP is analogous to the boundary of a 3 d bosonic symmetry- protected topological state with only on-site symmetries.

Triangular Black Phosphorus Atomic Layers by Liquid Exfoliation.

PubMed

Seo, Soonjoo; Lee, Hyun Uk; Lee, Soon Chang; Kim, Yooseok; Kim, Hyeran; Bang, Junhyeok; Won, Jonghan; Kim, Youngjun; Park, Byoungnam; Lee, Jouhahn

2016-03-30

Few-layer black phosphorus (BP) is the most promising material among the two-dimensional materials due to its layered structure and the excellent semiconductor properties. Currently, thin BP atomic layers are obtained mostly by mechanical exfoliation of bulk BP, which limits applications in thin-film based electronics due to a scaling process. Here we report highly crystalline few-layer black phosphorus thin films produced by liquid exfoliation. We demonstrate that the liquid-exfoliated BP forms a triangular crystalline structure on SiO2/Si (001) and amorphous carbon. The highly crystalline BP layers are faceted with a preferred orientation of the (010) plane on the sharp edge, which is an energetically most favorable facet according to the density functional theory calculations. Our results can be useful in understanding the triangular BP structure for large-area applications in electronic devices using two-dimensional materials. The sensitivity and selectivity of liquid-exfoliated BP to gas vapor demonstrate great potential for practical applications as sensors.

Triangular Black Phosphorus Atomic Layers by Liquid Exfoliation

PubMed Central

Seo, Soonjoo; Lee, Hyun Uk; Lee, Soon Chang; Kim, Yooseok; Kim, Hyeran; Bang, Junhyeok; Won, Jonghan; Kim, Youngjun; Park, Byoungnam; Lee, Jouhahn

2016-01-01

Few-layer black phosphorus (BP) is the most promising material among the two-dimensional materials due to its layered structure and the excellent semiconductor properties. Currently, thin BP atomic layers are obtained mostly by mechanical exfoliation of bulk BP, which limits applications in thin-film based electronics due to a scaling process. Here we report highly crystalline few-layer black phosphorus thin films produced by liquid exfoliation. We demonstrate that the liquid-exfoliated BP forms a triangular crystalline structure on SiO2/Si (001) and amorphous carbon. The highly crystalline BP layers are faceted with a preferred orientation of the (010) plane on the sharp edge, which is an energetically most favorable facet according to the density functional theory calculations. Our results can be useful in understanding the triangular BP structure for large-area applications in electronic devices using two-dimensional materials. The sensitivity and selectivity of liquid-exfoliated BP to gas vapor demonstrate great potential for practical applications as sensors. PMID:27026070

Nonlinear dust-lattice waves: a modified Toda lattice

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cramer, N. F.

Charged dust grains in a plasma interact with a Coulomb potential, but also with an exponential component to the potential, due to Debye shielding in the background plasma. Here we investigate large-amplitude oscillations and waves in dust-lattices, employing techniques used in Toda lattice analysis. The lattice consists of a linear chain of particles, or a periodic ring as occurs in experimentally observed dust particle clusters. The particle motion has a triangular waveform, and chaotic motion for large amplitude motion of a grain.

The kink-soliton and antikink-soliton in quasi-one-dimensional nonlinear monoatomic lattice

NASA Astrophysics Data System (ADS)

Xu, Quan; Tian, Qiang

2005-04-01

The quasi-one-dimensional nonlinear monoatomic lattice is analyzed. The kink-soliton and antikink-soliton are presented. When the interaction of the lattice is strong in the x-direction and weak in the y-direction, the two-dimensional (2D) lattice changes to a quasi-one-dimensional lattice. Taking nearest-neighbor interaction into account, the vibration equation can be transformed into the KPI, KPII and MKP equation. Considering the cubic nonlinear potential of the vibration in the lattice, the kink-soliton solution is presented. Considering the quartic nonlinear potential and the cubic interaction potential, the kink-soliton and antikink-soliton solutions are presented.

Revisiting the Scale-Invariant, Two-Dimensional Linear Regression Method

ERIC Educational Resources Information Center

Patzer, A. Beate C.; Bauer, Hans; Chang, Christian; Bolte, Jan; Su¨lzle, Detlev

2018-01-01

The scale-invariant way to analyze two-dimensional experimental and theoretical data with statistical errors in both the independent and dependent variables is revisited by using what we call the triangular linear regression method. This is compared to the standard least-squares fit approach by applying it to typical simple sets of example data…

H-T Magnetic Phase Diagram of a Frustrated Triangular Lattice Antiferromagnet CuFeO 2

NASA Astrophysics Data System (ADS)

Mitsuda, Setsuo; Mase, Motoshi; Uno, Takahiro; Kitazawa, Hideaki; Katori, Hiroko

2000-01-01

By magnetization and specific heat measurements in an applied magnetic field up to 12 T, we obtained the magnetic field (H) versus temperature (T) phase diagram of a frustrated triangular lattice antiferromagnet (TLA), CuFeO2, where a partially disordered phase typical to Ising TLA exists as a thermally induced state for the 4-sublattice ground state as well as for the first-field-induced 5-sublattice-like state. The experimentally obtained H-T magnetic phase diagram is compared with that from Monte-Carlo simulation of a 2D Ising TLA model with competing exchange interactions up to 3rd neighbors.

Evidence for a spinon Fermi surface in a triangular-lattice quantum-spin-liquid candidate

DOE PAGES

Shen, Yao; Li, Yao-Dong; Wo, Hongliang; ...

2016-12-05

A quantum spin liquid is an exotic quantum state of matter in which spins are highly entangled and remain disordered down to zero temperature. Such a state of matter is potentially relevant to high-temperature superconductivity and quantum-information applications, and experimental identification of a quantum spin liquid state is of fundamental importance for our understanding of quantum matter. Theoretical studies have proposed various quantum-spin-liquid ground states, most of which are characterized by exotic spin excitations with fractional quantum numbers (termed ‘spinons’). In this paper, we report neutron scattering measurements of the triangular-lattice antiferromagnet YbMgGaO 4 that reveal broad spin excitations coveringmore » a wide region of the Brillouin zone. The observed diffusive spin excitation persists at the lowest measured energy and shows a clear upper excitation edge, consistent with the particle–hole excitation of a spinon Fermi surface. Finally, our results therefore point to the existence of a quantum spin liquid state with a spinon Fermi surface in YbMgGaO 4, which has a perfect spin-1/2 triangular lattice as in the original proposal of quantum spin liquids.« less

Fabrication of novel two-dimensional nanopatterned conductive PEDOT:PSS films for organic optoelectronic applications.

PubMed

Petti, Lucia; Rippa, Massimo; Capasso, Rossella; Nenna, Giuseppe; De Girolamo Del Mauro, Anna; Pandolfi, Giuseppe; Maglione, Maria Grazia; Minarini, Carla

2013-06-12

This paper presents a novel strategy to fabricate two-dimensional poly(3,4 ethylenedioxythiophene):poly(styrene sulfonate) (PEDOT:PSS) photonic crystals (PCs) combining electron beam lithography (EBL) and plasma etching (PE) processes. The surface morphology of PEDOT:PSS PCs after mild oxygen plasma treatment was investigated by scanning electron microscopy. The effects on light extraction are studied experimentally. Vertical extraction of light was found to be strongly dependent on the geometric parameters of the PCs. By changing the lattice type from triangular to square and the geometrical parameters of the photonic structures, the resonance peak could be tuned from a narrow blue emission at 445 nm up to a green emission at 525 nm with a full width at half-maximum of 20 nm, which is in good agreement with Bragg's diffraction theory and free photon band structure. Both finite-difference time-domain and plane wave expansion methods are used to calculate the resonant frequencies and the photonic band structures in the two-dimensional photonic crystals showing a very good agreement with the experiment results. A 2D nanopatterned transparent anode was also fabricated onto a flexible polyethylene terephthalate (PET) substrate and it was integrated into an organic light-emitting diode (OLED). The obtained results fully confirm the feasibility of the developed process of micro/nano patterning PEDOT:PSS. Engineered polymer electrodes prepared by this unique method are useful in a wide variety of high-performance flexible organic optoelectronics.

Synthesis of parallel and antiparallel core-shell triangular nanoparticles

NASA Astrophysics Data System (ADS)

Bhattacharjee, Gourab; Satpati, Biswarup

2018-04-01

Core-shell triangular nanoparticles were synthesized by seed mediated growth. Using triangular gold (Au) nanoparticle as template, we have grown silver (Ag) shellto get core-shell nanoparticle. Here by changing the chemistry we have grown two types of core-shell structures where core and shell is having same symmetry and also having opposite symmetry. Both core and core-shell nanoparticles were characterized using transmission electron microscopy (TEM) and energy dispersive X-ray spectroscopy (EDX) to know the crystal structure and composition of these synthesized core-shell nanoparticles. From diffraction pattern analysis and energy filtered TEM (EFTEM) we have confirmed the crystal facet in core is responsible for such two dimensional growth of core-shell nanostructures.

Optimizing random searches on three-dimensional lattices

NASA Astrophysics Data System (ADS)

Yang, Benhao; Yang, Shunkun; Zhang, Jiaquan; Li, Daqing

2018-07-01

Search is a universal behavior related to many types of intelligent individuals. While most studies have focused on search in two or infinite-dimensional space, it is still missing how search can be optimized in three-dimensional space. Here we study random searches on three-dimensional (3d) square lattices with periodic boundary conditions, and explore the optimal search strategy with a power-law step length distribution, p(l) ∼l-μ, known as Lévy flights. We find that compared to random searches on two-dimensional (2d) lattices, the optimal exponent μopt on 3d lattices is relatively smaller in non-destructive case and remains similar in destructive case. We also find μopt decreases as the lattice length in z direction increases under high target density. Our findings may help us to understand the role of spatial dimension in search behaviors.

Landau damping of Bogoliubov excitations in two- and three-dimensional optical lattices at finite temperatures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsuchiya, Shunji; Department of Physics, Waseda University, 3-4-1 Okubo, Tokyo 169-8555; Griffin, Allan

2005-11-15

We study the Landau damping of Bogoliubov excitations in two- and three-dimensional optical lattices at finite temperatures, extending our recent work on one-dimensional (1D) optical lattices. We use a Bose-Hubbard tight-binding model and the Popov approximation to calculate the temperature dependence of the number of condensate atoms n{sup c0}(T) in each lattice well. As with 1D optical lattices, damping only occurs if the Bogoliubov excitations exhibit anomalous dispersion (i.e., the excitation energy bends upward at low momentum), analogous to the case of phonons in superfluid {sup 4}He. This leads to the disappearance of all damping processes in a D-dimensional simplemore » cubic optical lattice when Un{sup c0}{>=}6DJ, where U is the on-site interaction, and J is the hopping matrix element.« less

Development of a solution adaptive unstructured scheme for quasi-3D inviscid flows through advanced turbomachinery cascades

NASA Technical Reports Server (NTRS)

Usab, William J., Jr.; Jiang, Yi-Tsann

1991-01-01

The objective of the present research is to develop a general solution adaptive scheme for the accurate prediction of inviscid quasi-three-dimensional flow in advanced compressor and turbine designs. The adaptive solution scheme combines an explicit finite-volume time-marching scheme for unstructured triangular meshes and an advancing front triangular mesh scheme with a remeshing procedure for adapting the mesh as the solution evolves. The unstructured flow solver has been tested on a series of two-dimensional airfoil configurations including a three-element analytic test case presented here. Mesh adapted quasi-three-dimensional Euler solutions are presented for three spanwise stations of the NASA rotor 67 transonic fan. Computed solutions are compared with available experimental data.

Discovering phases, phase transitions, and crossovers through unsupervised machine learning: A critical examination

NASA Astrophysics Data System (ADS)

Hu, Wenjian; Singh, Rajiv R. P.; Scalettar, Richard T.

2017-06-01

We apply unsupervised machine learning techniques, mainly principal component analysis (PCA), to compare and contrast the phase behavior and phase transitions in several classical spin models—the square- and triangular-lattice Ising models, the Blume-Capel model, a highly degenerate biquadratic-exchange spin-1 Ising (BSI) model, and the two-dimensional X Y model—and we examine critically what machine learning is teaching us. We find that quantified principal components from PCA not only allow the exploration of different phases and symmetry-breaking, but they can distinguish phase-transition types and locate critical points. We show that the corresponding weight vectors have a clear physical interpretation, which is particularly interesting in the frustrated models such as the triangular antiferromagnet, where they can point to incipient orders. Unlike the other well-studied models, the properties of the BSI model are less well known. Using both PCA and conventional Monte Carlo analysis, we demonstrate that the BSI model shows an absence of phase transition and macroscopic ground-state degeneracy. The failure to capture the "charge" correlations (vorticity) in the BSI model (X Y model) from raw spin configurations points to some of the limitations of PCA. Finally, we employ a nonlinear unsupervised machine learning procedure, the "autoencoder method," and we demonstrate that it too can be trained to capture phase transitions and critical points.

Quantum phase transition in strongly correlated systems

NASA Astrophysics Data System (ADS)

Jiang, Longhua

In this thesis, we investigated the strongly correlated phenomena in bilayer quantum Hall effect, inhomogeneous superconductivity and Boson Hubbard model. Bilayer quantum Hall system is studied in chapter 2. By using the Composite Boson (CB) theory developed by J. Ye, we derive the ground state, quasihole and a quasihole-pair wave functions from the CB theory and its dual action. We find that the ground state wave function is the product of two parts, one in the charge sector which is the well known Halperin's (111) wave function and the other in the spin sector which is non-trivial at any finite d due to the gapless mode. So the total groundstate wave function differs from the well known (111) wave function at any finite d. In addition to commonly known multiplicative factors, the quasihole and quasihole-pair wave functions also contain non-trivial normalization factors multiplying the correct ground state wave function. Then we continue to study the quantum phase transition from the excitonic superfluid (ESF) to a possible pseudo-spin density wave (PSDW) at some intermediate distances driven by the magneto-roton minimum collapsing at a finite wavevector. We analyze the properties of the PSDW and explicitly show that a square lattice is the favored lattice. We suggest that correlated hopping of vacancies in the active and passive layers in the PSDW state leads to very large and temperature-dependent drag, consistent with the experimental data. Comparisons with previous microscopic numerical calculations are made. Further experimental implications are given. In chapter 3, we investigate inhomogeneous superconductivity. Starting from the Ginzburg-Landau free energy describing the normal state to Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state transition, we evaluate the free energy of seven most common lattice structures: stripe, square, triangular, Simple Cubic (SC), Face centered Cubic (FCC), Body centered Cubic (BCC) and Quasicrystal (QC). We find that the stripe phase, which is the original LO state, is the most stable phase. This result may be relevant to the detection of the FFLO state in some heavy fermion compounds and the pairing lattice structure of fermions with unequal populations on the BCS side of the Feshbach resonance in ultra-cold atoms. In chapter 4, the Boson Hubbard model is studied by duality transformation. Interacting bosons at filling factor f = p/q hopping on a lattice can be mapped to interacting vortices hopping on the dual lattice subject to a fluctuating dual " magnetic field" whose average strength through a dual plaquette is equal to the boson density f = p/q. So the kinetic term of the vortices is the same as the Hofstadter problem of electrons moving in a lattice in the presence of f = p/q flux per plaquette. Motivated by this mapping, we study the Hofstadter bands of vortices hopping in the presence of magnetic flux f = p/q per plaquette on the 5 most common bipartite and frustrated lattices namely square, honeycomb, triangular, dice and kagome lattices. We count the total number of bands and determine the number of minima in the lowest band and their locations. We also numerically calculate the bandwidths of the lowest Hofstadter bands in these lattices, which directly measure the mobility of the dual vortices. The less mobile the dual vortices are, the more likely the bosons are in a superfluid state. We find that, except for the kagome lattice at odd q, they all satisfy the exponential decay law W = Ae-cq even at the smallest q. At given q, the bandwidth W decreases in the order: triangle, square and honeycomb lattice. This indicates that the domain of the superfluid state of the original bosons increases in the order of the corresponding direct lattices: honeycome, square and triangular. When q = 2, we find that the lowest Hofstadter band is completely flat for both kagome and dice lattices. There is a gap on the kagome lattice, but no gap on dice lattice. This indicates that the boson ground state at half filling with nearest neighbor hopping on kagome lattice is always a superfluid state. The superfluid state remains stable slightly away from half filling. Our results show that the behaviors of bosons at or near half filling on kagome lattice are quite distinct from those on square, honeycomb and triangular lattices studied previously.

Temperature dependences of the time of electron-electron interactions in two-dimensional heterojunction

NASA Astrophysics Data System (ADS)

Bukhenskyy, K. V.; Dubois, A. B.; Kucheryavyy, S. I.; Mashnina, S. N.; Safoshkin, A. S.; Baukov, A. A.; Shchigorev, E. Yu

2017-12-01

The article discusses the joint solution of the Schrödinger and Poisson equations for two-dimensional semiconductor heterojunction. The application of a triangular potential of well approximation for the calculation of the electron-electron interaction is offered in the paper. The influence of the parameters of the selected approximation was analyzed.

Symmetry-protected gapless Z2 spin liquids

NASA Astrophysics Data System (ADS)

Lu, Yuan-Ming

2018-03-01

Despite rapid progress in understanding gapped topological states, much less is known about gapless topological phases of matter, especially in strongly correlated electrons. In this work, we discuss a large class of robust gapless quantum spin liquids in frustrated magnets made of half-integer spins, which are described by gapless fermionic spinons coupled to dynamical Z2 gauge fields. Requiring U(1 ) spin conservation, time-reversal, and certain space-group symmetries, we show that certain spinon symmetry fractionalization class necessarily leads to a gapless spectrum. These gapless excitations are stable against any perturbations, as long as the required symmetries are preserved. Applying these gapless criteria to spin-1/2 systems on square, triangular, and kagome lattices, we show that all gapped symmetric Z2 spin liquids in Abrikosov-fermion representation can also be realized in Schwinger-boson representation. This leads to 64 gapped Z2 spin liquids on square lattice, and 8 gapped states on both kagome and triangular lattices.

Optimum Laser Beam Characteristics for Achieving Smoother Ablations in Laser Vision Correction.

PubMed

Verma, Shwetabh; Hesser, Juergen; Arba-Mosquera, Samuel

2017-04-01

Controversial opinions exist regarding optimum laser beam characteristics for achieving smoother ablations in laser-based vision correction. The purpose of the study was to outline a rigorous simulation model for simulating shot-by-shot ablation process. The impact of laser beam characteristics like super Gaussian order, truncation radius, spot geometry, spot overlap, and lattice geometry were tested on ablation smoothness. Given the super Gaussian order, the theoretical beam profile was determined following Lambert-Beer model. The intensity beam profile originating from an excimer laser was measured with a beam profiler camera. For both, the measured and theoretical beam profiles, two spot geometries (round and square spots) were considered, and two types of lattices (reticular and triangular) were simulated with varying spot overlaps and ablated material (cornea or polymethylmethacrylate [PMMA]). The roughness in ablation was determined by the root-mean-square per square root of layer depth. Truncating the beam profile increases the roughness in ablation, Gaussian profiles theoretically result in smoother ablations, round spot geometries produce lower roughness in ablation compared to square geometry, triangular lattices theoretically produce lower roughness in ablation compared to the reticular lattice, theoretically modeled beam profiles show lower roughness in ablation compared to the measured beam profile, and the simulated roughness in ablation on PMMA tends to be lower than on human cornea. For given input parameters, proper optimum parameters for minimizing the roughness have been found. Theoretically, the proposed model can be used for achieving smoothness with laser systems used for ablation processes at relatively low cost. This model may improve the quality of results and could be directly applied for improving postoperative surface quality.

The A{sup 2+}Mn{sub 5}(SO{sub 4}){sub 6} family of triangular lattice, ferrimagnetic sulfates

DOE Office of Scientific and Technical Information (OSTI.GOV)

West, D.V., E-mail: barelytone@gmail.co; McQueen, T.M.; Posen, I.D.

2009-06-15

A new family of anhydrous sulfates, A{sup 2+}Mn{sub 5}(SO{sub 4}){sub 6} (A=Pb, Ba, Sr) is reported. The crystal structures of PbMn{sub 5}(SO{sub 4}){sub 6} and SrMn{sub 5}(SO{sub 4}){sub 6} are solved by powder X-ray and neutron diffraction. BaMn{sub 5}(SO{sub 4}){sub 6} is isostructural. PbMn{sub 5}(SO{sub 4}){sub 6} crystallizes with P3-bar symmetry and unit cell parameters of a=14.551(1) A and c=7.535(1) A. The structure has rich features, including dimers of face-sharing MnO{sub 6} octahedra, and two complementary triangular layers of Mn atoms. All compounds undergo a magnetic ordering transition at 10 K, below which, the magnetic susceptibility of the compounds variesmore » systematically with the radius of the non-magnetic cation. Low temperature neutron diffraction shows that the complementary triangular layers result in a ferrimagnet with a net moment corresponding to one high spin Mn{sup 2+} per unit cell, correlating well with the magnetization data. The non-magnetic variant PbMg{sub 5}(SO{sub 4}){sub 6} is also reported. - Graphical abstract: A new family sulfates, A{sup 2+}Mn{sub 5}(SO{sub 4}){sub 6} (A=Pb, Ba, Sr) is reported. Structures are solved by powder neutron diffraction. PbMn{sub 5}(SO{sub 4}){sub 6} is trigonal with lattice parameters of a=14.551(1) A and c=7.535(1) A. The structure has dimers of face-sharing MnO{sub 6} octahedra, and two complementary triangular layers of Mn atoms that result in a ferrimagnet. All compounds magnetically order at 10 K. Low field susceptibility varies systematically with non-magnetic cation radius.« less

Spin-Glass Ground State in a Triangular-Lattice Compound YbZnGaO4

NASA Astrophysics Data System (ADS)

Ma, Zhen; Wang, Jinghui; Dong, Zhao-Yang; Zhang, Jun; Li, Shichao; Zheng, Shu-Han; Yu, Yunjie; Wang, Wei; Che, Liqiang; Ran, Kejing; Bao, Song; Cai, Zhengwei; Čermák, P.; Schneidewind, A.; Yano, S.; Gardner, J. S.; Lu, Xin; Yu, Shun-Li; Liu, Jun-Ming; Li, Shiyan; Li, Jian-Xin; Wen, Jinsheng

2018-02-01

We report on comprehensive results identifying the ground state of a triangular-lattice structured YbZnGaO4 as a spin glass, including no long-range magnetic order, prominent broad excitation continua, and the absence of magnetic thermal conductivity. More crucially, from the ultralow-temperature ac susceptibility measurements, we unambiguously observe frequency-dependent peaks around 0.1 K, indicating the spin-glass ground state. We suggest this conclusion holds also for its sister compound YbMgGaO4 , which is confirmed by the observation of spin freezing at low temperatures. We consider disorder and frustration to be the main driving force for the spin-glass phase.

Quantum gap and spin-wave excitations in the Kitaev model on a triangular lattice

NASA Astrophysics Data System (ADS)

Avella, Adolfo; Di Ciolo, Andrea; Jackeli, George

2018-05-01

We study the effects of quantum fluctuations on the dynamical generation of a gap and on the evolution of the spin-wave spectra of a frustrated magnet on a triangular lattice with bond-dependent Ising couplings, analog of the Kitaev honeycomb model. The quantum fluctuations lift the subextensive degeneracy of the classical ground-state manifold by a quantum order-by-disorder mechanism. Nearest-neighbor chains remain decoupled and the surviving discrete degeneracy of the ground state is protected by a hidden model symmetry. We show how the four-spin interaction, emergent from the fluctuations, generates a spin gap shifting the nodal lines of the linear spin-wave spectrum to finite energies.

Polarization response of RHIC electron lens lattices

DOE PAGES

Ranjbar, V. H.; Méot, F.; Bai, M.; ...

2016-10-10

Depolarization response for a system of two orthogonal snakes at irrational tunes is studied in depth using lattice independent spin integration. Particularly, we consider the effect of overlapping spin resonances in this system, to understand the impact of phase, tune, relative location and threshold strengths of the spin resonances. Furthermore, these results are benchmarked and compared to two dimensional direct tracking results for the RHIC e-lens lattice and the standard lattice. We then consider the effect of longitudinal motion via chromatic scans using direct six dimensional lattice tracking.

Vortex lattices in binary mixtures of repulsive superfluids

NASA Astrophysics Data System (ADS)

Mingarelli, Luca; Keaveny, Eric E.; Barnett, Ryan

2018-04-01

We present an extension of the framework introduced in previous work [L. Mingarelli, E. E. Keaveny, and R. Barnett, J. Phys.: Condens. Matter 28, 285201 (2016), 10.1088/0953-8984/28/28/285201] to treat multicomponent systems, showing that new degrees of freedom are necessary in order to obtain the desired boundary conditions. We then apply this extended framework to the coupled Gross-Pitaevskii equations to investigate the ground states of two-component systems with equal masses, thereby extending previous work in the lowest Landau limit [E. J. Mueller and T.-L. Ho, Phys. Rev. Lett. 88, 180403 (2002), 10.1103/PhysRevLett.88.180403] to arbitrary interactions within Gross-Pitaevskii theory. We show that away from the lowest Landau level limit, the predominant vortex lattice consists of two interlaced triangular lattices. Finally, we derive a linear relation which accurately describes the phase boundaries in the strong interacting regimes.

Phase diagram of the triangular-lattice Potts antiferromagnet

DOE PAGES

Jacobsen, Jesper Lykke; Salas, Jesus; Scullard, Christian R.

2017-07-28

Here, we study the phase diagram of the triangular-lattice Q-state Potts model in the realmore » $(Q, v)$ -plane, where $$v={\\rm e}^J-1$$ is the temperature variable. Our first goal is to provide an obviously missing feature of this diagram: the position of the antiferromagnetic critical curve. This curve turns out to possess a bifurcation point with two branches emerging from it, entailing important consequences for the global phase diagram. We have obtained accurate numerical estimates for the position of this curve by combining the transfer-matrix approach for strip graphs with toroidal boundary conditions and the recent method of critical polynomials. The second goal of this work is to study the corresponding $$A_{p-1}$$ RSOS model on the torus, for integer $$p=4, 5, \\ldots, 8$$ . We clarify its relation to the corresponding Potts model, in particular concerning the role of boundary conditions. For certain values of p, we identify several new critical points and regimes for the RSOS model and we initiate the study of the flows between the corresponding field theories.« less

Magnetic phase diagram and multiferroicity of Ba 3 MnNb 2 O 9 : A spin - 5 2 triangular lattice antiferromagnet with weak easy-axis anisotropy

DOE PAGES

Lee, M.; Choi, E. S.; Huang, X.; ...

2014-12-01

Here we have performed magnetic, electric, thermal and neutron powder diffraction (NPD) experiments as well as density functional theory (DFT) calculations on Ba 3MnNb 2 O 9. All results suggest that Ba 3MnNb 2 O 9 is a spin-5/2 triangular lattice antiferromagnet (TLAF) with weak easy-axis anisotropy. At zero field, we observed a narrow two-step transition at T N1 = 3.4 K and T N2 = 3.0 K. The neutron diffraction measurement and the DFT calculation indicate a 120 spin structure in ab plane with out-of-plane canting at low temperatures. With increasing magnetic field, the 120 spin structure evolves intomore » up-up-down (uud) and oblique phases showing successive magnetic phase transitions, which fits well to the theoretical prediction for the 2D Heisenberg TLAF with classical spins. Ultimately, multiferroicity is observed when the spins are not collinear but suppressed in the uud and oblique phases.« less

Spontaneous supersymmetry breaking in two dimensional lattice super QCD

DOE PAGES

Catterall, Simon; Veernala, Aarti

2015-10-02

We report on a non-perturbative study of two dimensional N=(2,2) super QCD. Our lattice formulation retains a single exact supersymmetry at non-zero lattice spacing, and contains N f fermions in the fundamental representation of a U(N c) gauge group. The lattice action we employ contains an additional Fayet-Iliopoulos term which is also invariant under the exact lattice supersymmetry. This work constitutes the first numerical study of this theory which serves as a toy model for understanding some of the issues that are expected to arise in four dimensional super QCD. As a result, we present evidence that the exact supersymmetrymore » breaks spontaneously when N f < N c in agreement with theoretical expectations.« less

Tiling a figure using a height in a tree

DOE Office of Scientific and Technical Information (OSTI.GOV)

Remila, E.

1996-12-31

We first give a new presentation of an algorithm from Thurston of tiling with lozenges formed from two cells of the triangular lattice A. Secondly we extend the method to get a linear algorithm of tiling with leaning dominoes (parallelograms formed from four cells of {Lambda}) and triangles (formed from four cells of {Lambda}). Thirdly, we produce a quadratic algorithm of tiling with leaning dominoes.

Computing Trimmed, Mean-Camber Surfaces At Minimum Drag

NASA Technical Reports Server (NTRS)

Lamar, John E.; Hodges, William T.

1995-01-01

VLMD computer program determines subsonic mean-camber surfaces of trimmed noncoplanar planforms with minimum vortex drag at specified lift coefficient. Up to two planforms designed together. Method used that of subsonic vortex lattice method of chord loading specification, ranging from rectangular to triangular, left specified by user. Program versatile and applied to isolated wings, wing/canard configurations, tandem wing, and wing/-winglet configuration. Written in FORTRAN.

Investigation of a Structural Phase Transition and Magnetic Structure of Na 2BaFe(VO 4) 2: A Triangular Magnetic Lattice with a Ferromagnetic Ground State

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sanjeewa, Liurukara D.; Garlea, Vasile O.; McGuire, Michael A.

The structural and magnetic properties of a glaserite-type Na 2BaFe(VO 4) 2 compound, featuring a triangular magnetic lattice of Fe 2+ (S = 2), are reported. Temperature dependent X-ray single crystal studies indicate that at room temperature the system adopts a trigonal Pmore » $$\\bar{3}$$ m1 structure and undergoes a structural phase transition to a C2/c monoclinic phase slightly below room temperature (T s = 288 K). This structural transition involves a tilting of Fe–O–V bond angles and strongly influences the magnetic correlation within the Fe triangular lattice. The magnetic susceptibility measurements reveal a ferromagnetic transition near 7 K. Single crystal neutron diffraction confirms the structural distortion and the ferromagnetic spin ordering in Na 2BaFe(VO 4) 2. The magnetic structure of the ordered state is modeled in the magnetic space group C2'/c' that implies a ferromagnetic order of the a and c moment components and antiferromagnetic arrangement for the b components. Altogether, the Fe magnetic moments form ferromagnetic layers that are stacked along the c-axis, where the spins point along one of the (111) facets of the FeO 6 octahedron.« less

Absence of Long-Range Order in a Triangular Spin System with Dipolar Interactions

NASA Astrophysics Data System (ADS)

Keleş, Ahmet; Zhao, Erhai

2018-05-01

The antiferromagnetic Heisenberg model on the triangular lattice is perhaps the best known example of frustrated magnets, but it orders at low temperatures. Recent density matrix renormalization group (DMRG) calculations find that the next nearest neighbor interaction J2 enhances the frustration, and it leads to a spin liquid for J2/J1∈(0.08 ,0.15 ). In addition, a DMRG study of a dipolar Heisenberg model with longer range interactions gives evidence for a spin liquid at a small dipole tilting angle θ ∈[0 ,1 0 ° ). In both cases, the putative spin liquid region appears to be small. Here, we show that for the triangular lattice dipolar Heisenberg model, a robust quantum paramagnetic phase exists in a surprisingly wide region, θ ∈[0 ,5 4 ° ) , for dipoles tilted along the lattice diagonal direction. We obtain the phase diagram of the model by functional renormalization group (RG), which treats all magnetic instabilities on equal footing. The quantum paramagnetic phase is characterized by a smooth continuous flow of vertex functions and spin susceptibility down to the lowest RG scale, in contrast to the apparent breakdown of RG flow in phases with stripe or spiral order. Our finding points to a promising direction to search for quantum spin liquids in ultracold dipolar molecules.

Investigation of a Structural Phase Transition and Magnetic Structure of Na 2BaFe(VO 4) 2: A Triangular Magnetic Lattice with a Ferromagnetic Ground State

DOE PAGES

Sanjeewa, Liurukara D.; Garlea, Vasile O.; McGuire, Michael A.; ...

2017-12-07

The structural and magnetic properties of a glaserite-type Na 2BaFe(VO 4) 2 compound, featuring a triangular magnetic lattice of Fe 2+ (S = 2), are reported. Temperature dependent X-ray single crystal studies indicate that at room temperature the system adopts a trigonal Pmore » $$\\bar{3}$$ m1 structure and undergoes a structural phase transition to a C2/c monoclinic phase slightly below room temperature (T s = 288 K). This structural transition involves a tilting of Fe–O–V bond angles and strongly influences the magnetic correlation within the Fe triangular lattice. The magnetic susceptibility measurements reveal a ferromagnetic transition near 7 K. Single crystal neutron diffraction confirms the structural distortion and the ferromagnetic spin ordering in Na 2BaFe(VO 4) 2. The magnetic structure of the ordered state is modeled in the magnetic space group C2'/c' that implies a ferromagnetic order of the a and c moment components and antiferromagnetic arrangement for the b components. Altogether, the Fe magnetic moments form ferromagnetic layers that are stacked along the c-axis, where the spins point along one of the (111) facets of the FeO 6 octahedron.« less

Classical simulation of infinite-size quantum lattice systems in two spatial dimensions.

PubMed

Jordan, J; Orús, R; Vidal, G; Verstraete, F; Cirac, J I

2008-12-19

We present an algorithm to simulate two-dimensional quantum lattice systems in the thermodynamic limit. Our approach builds on the projected entangled-pair state algorithm for finite lattice systems [F. Verstraete and J. I. Cirac, arxiv:cond-mat/0407066] and the infinite time-evolving block decimation algorithm for infinite one-dimensional lattice systems [G. Vidal, Phys. Rev. Lett. 98, 070201 (2007)10.1103/PhysRevLett.98.070201]. The present algorithm allows for the computation of the ground state and the simulation of time evolution in infinite two-dimensional systems that are invariant under translations. We demonstrate its performance by obtaining the ground state of the quantum Ising model and analyzing its second order quantum phase transition.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ranjbar, V. H.; Méot, F.; Bai, M.

Depolarization response for a system of two orthogonal snakes at irrational tunes is studied in depth using lattice independent spin integration. Particularly, we consider the effect of overlapping spin resonances in this system, to understand the impact of phase, tune, relative location and threshold strengths of the spin resonances. Furthermore, these results are benchmarked and compared to two dimensional direct tracking results for the RHIC e-lens lattice and the standard lattice. We then consider the effect of longitudinal motion via chromatic scans using direct six dimensional lattice tracking.

Frustrated Magnetism in Low-Dimensional Lattices

NASA Astrophysics Data System (ADS)

Tovar, Mayra

2011-12-01

In this dissertation we present the results of a theoretical investigation of spin models on two-dimensional and quasi one-dimensional lattices, all unified under the concept of quantum frustrated antiferromagnetism, and all discussing various aspects of the antiferromagnetic Heisenberg model on the kagome lattice. In the Introduction (Chapter 1), we discuss at some length such concepts as frustration and superexchange, among others, which are of common relevance in the rest of the chapters. In Chapter 2, we study the effect of Dzyaloshinskii-Moriya (DM) interactions on the zero-temperature magnetic susceptibility of systems whose low energy can be described by short-range valence bond states. Our work shows that this treatment is consistent with the experimentally observed non-vanishing susceptibility---in the specified temperature limit---of the spin-1/2 kagome antiferromagnetic compound ZnCu3(OH)6Cl2, also known as herbertsmithite. Although the objective of this work is explaining the aforementioned characteristic of the experimental system, our methods are more general and we apply them to the checkerboard and Shastry-Sutherland lattices as well. In Chapter 3, we discuss our findings in the study of ghost-mediated domain wall interactions in the diamondback ladder. These domain walls are the the spin excitations---the kinks and the antikinks---separating the ground states along one chain of the ladder. While as individual entities an antikink is energy costly and a kink energy free, our study finds that both interact via the ghosts that they produce in the opposite side of the ladder from where they are located. Through the study of these ghosts, we find that domain walls proliferate in the system above a critical value of the system's coupling constants. It is this proliferation that makes their treatment as free, non-interacting particles impossible, so we study here their interactions both quantitatively and qualitatively, in a region where the latter are yet not very strong, namely below the critical point. Based on the calculated two-body interaction potential, domain walls interact attractively (repulsively) when separated at even (odd) distances, with a strength that decays as 1/sp, where s is their separation and p<1. We also consider higher-order interactions. In the last chapter, Chapter 4, we present our study of the spin-1 kagome Heisenberg antiferromagnet. Our approach is to first consider an SU(2)-symmetric parent Hamiltonian with known ground states on the S=1 kagome lattice, in which nearest-neighbor Heisenberg interactions are already present. We then enhance these interactions by an additional Heisenberg term added perturbatively in order to move the system closer to a pure Heisenberg antiferromagnet. The results of this enhancement is obtaining a description of the system in terms of an effective Hamiltonian, namely a transverse field Ising AF on the triangular lattice. Based on the particular values of this effective Hamiltonian, our system is found to be in the order-by-disorder phase.

Critical behavior of a chiral superfluid in a bipartite square lattice

NASA Astrophysics Data System (ADS)

Okamoto, Junichi; Huang, Wen-Min; Höppner, Robert; Mathey, Ludwig

2018-01-01

We study the critical behavior of Bose-Einstein condensation in the second band of a bipartite optical square lattice in a renormalization group framework at one-loop order. Within our field theoretical representation of the system, we approximate the system as a two-component Bose gas in three dimensions. We demonstrate that the system is in a different universality class than the previously studied condensation in a frustrated triangular lattice due to an additional Umklapp scattering term, which stabilizes the chiral superfluid order at low temperatures. We derive the renormalization group flow of the system and show that this order persists in the low energy limit. Furthermore, the renormalization flow suggests that the phase transition from the thermal phase to the chiral superfluid state is first order.

Merging of the Dirac points in electronic artificial graphene

NASA Astrophysics Data System (ADS)

Feilhauer, J.; Apel, W.; Schweitzer, L.

2015-12-01

Theory predicts that graphene under uniaxial compressive strain in an armchair direction should undergo a topological phase transition from a semimetal into an insulator. Due to the change of the hopping integrals under compression, both Dirac points shift away from the corners of the Brillouin zone towards each other. For sufficiently large strain, the Dirac points merge and an energy gap appears. However, such a topological phase transition has not yet been observed in normal graphene (due to its large stiffness) neither in any other electronic system. We show numerically and analytically that such a merging of the Dirac points can be observed in electronic artificial graphene created from a two-dimensional electron gas by application of a triangular lattice of repulsive antidots. Here, the effect of strain is modeled by tuning the distance between the repulsive potentials along the armchair direction. Our results show that the merging of the Dirac points should be observable in a recent experiment with molecular graphene.

Non-classical photon correlation in a two-dimensional photonic lattice.

PubMed

Gao, Jun; Qiao, Lu-Feng; Lin, Xiao-Feng; Jiao, Zhi-Qiang; Feng, Zhen; Zhou, Zheng; Gao, Zhen-Wei; Xu, Xiao-Yun; Chen, Yuan; Tang, Hao; Jin, Xian-Min

2016-06-13

Quantum interference and quantum correlation, as two main features of quantum optics, play an essential role in quantum information applications, such as multi-particle quantum walk and boson sampling. While many experimental demonstrations have been done in one-dimensional waveguide arrays, it remains unexplored in higher dimensions due to tight requirement of manipulating and detecting photons in large-scale. Here, we experimentally observe non-classical correlation of two identical photons in a fully coupled two-dimensional structure, i.e. photonic lattice manufactured by three-dimensional femtosecond laser writing. Photon interference consists of 36 Hong-Ou-Mandel interference and 9 bunching. The overlap between measured and simulated distribution is up to 0.890 ± 0.001. Clear photon correlation is observed in the two-dimensional photonic lattice. Combining with controllably engineered disorder, our results open new perspectives towards large-scale implementation of quantum simulation on integrated photonic chips.

Design and fabrication of one-dimensional and two- dimensional photonic bandgap devices

NASA Astrophysics Data System (ADS)

Lim, Kuo-Yi

1999-10-01

One-dimensional and two-dimensional photonic bandgap devices have been designed and fabricated using III-V compound semiconductors. The one-dimensional photonic bandgap devices consist of monorail and air-bridge waveguide microcavities, while the two-dimensional photonic bandgap devices consist of light-emitting devices with enhanced extraction efficiency. Fabrication techniques such as gas source molecular beam epitaxy, direct-write electron-beam lithography, reactive ion etching and thermal oxidation of AlxGa1- xAs have been employed. The III-V thermal oxide, in particular, is used as an index confinement material, as a sacrificial material for micromechanical fabrication of the air-bridge microcavity, and in the realization of a wide-bandwidth distributed Bragg reflector. The one-dimensional photonic bandgap waveguide microcavities have been designed to operate in the wavelength regimes of 4.5 m m and 1.55 m m. The devices designed to operate in the 1.55 m m wavelength regime have been optically characterized. The transmission spectra exhibit resonances at around 1.55 m m and cavity quality factors (Q's) ranging from 136 to 334. The resonant modal volume is calculated to be about 0.056 m m3. Tunability in the resonance wavelengths has also been demonstrated by changing the size of the defect in the one-dimensional photonic crystal. The two-dimensional photonic bandgap light-emitting device consists of a In0.51Ga0.49P/In0.2Ga0.8As/In 0.51Ga0.49P quantum well emitting at 980nm with a triangular photonic lattice of holes in the top cladding layer of the quantum well. The photonic crystal prohibits the propagation of guided modes in the semiconductor, thus enhancing the extraction of light vertical to the light-emitting device. A wide-bandwidth GaAs/AlxOy distributed Bragg reflector mirror under the quantum well structure further enhances the extraction of light from the devices. The extraction efficiency of the two-dimensional photonic bandgap light-emitting device is expected to be at least 5 times that of a device without the two-dimensional photonic crystal. A photoluminescence measurement setup has been modified to optically characterize these devices. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)

SFM-FDTD analysis of triangular-lattice AAA structure: Parametric study of the TEM mode

NASA Astrophysics Data System (ADS)

Hamidi, M.; Chemrouk, C.; Belkhir, A.; Kebci, Z.; Ndao, A.; Lamrous, O.; Baida, F. I.

2014-05-01

This theoretical work reports a parametric study of enhanced transmission through annular aperture array (AAA) structure arranged in a triangular lattice. The effect of the incidence angle in addition to the inner and outer radii values on the evolution of the transmission spectra is carried out. To this end, a 3D Finite-Difference Time-Domain code based on the Split Field Method (SFM) is used to calculate the spectral response of the structure for any angle of incidence. In order to work through an orthogonal unit cell which presents the advantage to reduce time and space of computation, special periodic boundary conditions are implemented. This study provides a new modeling of AAA structures useful for producing tunable ultra-compact devices.

Partially Disordered Phase in Frustrated Triangular Lattice Antiferromagnet CuFeO 2

NASA Astrophysics Data System (ADS)

Mitsuda, Setsuo; Kasahara, Noriaki; Uno, Takahiro; Mase, Motoshi

1998-12-01

We reinvestigated successive magnetic phase transitions (T N1˜14.0 K, T N2˜10.5 K) in a frustrated triangular lattice antiferromagnet (TLA) CuFeO2 by neutron diffraction measurements using single crystals. The magnetic structure of the intermediate-temperature phase between T N1 and T N2 is found to be a quasi-long range ordered sinusoidally amplitude-modulated structure with a temperature dependent propagation wave vector (q q 0). These features of successive phase transitions are well explained by reinvestigated Monte-Carlo simulation of a 2D Ising TLA with competing exchange interactions up to 3rd neighbors, in spite of the Heisenberg spin character of orbital singlet Fe3+ magnetic ions.

Verification of Three Dimensional Triangular Prismatic Discrete Ordinates Transport Code ENSEMBLE-TRIZ by Comparison with Monte Carlo Code GMVP

NASA Astrophysics Data System (ADS)

Homma, Yuto; Moriwaki, Hiroyuki; Ohki, Shigeo; Ikeda, Kazumi

2014-06-01

This paper deals with verification of three dimensional triangular prismatic discrete ordinates transport calculation code ENSEMBLE-TRIZ by comparison with multi-group Monte Carlo calculation code GMVP in a large fast breeder reactor. The reactor is a 750 MWe electric power sodium cooled reactor. Nuclear characteristics are calculated at beginning of cycle of an initial core and at beginning and end of cycle of equilibrium core. According to the calculations, the differences between the two methodologies are smaller than 0.0002 Δk in the multi-plication factor, relatively about 1% in the control rod reactivity, and 1% in the sodium void reactivity.

Efficient generation of discontinuity-preserving adaptive triangulations from range images.

PubMed

Garcia, Miguel Angel; Sappa, Angel Domingo

2004-10-01

This paper presents an efficient technique for generating adaptive triangular meshes from range images. The algorithm consists of two stages. First, a user-defined number of points is adaptively sampled from the given range image. Those points are chosen by taking into account the surface shapes represented in the range image in such a way that points tend to group in areas of high curvature and to disperse in low-variation regions. This selection process is done through a noniterative, inherently parallel algorithm in order to gain efficiency. Once the image has been subsampled, the second stage applies a two and one half-dimensional Delaunay triangulation to obtain an initial triangular mesh. To favor the preservation of surface and orientation discontinuities (jump and crease edges) present in the original range image, the aforementioned triangular mesh is iteratively modified by applying an efficient edge flipping technique. Results with real range images show accurate triangular approximations of the given range images with low processing times.

Mechanics of evolving thin film structures

NASA Astrophysics Data System (ADS)

Liang, Jim

In the Stranski-Krastanov system, the lattice mismatch between the film and the substrate causes the film to break into islands. During annealing, both the surface energy and the elastic energy drive the islands to coarsen. Motivated by several related studies, we suggest that stable islands should form when a stiff ceiling is placed at a small gap above the film. We show that the role of elasticity is reversed: with the ceiling, the total elastic energy stored in the system increases as the islands coarsen laterally. Consequently, the islands select an equilibrium size to minimize the combined elastic energy and surface energy. In lithographically-induced self-assembly, when a two-phase fluid confined between parallel substrates is subjected to an electric field, one phase can self-assemble into a triangular lattice of islands in another phase. We describe a theory of the stability of the island lattice. The islands select the equilibrium diameter to minimize the combined interface energy and electrostatic energy. Furthermore, we study compressed SiGe thin film islands fabricated on a glass layer, which itself lies on a silicon wafer. Upon annealing, the glass flows, and the islands relax. A small island relaxes by in-plane expansion. A large island, however, wrinkles at the center before the in-plane relaxation arrives. The wrinkles may cause significant tensile stress in the island, leading to fracture. We model the island by the von Karman plate theory and the glass layer by the Reynolds lubrication theory. Numerical simulations evolve the in-plane expansion and the wrinkles simultaneously. We determine the critical island size, below which in-plane expansion prevails over wrinkling. Finally, in devices that integrate dissimilar materials in small dimensions, crack extension in one material often accompanies inelastic deformation in another. We analyze a channel crack advancing in an elastic film under tension, while an underlayer creeps. We use a two-dimensional shear lag model to approximate the three-dimensional fracture process. Based on the computational results, we propose new experiments to measure fracture toughness and creep laws in small structures. Similarly, we study delayed crack initiation, steady crack growth, and transient crack growth when the underlayer is viscoelastic.

Properties of plane discrete Poisson-Voronoi tessellations on triangular tiling formed by the Kolmogorov-Johnson-Mehl-Avrami growth of triangular islands

NASA Astrophysics Data System (ADS)

Korobov, A.

2011-08-01

Discrete uniform Poisson-Voronoi tessellations of two-dimensional triangular tilings resulting from the Kolmogorov-Johnson-Mehl-Avrami (KJMA) growth of triangular islands have been studied. This shape of tiles and islands, rarely considered in the field of random tessellations, is prompted by the birth-growth process of Ir(210) faceting. The growth mode determines a triangular metric different from the Euclidean metric. Kinetic characteristics of tessellations appear to be metric sensitive, in contrast to area distributions. The latter have been studied for the variant of nuclei growth to the first impingement in addition to the conventional case of complete growth. Kiang conjecture works in both cases. The averaged number of neighbors is six for all studied densities of random tessellations, but neighbors appear to be mainly different in triangular and Euclidean metrics. Also, the applicability of the obtained results for simulating birth-growth processes when the 2D nucleation and impingements are combined with the 3D growth in the particular case of similar shape and the same orientation of growing nuclei is briefly discussed.

Properties of plane discrete Poisson-Voronoi tessellations on triangular tiling formed by the Kolmogorov-Johnson-Mehl-Avrami growth of triangular islands.

PubMed

Korobov, A

2011-08-01

Discrete uniform Poisson-Voronoi tessellations of two-dimensional triangular tilings resulting from the Kolmogorov-Johnson-Mehl-Avrami (KJMA) growth of triangular islands have been studied. This shape of tiles and islands, rarely considered in the field of random tessellations, is prompted by the birth-growth process of Ir(210) faceting. The growth mode determines a triangular metric different from the Euclidean metric. Kinetic characteristics of tessellations appear to be metric sensitive, in contrast to area distributions. The latter have been studied for the variant of nuclei growth to the first impingement in addition to the conventional case of complete growth. Kiang conjecture works in both cases. The averaged number of neighbors is six for all studied densities of random tessellations, but neighbors appear to be mainly different in triangular and Euclidean metrics. Also, the applicability of the obtained results for simulating birth-growth processes when the 2D nucleation and impingements are combined with the 3D growth in the particular case of similar shape and the same orientation of growing nuclei is briefly discussed.

Strongly Interacting Fermi Gases In Two Dimensions

DTIC Science & Technology

2012-01-03

Correlated Quantum Fluids: From Ultracold Quantum Gases to QCD Plasmas. Figure 2 Spin Transport in Spin-Imbalanced, strongly interacting...atoms becomes confined to a stack of two-dimensional layers formed by a one-dimensional optical lattice . Decreasing the dimensionality leads to the...opening of a gap in radiofrequency spectra, even on the BCS-side of a Feshbach resonance. With increasing lattice depth, the measured binding energy

Domain decomposition methods in aerodynamics

NASA Technical Reports Server (NTRS)

Venkatakrishnan, V.; Saltz, Joel

1990-01-01

Compressible Euler equations are solved for two-dimensional problems by a preconditioned conjugate gradient-like technique. An approximate Riemann solver is used to compute the numerical fluxes to second order accuracy in space. Two ways to achieve parallelism are tested, one which makes use of parallelism inherent in triangular solves and the other which employs domain decomposition techniques. The vectorization/parallelism in triangular solves is realized by the use of a recording technique called wavefront ordering. This process involves the interpretation of the triangular matrix as a directed graph and the analysis of the data dependencies. It is noted that the factorization can also be done in parallel with the wave front ordering. The performances of two ways of partitioning the domain, strips and slabs, are compared. Results on Cray YMP are reported for an inviscid transonic test case. The performances of linear algebra kernels are also reported.

Tricriticality of the Blume-Emery-Griffiths model in thin films of stacked triangular lattices

NASA Astrophysics Data System (ADS)

El Hog, Sahbi; Diep, H. T.

2016-03-01

We study in this paper the Blume-Emery-Griffiths model in a thin film of stacked triangular lattices. The model is described by three parameters: bilinear exchange interaction between spins J, quadratic exchange interaction K and single-ion anisotropy D. The spin Si at the lattice site i takes three values (-1, 0, +1). This model can describe the mixing phase of He-4 (Si = +1,-1) and He-3 (Si = 0) at low temperatures. Using Monte Carlo simulations, we show that there exists a critical value of D below (above) which the transition is of second-(first-)order. In general, the temperature dependence of the concentrations of He-3 is different from layer by layer. At a finite temperature in the superfluid phase, the film surface shows a deficit of He-4 with respect to interior layers. However, effects of surface interaction parameters can reverse this situation. Effects of the film thickness on physical properties will be also shown as functions of temperature.

Pressure effects on the magnetoelectric properties of a multiferroic triangular-lattice antiferromagnet CuCrO2

NASA Astrophysics Data System (ADS)

Aoyama, Takuya; Miyake, Atsushi; Kagayama, Tomoko; Shimizu, Katsuya; Kimura, Tsuyoshi

2013-03-01

Effects of high pressure exceeding 10 GPa on spin-driven ferroelectricity were investigated for a multiferroic, triangular-lattice antiferromagnet (TLA), CuCrO2. For this purpose, we developed a system which enables us to measure ferroelectric polarization under a pressure of 10 GPa by using a diamond anvil cell. We found that the magnetic transition temperature accompanying the ferroelectric one in CuCrO2 was remarkably enhanced by applying pressure. The result is simply explained by considering the pressure-induced enhancement of inter- and/or intralayer magnetic interaction due to the compression of the lattice. In addition, the coercive electric field for the polarization reversal was also increased with increasing pressure, while the amplitude of the ferroelectric polarization was steeply suppressed at around 8 GPa. A possible origin of the observed pressure effects on the ferroelectric property in the multiferroic TLA is discussed in terms of a ferroelectric-antiferroelectric transition and structural domain rearrangement by uniaxial stress.

Magnetic excitations in the spin-1/2 triangular-lattice antiferromagnet Cs 2CuBr 4

DOE PAGES

Zvyagin, S. A.; Ozerov, M.; Kamenskyi, D.; ...

2015-11-27

We present on high- field electron spin resonance (ESR) studies of magnetic excitations in the spin- 1/2 triangular-lattice antiferromagnet Cs 2CuBr 4. Frequency- field diagrams of ESR excitations are measured for different orientations of magnetic fields up to 25 T. We show that the substantial zero- field energy gap, Δ ≈ 9.5 K, observed in the low-temperature excitation spectrum of Cs 2CuBr 4 [Zvyagin et al:, Phys. Rev. Lett. 112, 077206 (2014)], is present well above T N. Noticeably, the transition into the long-range magnetically ordered phase does not significantly affect the size of the gap, suggesting that even belowmore » T N the high-energy spin dynamics in Cs 2CuBr 4 is determined by short-range-order spin correlations. The experimental data are compared with results of model spin-wave-theory calculations for spin-1/2 triangle-lattice antiferromagnet.« less

Chimera states in Gaussian coupled map lattices

NASA Astrophysics Data System (ADS)

Li, Xiao-Wen; Bi, Ran; Sun, Yue-Xiang; Zhang, Shuo; Song, Qian-Qian

2018-04-01

We study chimera states in one-dimensional and two-dimensional Gaussian coupled map lattices through simulations and experiments. Similar to the case of global coupling oscillators, individual lattices can be regarded as being controlled by a common mean field. A space-dependent order parameter is derived from a self-consistency condition in order to represent the collective state.

Triangular node for Transmission-Line Modeling (TLM) applied to bio-heat transfer.

PubMed

Milan, Hugo F M; Gebremedhin, Kifle G

2016-12-01

Transmission-Line Modeling (TLM) is a numerical method used to solve complex and time-domain bio-heat transfer problems. In TLM, rectangles are used to discretize two-dimensional problems. The drawback in using rectangular shapes is that instead of refining only the domain of interest, a large additional domain will also be refined in the x and y axes, which results in increased computational time and memory space. In this paper, we developed a triangular node for TLM applied to bio-heat transfer that does not have the drawback associated with the rectangular nodes. The model includes heat source, blood perfusion (advection), boundary conditions and initial conditions. The boundary conditions could be adiabatic, temperature, heat flux, or convection. A matrix equation for TLM, which simplifies the solution of time-domain problems or solves steady-state problems, was also developed. The predicted results were compared against results obtained from the solution of a simplified two-dimensional problem, and they agreed within 1% for a mesh length of triangular faces of 59µm±9µm (mean±standard deviation) and a time step of 1ms. Copyright © 2016 Elsevier Ltd. All rights reserved.

Muon spin rotation study of spin dimers on a triangular lattice in Ba3 MRu2 O9

NASA Astrophysics Data System (ADS)

Ziat, Djamel; Verrier, Aimé; Quilliam, Jeffrey; Aczel, Adam; Sinclair, Ryan; Chen, Qiang; Zhou, Haidong

The family of hexagonal perovskites, Ba3 MA2 O9 has recently been proven to be fertile ground for the discovery of new, exotic magnetic phases, including several quantum spin liquid candidates. The 6H-perovskites can also accommodate spin dimers on a triangular lattice, as in the ruthenate materials Ba3MRu2O9. We will present measurements on materials containing M3 + (M = Y, La, Lu, In), which give rise to mixed valence Ru4.5 + ions wherein the orbital and charge degrees of freedom must also be considered. In particular, muon spin rotation (µSR) experiments, have allowed us to probe the nature of the magnetically ordered ground state of these materials at low temperatures.

Chiral d -wave superconductivity in a triangular surface lattice mediated by long-range interaction

NASA Astrophysics Data System (ADS)

Cao, Xiaodong; Ayral, Thomas; Zhong, Zhicheng; Parcollet, Olivier; Manske, Dirk; Hansmann, Philipp

2018-04-01

Adatom systems on the Si(111) surface have recently attracted an increasing attention as strongly correlated systems with a rich phase diagram. We study these materials by a single band model on the triangular lattice, including 1 /r long-range interaction. Employing the recently proposed TRILEX method, we find an unconventional superconducting phase of chiral d -wave symmetry in hole-doped systems. Contrary to usual scenarios where charge and spin fluctuations are seen to compete, here the superconductivity is driven simultaneously by both charge and spin fluctuations and crucially relies on the presence of the long-range tail of the interaction. We provide an analysis of the relevant collective bosonic modes and predict how a cumulative charge and spin paring mechanism leads to superconductivity in doped silicon adatom materials.

Critical Anisotropies of a Geometrically-Frustrated Triangular-Lattice

DOE Office of Scientific and Technical Information (OSTI.GOV)

Swanson, Mason R; Haraldsen, Jason T; Fishman, Randy Scott

2009-01-01

This work examines the critical anisotropy required for the local stability of the collinear ground states of a geometrically-frustrated triangular-lattice antiferromagnet (TLA). Using a Holstein-Primakoff expansion, we calculate the spin-wave frequencies for the 1, 2, 3, 4, and 8-sublattice (SL) ground states of a TLA with up to third neighbor interactions. Local stability requires that all spin-wave frequencies are real and positive. The 2, 4, and 8-SL phases break up into several regions where the critical anisotropy is a different function of the exchange parameters. We find that the critical anisotropy is a continuous function everywhere except across the 2-SL/3-SLmore » and 3-SL/4-SL phase boundaries, where the 3-SL phase has the higher critical anisotropy.« less

Impact of ultrasonic assisted triangular lattice like arranged dispersion of nanoparticles on physical and mechanical properties of epoxy-TiO2 nanocomposites.

PubMed

Goyat, M S; Ghosh, P K

2018-04-01

Emerging ex-situ technique, ultrasonic dual mixing (UDM) offers unique and hitherto unapproachable opportunities to alter the physical and mechanical properties of polymer nanocomposites. In this study, triangular lattice-like arranged dispersion of TiO 2 nanoparticles (average size ∼ 48 nm) in the epoxy polymer has been attained via concurrent use of a probe ultra-sonicator and 4 blades pitched impeller which collectively named as UDM technique. The UDM processing of neat epoxy reveals the generation of triangular lattice-like arranged nanocavities with nanoscale inter-cavity spacing. The UDM processing of epoxy-TiO 2 nanocomposites reveals two unique features such as partial and complete entrapping of the nanoparticles by the nanocavities leading the arranged dispersion of particles in the epoxy matrix. Pristine TiO 2 nanoparticles were dispersed in the epoxy polymer at loading fractions of up to 20% by weight. The results display that the arranged dispersion of nanoparticles is very effective at enhancing the glass transition temperature (T g ) and tensile properties of the epoxy at loading fractions of 10 wt%. We quantify a direct relationship among three important parameters such as nanoparticle content, cluster size, and inter-particle spacing. Our results offer a novel understanding of these parameters on the T g and tensile properties of the epoxy nanocomposites. The tensile fracture surfaces revealed several toughening mechanisms such as particle pull-out, plastic void growth, crack deflection, crack bridging and plastic deformation. We show that a strong nanoparticle-matrix interface led to the enhanced mechanical properties due to leading toughening mechanisms such as crack deflection, plastic deformation and particle pull-out. We showed that the UDM has an inordinate prospective to alter the dispersion state of nanoparticles in viscous polymer matrices. Copyright © 2017 Elsevier B.V. All rights reserved.

The nature of turbulence in a triangular lattice gas automaton

NASA Astrophysics Data System (ADS)

Duong-Van, Minh; Feit, M. D.; Keller, P.; Pound, M.

1986-12-01

Power spectra calculated from the coarse-graining of a simple lattice gas automaton, and those of time averaging other stochastic times series that we have investigated, have exponents in the range -1.6 to -2, consistent with observation of fully developed turbulence. This power spectrum is a natural consequence of coarse-graining; the exponent -2 represents the continuum limit.

Possible extinction of Berezinskii-Kosterlitz-Thouless transition by diagonal interactions in the checkerboard lattice

NASA Astrophysics Data System (ADS)

Lopes, R. J. C.; Moura, A. R.

2018-06-01

We study the thermodynamics of the classical anisotropic antiferromagnetic Heisenberg model in a checkerboard lattice. The checkerboard lattice is distinguished from the antiferromagnetic square lattice (with coupling constant J) by the presence of a diagonal crossing (coupling constant J‧) in half of the sites. This lattice model is the direct analog of the three-dimensional pyrochlore lattice on a two-dimensional surface. Besides, we considered a single-ion anisotropy D that breaks the O (3) symmetry and contributes to planar spin fields. Since the model is two-dimensional endowed with an O (2) symmetry, a Berezinskii-Kosterlitz-Thouless (BKT) transition is expected to take place. We also investigated the BKT temperature as a function of the coupling constants J‧ and D. The problem is developed through a continuous representation given by the O (3) Nonlinear Sigma Model (NLSM). Computer simulations were also carried out, and the results were in accordance with the analytical model.

Exciton Polaritons in a Two-Dimensional Lieb Lattice with Spin-Orbit Coupling

NASA Astrophysics Data System (ADS)

Whittaker, C. E.; Cancellieri, E.; Walker, P. M.; Gulevich, D. R.; Schomerus, H.; Vaitiekus, D.; Royall, B.; Whittaker, D. M.; Clarke, E.; Iorsh, I. V.; Shelykh, I. A.; Skolnick, M. S.; Krizhanovskii, D. N.

2018-03-01

We study exciton polaritons in a two-dimensional Lieb lattice of micropillars. The energy spectrum of the system features two flat bands formed from S and Px ,y photonic orbitals, into which we trigger bosonic condensation under high power excitation. The symmetry of the orbital wave functions combined with photonic spin-orbit coupling gives rise to emission patterns with pseudospin texture in the flat band condensates. Our Letter shows the potential of polariton lattices for emulating flat band Hamiltonians with spin-orbit coupling, orbital degrees of freedom, and interactions.

Exciton Polaritons in a Two-Dimensional Lieb Lattice with Spin-Orbit Coupling.

PubMed

Whittaker, C E; Cancellieri, E; Walker, P M; Gulevich, D R; Schomerus, H; Vaitiekus, D; Royall, B; Whittaker, D M; Clarke, E; Iorsh, I V; Shelykh, I A; Skolnick, M S; Krizhanovskii, D N

2018-03-02

We study exciton polaritons in a two-dimensional Lieb lattice of micropillars. The energy spectrum of the system features two flat bands formed from S and P_{x,y} photonic orbitals, into which we trigger bosonic condensation under high power excitation. The symmetry of the orbital wave functions combined with photonic spin-orbit coupling gives rise to emission patterns with pseudospin texture in the flat band condensates. Our Letter shows the potential of polariton lattices for emulating flat band Hamiltonians with spin-orbit coupling, orbital degrees of freedom, and interactions.

Etched distributed Bragg reflectors as three-dimensional photonic crystals: photonic bands and density of states.

PubMed

Pavarini, E; Andreani, L C

2002-09-01

The photonic band dispersion and density of states (DOS) are calculated for the three-dimensional (3D) hexagonal structure corresponding to a distributed Bragg reflector patterned with a 2D triangular lattice of circular holes. Results for the Si/SiO(2) and GaAs/Al(x)Ga(1-x)As systems determine the optimal parameters for which a gap in the 2D plane occurs and overlaps the 1D gap of the multilayer. The DOS is considerably reduced in correspondence with the overlap of 2D and 1D gaps. Also, the local density of states (i.e., the DOS weighted with the squared electric field at a given point) has strong variations depending on the position. Both results imply substantial changes of spontaneous emission rates and patterns for a local emitter embedded in the structure and make this system attractive for the fabrication of a 3D photonic crystal with controlled radiative properties.

First-Principles Prediction of New Electrides with Nontrivial Band Topology Based on One-Dimensional Building Blocks

NASA Astrophysics Data System (ADS)

Park, Changwon; Kim, Sung Wng; Yoon, Mina

2018-01-01

We introduce a new class of electrides with nontrivial band topology by coupling materials database searches and first-principles-calculations-based analysis. Cs3O and Ba3N are for the first time identified as a new class of electrides, consisting of one-dimensional (1D) nanorod building blocks. Their crystal structures mimic β -TiCl3 with the position of anions and cations exchanged. Unlike the weakly coupled nanorods of β -TiCl3 , Cs3O and Ba3N retain 1D anionic electrons along the hollow interrod sites; additionally, a strong interrod interaction in C3O and Ba3N induces band inversion in a 2D superatomic triangular lattice, resulting in Dirac-node lines. The new class of electrides can serve as a prototype for new electrides with a large cavity space that can be utilized for various applications such as gas storage, ion transport, and metal intercalation.

Lattice Truss Structural Response Using Energy Methods

NASA Technical Reports Server (NTRS)

Kenner, Winfred Scottson

1996-01-01

A deterministic methodology is presented for developing closed-form deflection equations for two-dimensional and three-dimensional lattice structures. Four types of lattice structures are studied: beams, plates, shells and soft lattices. Castigliano's second theorem, which entails the total strain energy of a structure, is utilized to generate highly accurate results. Derived deflection equations provide new insight into the bending and shear behavior of the four types of lattices, in contrast to classic solutions of similar structures. Lattice derivations utilizing kinetic energy are also presented, and used to examine the free vibration response of simple lattice structures. Derivations utilizing finite element theory for unique lattice behavior are also presented and validated using the finite element analysis code EAL.

Coherent and radiative couplings through two-dimensional structured environments

NASA Astrophysics Data System (ADS)

Galve, F.; Zambrini, R.

2018-03-01

We study coherent and radiative interactions induced among two or more quantum units by coupling them to two-dimensional (2D) lattices acting as structured environments. This model can be representative of atoms trapped near photonic crystal slabs, trapped ions in Coulomb crystals, or to surface acoustic waves on piezoelectric materials, cold atoms on state-dependent optical lattices, or even circuit QED architectures, to name a few. We compare coherent and radiative contributions for the isotropic and directional regimes of emission into the lattice, for infinite and finite lattices, highlighting their differences and existing pitfalls, e.g., related to long-time or large-lattice limits. We relate the phenomenon of directionality of emission with linear-shaped isofrequency manifolds in the dispersion relation, showing a simple way to disrupt it. For finite lattices, we study further details such as the scaling of resonant number of lattice modes for the isotropic and directional regimes, and relate this behavior with known van Hove singularities in the infinite lattice limit. Furthermore, we export the understanding of emission dynamics with the decay of entanglement for two quantum, atomic or bosonic, units coupled to the 2D lattice. We analyze in some detail completely subradiant configurations of more than two atoms, which can occur in the finite lattice scenario, in contrast with the infinite lattice case. Finally, we demonstrate that induced coherent interactions for dark states are zero for the finite lattice.

Regularized lattice Bhatnagar-Gross-Krook model for two- and three-dimensional cavity flow simulations.

PubMed

Montessori, A; Falcucci, G; Prestininzi, P; La Rocca, M; Succi, S

2014-05-01

We investigate the accuracy and performance of the regularized version of the single-relaxation-time lattice Boltzmann equation for the case of two- and three-dimensional lid-driven cavities. The regularized version is shown to provide a significant gain in stability over the standard single-relaxation time, at a moderate computational overhead.

Exploring photonic topological insulator states in a circuit-QED lattice

NASA Astrophysics Data System (ADS)

Li, Jing-Ling; Shan, Chuan-Jia; Zhao, Feng

2018-04-01

We propose a simple protocol to explore the topological properties of photonic integer quantum Hall states in a one-dimensional circiut-QED lattice. By periodically modulating the on-site photonic energies in such a lattice, we demonstrate that this one-dimensional lattice model can be mapped into a two-dimensional integer quantum Hall insulator model. Based on the lattice-based cavity input-output theory, we show that both the photonic topological protected edge states and topological invariants can be clearly measured from the final steady state of the resonator lattice after taking into account cavity dissipation. Interestingly, we also find that the measurement signals associated with the above topological features are quite unambitious even in five coupled dissipative resonators. Our work opens up a new prospect of exploring topological states with a small-size dissipative quantum artificial lattice, which is quite attractive to the current quantum optics community.

Two-dimensional Ising model on random lattices with constant coordination number

NASA Astrophysics Data System (ADS)

Schrauth, Manuel; Richter, Julian A. J.; Portela, Jefferson S. E.

2018-02-01

We study the two-dimensional Ising model on networks with quenched topological (connectivity) disorder. In particular, we construct random lattices of constant coordination number and perform large-scale Monte Carlo simulations in order to obtain critical exponents using finite-size scaling relations. We find disorder-dependent effective critical exponents, similar to diluted models, showing thus no clear universal behavior. Considering the very recent results for the two-dimensional Ising model on proximity graphs and the coordination number correlation analysis suggested by Barghathi and Vojta [Phys. Rev. Lett. 113, 120602 (2014), 10.1103/PhysRevLett.113.120602], our results indicate that the planarity and connectedness of the lattice play an important role on deciding whether the phase transition is stable against quenched topological disorder.

An effective lattice Boltzmann flux solver on arbitrarily unstructured meshes

NASA Astrophysics Data System (ADS)

Wu, Qi-Feng; Shu, Chang; Wang, Yan; Yang, Li-Ming

2018-05-01

The recently proposed lattice Boltzmann flux solver (LBFS) is a new approach for the simulation of incompressible flow problems. It applies the finite volume method (FVM) to discretize the governing equations, and the flux at the cell interface is evaluated by local reconstruction of lattice Boltzmann solution from macroscopic flow variables at cell centers. In the previous application of the LBFS, the structured meshes have been commonly employed, which may cause inconvenience for problems with complex geometries. In this paper, the LBFS is extended to arbitrarily unstructured meshes for effective simulation of incompressible flows. Two test cases, the lid-driven flow in a triangular cavity and flow around a circular cylinder, are carried out for validation. The obtained results are compared with the data available in the literature. Good agreement has been achieved, which demonstrates the effectiveness and reliability of the LBFS in simulating flows on arbitrarily unstructured meshes.

Matter-wave propagation in optical lattices: geometrical and flat-band effects

DOE PAGES

Metcalf, Mekena; Chern, Gia-Wei; Di Ventra, Massimiliano; ...

2016-03-17

Here we report that the geometry of optical lattices can be engineered allowing the study of atomic transport along paths arranged in patterns that are otherwise difficult to probe in the solid state. A question feasible to atomic systems is related to the speed of propagation of matter-waves as a function of the lattice geometry. To address this issue, we have investigated theoretically the quantum transport of non-interacting and weakly-interacting ultracold fermionic atoms in several 2D optical lattice geometries. We find that the triangular lattice has a higher propagation velocity compared to the square lattice, and the cross-linked square latticemore » has an even faster propagation velocity. The increase results from the mixing of the momentum states which leads to different group velocities in quantum systems. Standard band theory provides an explanation and allows for a systematic way to search and design systems with controllable matter-wave propagation. Moreover, the presence of a flat band such as in a two-leg ladder geometry leads to a dynamical density discontinuity due to its localized atoms. Lastly, we discuss possible realizations of those dynamical phenomena.« less

Bose and Fermi Gases of Ultracold Ytterbium in a Triangular Optical Lattice

NASA Astrophysics Data System (ADS)

Thobe, Alexander; Doerscher, Soeren; Hundt, Bastian; Kochanke, Andre; Becker, Christoph; Sengstock, Klaus

2013-05-01

Quantum gases of alkaline-earth like atoms such as Calcium, Strontium and Ytterbium (Yb) open up exciting new possibilities for the study of many body physics in optical lattices, ranging from SU(N) symmetric spin Hamiltonians to the Kondo Lattice Model. Here, we present experimental studies of ultracold bosonic and fermionic Yb quantum gases. Unlike other experiments studying ultracold alkaline earth-like atoms, we have implemented a 2D-MOT instead of a Zeeman slower as a source of cold atoms. From the 2D-MOT, operating on the broad 1S0 -->1P1 transtition, the atoms are directly loaded into the 3D-MOT operating on a narrow intercombination line. The atoms are then evaporatively cooled to quantum degeneracy in a crossed optical dipole trap. With this setup we routinely produce BECs and degenerate Fermi gases of different Yb isotopes. Moreover, we present first results on spectroscopy of an interacting fermi gas on the ultranarrow 1S0 -->3P0 clock transition in a magic wavelength optical lattice. In future experiments, this spectroscopy will serve as a versatile tool for interaction sensing and selective addressing of atoms in a wavelength tunable, state dependent, triangular optical lattice, which we are currently implementing. This work is supported by DFG within SFB 925 and GrK 1355, as well as EU FETOpen (iSense).

Magnetic and magnetocaloric properties of the exactly solvable mixed-spin Ising model on a decorated triangular lattice in a magnetic field

NASA Astrophysics Data System (ADS)

Gálisová, Lucia; Strečka, Jozef

2018-05-01

The ground state, zero-temperature magnetization process, critical behaviour and isothermal entropy change of the mixed-spin Ising model on a decorated triangular lattice in a magnetic field are exactly studied after performing the generalized decoration-iteration mapping transformation. It is shown that both the inverse and conventional magnetocaloric effect can be found near the absolute zero temperature. The former phenomenon can be found in a vicinity of the discontinuous phase transitions and their crossing points, while the latter one occurs in some paramagnetic phases due to a spin frustration to be present at zero magnetic field. The inverse magnetocaloric effect can also be detected slightly above continuous phase transitions following the power-law dependence | - ΔSisomin | ∝hn, where n depends basically on the ground-state spin ordering.

A two-dimensional DNA lattice implanted polymer solar cell.

PubMed

Lee, Keun Woo; Kim, Kyung Min; Lee, Junwye; Amin, Rashid; Kim, Byeonghoon; Park, Sung Kye; Lee, Seok Kiu; Park, Sung Ha; Kim, Hyun Jae

2011-09-16

A double crossover tile based artificial two-dimensional (2D) DNA lattice was fabricated and the dry-wet method was introduced to recover an original DNA lattice structure in order to deposit DNA lattices safely on the organic layer without damaging the layer. The DNA lattice was then employed as an electron blocking layer in a polymer solar cell causing an increase of about 10% up to 160% in the power conversion efficiency. Consequently, the resulting solar cell which had an artificial 2D DNA blocking layer showed a significant enhancement in power conversion efficiency compared to conventional polymer solar cells. It should be clear that the artificial DNA nanostructure holds unique physical properties that are extremely attractive for various energy-related and photonic applications.

Force Evaluation in the Lattice Boltzmann Method Involving Curved Geometry

NASA Technical Reports Server (NTRS)

Mei, Renwei; Yu, Dazhi; Shyy, Wei; Luo, Li-Shi; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

The present work investigates two approaches for force evaluation in the lattice Boltzmann equation: the momentum- exchange method and the stress-integration method on the surface of a body. The boundary condition for the particle distribution functions on curved geometries is handled with second order accuracy based on our recent works. The stress-integration method is computationally laborious for two-dimensional flows and in general difficult to implement for three-dimensional flows, while the momentum-exchange method is reliable, accurate, and easy to implement for both two-dimensional and three-dimensional flows. Several test cases are selected to evaluate the present methods, including: (i) two-dimensional pressure-driven channel flow; (ii) two-dimensional uniform flow past a column of cylinders; (iii) two-dimensional flow past a cylinder asymmetrically placed in a channel (with vortex shedding); (iv) three-dimensional pressure-driven flow in a circular pipe; and (v) three-dimensional flow past a sphere. The drag evaluated by using the momentum-exchange method agrees well with the exact or other published results.

Study of propellant dynamics in a shuttle type launch vehicle

NASA Technical Reports Server (NTRS)

Jones, C. E.; Feng, G. C.

1972-01-01

A method and an associated digital computer program for evaluating the vibrational characteristics of large liquid-filled rigid wall tanks of general shape are presented. A solution procedure was developed in which slosh modes and frequencies are computed for systems mathematically modeled as assemblages of liquid finite elements. To retain sparsity in the assembled system mass and stiffness matrices, a compressible liquid element formulation was incorporated in the program. The approach taken in the liquid finite element formulation is compatible with triangular and quadrilateral structural finite elements so that the analysis of liquid motion can be coupled with flexible tank wall motion at some future time. The liquid element repertoire developed during the course of this study consists of a two-dimensional triangular element and a three-dimensional tetrahedral element.

Large-N solution of the Sp(N) Heisenberg quantum antiferromagnet on the anisotropic triangular lattice in a magnetic field.

NASA Astrophysics Data System (ADS)

Chung, Chung-Hou; Marston, Brad

2002-03-01

We study the Sp(N) generalization of the physical Sp(1) \\cong SU(2) Heisenberg antiferromagnet on the anisotropic triangular lattice( C. H. Chung, J. B. Marston and R. H. McKenzie, Journal of Physics: Condensed Matter 13), 5159 (2001). in a magnetic field. The model is relevant for describing recent experiments on the magnetic phases of the quasi-2D system Cs_2CuCl4 in a magnetic field(R. Coldea, D. A. Tennant, A. M. Tsvelik, and Z. Tylczynski, Phys. Rev. Lett. 86), 1335 (2001).. We solve the model in the large-N limit and study the effect of a magnetic field on the incommensurate magnetic order. Below a critical field the spins form a ``cone'' of polarization, in apparent agreement with neutron scattering experiments when the magnetic field is oriented perpendicular to the lattice. The incommensuration increases with increasing field strength. Above the critical field the spins are fully polarized. We have difficulty treating Dzyaloshinskii-Moriya interactions which are believed to be important for in-plane fields.

Noncircular skyrmion and its anisotropic response in thin films of chiral magnets under a tilted magnetic field

DOE PAGES

Lin, Shi-Zeng; Saxena, Avadh

2015-11-03

Here we study the equilibrium and dynamical properties of skyrmions in thin films of chiral magnets with oblique magnetic field. The shape of an individual skyrmion is non-circular and the skyrmion density decreases with the tilt angle from the normal of films. As a result, the interaction between two skyrmions depends on the relative angle between them in addition to their separation. The triangular lattice of skyrmions under a perpendicular magnetic field is distorted into a centered rectangular lattice for a tilted magnetic field. For a low skyrmion density, skyrmions form a chain like structure. Lastly, the dynamical response ofmore » the non-circular skyrmions depends on the direction of external currents.« less

Resonant Zener tunneling in two-dimensional periodic photonic lattices.

PubMed

Desyatnikov, Anton S; Kivshar, Yuri S; Shchesnovich, Valery S; Cavalcanti, Solange B; Hickmann, Jandir M

2007-02-15

We study Zener tunneling in two-dimensional photonic lattices and derive, for the case of hexagonal symmetry, the generalized Landau-Zener-Majorana model describing resonant interaction between high-symmetry points of the photonic spectral bands. We demonstrate that this effect can be employed for the generation of Floquet-Bloch modes and verify the model by direct numerical simulations of the tunneling effect.

Controlling the energy of defects and interfaces in the amplitude expansion of the phase-field crystal model

NASA Astrophysics Data System (ADS)

Salvalaglio, Marco; Backofen, Rainer; Voigt, Axel; Elder, Ken R.

2017-08-01

One of the major difficulties in employing phase-field crystal (PFC) modeling and the associated amplitude (APFC) formulation is the ability to tune model parameters to match experimental quantities. In this work, we address the problem of tuning the defect core and interface energies in the APFC formulation. We show that the addition of a single term to the free-energy functional can be used to increase the solid-liquid interface and defect energies in a well-controlled fashion, without any major change to other features. The influence of the newly added term is explored in two-dimensional triangular and honeycomb structures as well as bcc and fcc lattices in three dimensions. In addition, a finite-element method (FEM) is developed for the model that incorporates a mesh refinement scheme. The combination of the FEM and mesh refinement to simulate amplitude expansion with a new energy term provides a method of controlling microscopic features such as defect and interface energies while simultaneously delivering a coarse-grained examination of the system.

Investigation on the properties of omnidirectional photonic band gaps in two-dimensional plasma photonic crystals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Hai-Feng, E-mail: hanlor@163.com; Nanjing Artillery Academy, Nanjing 211132; Liu, Shao-Bin

2016-01-15

The properties of omnidirectional photonic band gaps (OBGs) in two-dimensional plasma photonic crystals (2D PPCs) are theoretically investigated by the modified plane wave expansion method. In the simulation, we consider the off-plane incident wave vector. The configuration of 2D PPCs is the triangular lattices filled with the nonmagnetized plasma cylinders in the homogeneous and isotropic dielectric background. The calculated results show that the proposed 2D PPCs possess a flatbands region and the OBGs. Compared with the OBGs in the conventional 2D dielectric-air PCs, it can be obtained more easily and enlarged in the 2D PPCs with a similar structure. Themore » effects of configurational parameters of the PPCs on the OBGs also are studied. The simulated results demonstrate that the locations of OBGs can be tuned easily by manipulating those parameters except for changing plasma collision frequency. The achieved OBGs can be enlarged by optimizations. The OBGs of two novel configurations of PPCs with different cross sections are computed for a comparison. Both configurations have the advantages of obtaining the larger OBGs compared with the conventional configuration, since the symmetry of 2D PPCs is broken by different sizes of periodically inserted plasma cylinders or connected by the embedded plasma cylinders with thin veins. The analysis of the results shows that the bandwidths of OBGs can be tuned by changing geometric and physical parameters of such two PPCs structures. The theoretical results may open a new scope for designing the omnidirectional reflectors or mirrors based on the 2D PPCs.« less

Influence of Dzyaloshinskii-Moriya interaction and ballistic spin transport in the two and three-dimensional Heisenberg model

NASA Astrophysics Data System (ADS)

Lima, L. S.

2018-06-01

We study the effect of Dzyaloshisnkii-Moriya interaction on spin transport in the two and three-dimensional Heisenberg antiferromagnetic models in the square lattice and cubic lattice respectively. For the three-dimensional model, we obtain a large peak for the spin conductivity and therefore a finite AC conductivity. For the two-dimensional model, we have gotten the AC spin conductivity tending to the infinity at ω → 0 limit and a suave decreasing in the spin conductivity with increase of ω. We obtain a small influence of the Dzyaloshinskii-Moriya interaction on the spin conductivity in all cases analyzed.

Role-separating ordering in social dilemmas controlled by topological frustration

NASA Astrophysics Data System (ADS)

Amaral, Marco A.; Perc, Matjaž; Wardil, Lucas; Szolnoki, Attila; da Silva Júnior, Elton J.; da Silva, Jafferson K. L.

2017-03-01

``Three is a crowd" is an old proverb that applies as much to social interactions as it does to frustrated configurations in statistical physics models. Accordingly, social relations within a triangle deserve special attention. With this motivation, we explore the impact of topological frustration on the evolutionary dynamics of the snowdrift game on a triangular lattice. This topology provides an irreconcilable frustration, which prevents anticoordination of competing strategies that would be needed for an optimal outcome of the game. By using different strategy updating protocols, we observe complex spatial patterns in dependence on payoff values that are reminiscent to a honeycomb-like organization, which helps to minimize the negative consequence of the topological frustration. We relate the emergence of these patterns to the microscopic dynamics of the evolutionary process, both by means of mean-field approximations and Monte Carlo simulations. For comparison, we also consider the same evolutionary dynamics on the square lattice, where of course the topological frustration is absent. However, with the deletion of diagonal links of the triangular lattice, we can gradually bridge the gap to the square lattice. Interestingly, in this case the level of cooperation in the system is a direct indicator of the level of topological frustration, thus providing a method to determine frustration levels in an arbitrary interaction network.

Role-separating ordering in social dilemmas controlled by topological frustration.

PubMed

Amaral, Marco A; Perc, Matjaž; Wardil, Lucas; Szolnoki, Attila; da Silva Júnior, Elton J; da Silva, Jafferson K L

2017-03-01

''Three is a crowd" is an old proverb that applies as much to social interactions as it does to frustrated configurations in statistical physics models. Accordingly, social relations within a triangle deserve special attention. With this motivation, we explore the impact of topological frustration on the evolutionary dynamics of the snowdrift game on a triangular lattice. This topology provides an irreconcilable frustration, which prevents anticoordination of competing strategies that would be needed for an optimal outcome of the game. By using different strategy updating protocols, we observe complex spatial patterns in dependence on payoff values that are reminiscent to a honeycomb-like organization, which helps to minimize the negative consequence of the topological frustration. We relate the emergence of these patterns to the microscopic dynamics of the evolutionary process, both by means of mean-field approximations and Monte Carlo simulations. For comparison, we also consider the same evolutionary dynamics on the square lattice, where of course the topological frustration is absent. However, with the deletion of diagonal links of the triangular lattice, we can gradually bridge the gap to the square lattice. Interestingly, in this case the level of cooperation in the system is a direct indicator of the level of topological frustration, thus providing a method to determine frustration levels in an arbitrary interaction network.

Micropolar continuum modelling of bi-dimensional tetrachiral lattices

PubMed Central

Chen, Y.; Liu, X. N.; Hu, G. K.; Sun, Q. P.; Zheng, Q. S.

2014-01-01

The in-plane behaviour of tetrachiral lattices should be characterized by bi-dimensional orthotropic material owing to the existence of two orthogonal axes of rotational symmetry. Moreover, the constitutive model must also represent the chirality inherent in the lattices. To this end, a bi-dimensional orthotropic chiral micropolar model is developed based on the theory of irreducible orthogonal tensor decomposition. The obtained constitutive tensors display a hierarchy structure depending on the symmetry of the underlying microstructure. Eight additional material constants, in addition to five for the hemitropic case, are introduced to characterize the anisotropy under Z2 invariance. The developed continuum model is then applied to a tetrachiral lattice, and the material constants of the continuum model are analytically derived by a homogenization process. By comparing with numerical simulations for the discrete lattice, it is found that the proposed continuum model can correctly characterize the static and wave properties of the tetrachiral lattice. PMID:24808754

Multilayer DNA origami packed on hexagonal and hybrid lattices.

PubMed

Ke, Yonggang; Voigt, Niels V; Gothelf, Kurt V; Shih, William M

2012-01-25

"Scaffolded DNA origami" has been proven to be a powerful and efficient approach to construct two-dimensional or three-dimensional objects with great complexity. Multilayer DNA origami has been demonstrated with helices packing along either honeycomb-lattice geometry or square-lattice geometry. Here we report successful folding of multilayer DNA origami with helices arranged on a close-packed hexagonal lattice. This arrangement yields a higher density of helical packing and therefore higher resolution of spatial addressing than has been shown previously. We also demonstrate hybrid multilayer DNA origami with honeycomb-lattice, square-lattice, and hexagonal-lattice packing of helices all in one design. The availability of hexagonal close-packing of helices extends our ability to build complex structures using DNA nanotechnology. © 2011 American Chemical Society

Role of dimensionality in Axelrod's model for the dissemination of culture

NASA Astrophysics Data System (ADS)

Klemm, Konstantin; Eguíluz, Víctor M.; Toral, Raúl; Miguel, Maxi San

2003-09-01

We analyze a model of social interaction in one- and two-dimensional lattices for a moderate number of features. We introduce an order parameter as a function of the overlap between neighboring sites. In a one-dimensional chain, we observe that the dynamics is consistent with a second-order transition, where the order parameter changes continuously and the average domain diverges at the transition point. However, in a two-dimensional lattice the order parameter is discontinuous at the transition point characteristic of a first-order transition between an ordered and a disordered state.

Topological Superfluid and Majorana Zero Modes in Synthetic Dimension

PubMed Central

Yan, Zhongbo; Wan, Shaolong; Wang, Zhong

2015-01-01

Recently it has been shown that multicomponent spin-orbit-coupled fermions in one-dimensional optical lattices can be viewed as spinless fermions moving in two-dimensional synthetic lattices with synthetic magnetic flux. The quantum Hall edge states in these systems have been observed in recent experiments. In this paper we study the effect of an attractive Hubbard interaction. Since the Hubbard interaction is long-range in the synthetic dimension, it is able to efficiently induce Cooper pairing between the counterpropagating chiral edge states. The topological class of the resultant one-dimensional superfluid is determined by the parity (even/odd) of the Chern number in the two-dimensional synthetic lattice. We also show the presence of a chiral symmetry in our model, which implies Z classification and the robustness of multiple zero modes when this symmetry is unbroken. PMID:26515084

Unconventional phases in quantum spin and pseudospin systems in two dimensional and three dimensional lattices

NASA Astrophysics Data System (ADS)

Xu, Cenke

Several examples of quantum spin systems and pseudo spin systems have been studied, and unconventional states of matters and phase transitions have been realized in all these systems under consideration. In the p +/- ip superconductor Josephson lattice and the p--band cold atomic system trapped in optical lattices, novel phases which behave similarly to 1+1 dimensional systems are realized, despite the fact that the real physical systems are in two or three dimensional spaces. For instance, by employing a spin-wave analysis together with a new duality transformation, we establish the existence and stability of a novel gapless "critical phase", which we refer to as a "bond algebraic liquid". This novel critical phase is analogous to the 1+1 dimensional algebraic boson liquid phase. The reason for the novel physics is that there is a quasilocal gauge symmetry in the effective low energy Hamiltonian. In a spin-1 system on the kagome lattice, and a hard-core boson system on the honeycomb lattice, the low energy physics is controlled by two components of compact U(1) gauge symmetries that emerge at low energy. Making use of the confinement nature of the 2+1 dimensional compact gauge theories and the powerful duality between gauge theories and height field theories, the crystalline phase diagrams are studied for both systems, and the transitions to other phases are also considered. These phase diagrams might be accessible in strongly correlated materials, or atomic systems in optical lattices. A novel quantum ground state of matter is realized in a bosonic model on three dimensional fcc lattice with emergent low energy excitations. The novel phase obtained is a stable gapless boson liquid phase, with algebraic boson density correlations. The stability of this phase is protected against the instanton effect and superfluidity by self-duality and large gauge symmetries on both sides of the duality. The gapless collective excitations of this phase closely resemble the graviton, although they have a soft w ˜ k2 dispersion relation. The dynamics of this novel phase is described by a new set of Maxwell's equations.

Anomalous matching effect and attractive vortex interaction in 7.5-/μm triangular microhole lattice on Pb film

NASA Astrophysics Data System (ADS)

Ishida, Takekazu; Yoshida, Masaaki; Nakata, Shin'ichiro; Koyama, Tomio

2002-10-01

It is considerably exciting to explore the novel vortex physics in multiply connected superconductors. We prepare triangular microhole lattice on Pb film (TriMHoLP) by evaporation of a type-I superconductor Pb upon a capillary plate (6-μm hole and 7.5-μm pitch) in vacuum. We measure the magnetization of TriMHoLP in the RSO mode under low fields (| H|⩽4.7 G). The polarity of magnetization peaks is identical against the field reversal. The magnetization curves as a function of temperature taken in a field-cooling mode of RSO are always positive irrelevant to the field polarity. We show that a vortex-vortex interaction is not always repulsive in a low- κ superconductor. We consider that a spontaneous magnetization and an anomalous matching effect near Tc are relevant to the attractive interaction between vortices.

Effect of room temperature lattice vibration on the electron transport in graphene nanoribbons

NASA Astrophysics Data System (ADS)

Liu, Yue-Yang; Li, Bo-Lin; Chen, Shi-Zhang; Jiang, Xiangwei; Chen, Ke-Qiu

2017-09-01

We observe directly the lattice vibration and its multifold effect on electron transport in zigzag graphene nanoribbons in simulation by utilizing an efficient combined method. The results show that the electron transport fluctuates greatly due to the incessant lattice vibration of the nanoribbons. More interestingly, the lattice vibration behaves like a double-edged sword that it boosts the conductance of symmetric zigzag nanoribbons (containing an even number of zigzag chains along the width direction) while weakens the conductance of asymmetric nanoribbons. As a result, the reported large disparity between the conductances of the two kinds of nanoribbons at 0 K is in fact much smaller at room temperature (300 K). We also find that the spin filter effect that exists in perfect two-dimensional symmetric zigzag graphene nanoribbons is destroyed to some extent by lattice vibrations. Since lattice vibrations or phonons are usually inevitable in experiments, the research is very meaningful for revealing the important role of lattice vibrations play in the electron transport properties of two-dimensional materials and guiding the application of ZGNRs in reality.

Itinerant fermions on a triangular lattice: Unconventional magnetism and other ordered states

NASA Astrophysics Data System (ADS)

Ye, Mengxing; Chubukov, Andrey V.

2018-06-01

We consider a system of 2D fermions on a triangular lattice with well separated electron and hole pockets of similar sizes, centered at certain high-symmetry points in the Brillouin zone. We first analyze Stoner-type spin-density-wave (SDW) magnetism. We show that SDW order is degenerate at the mean-field level. Beyond mean-field, the degeneracy is lifted and is either 120∘ "triangular" order (same as for localized spins), or a collinear order with antiferromagnetic spin arrangement on two-thirds of sites, and nonmagnetic on the rest of sites. We also study a time-reversal symmetric directional spin bond order, which emerges when some interactions are repulsive and some are attractive. We show that this order is also degenerate at a mean-field level, but beyond mean-field the degeneracy is again lifted. We next consider the evolution of a magnetic order in a magnetic field starting from an SDW state in zero field. We show that a field gives rise to a canting of an SDW spin configuration. In addition, it necessarily triggers the directional bond order, which, we argue, is linearly coupled to the SDW order in a finite field. We derive the corresponding term in the free energy. Finally, we consider the interplay between an SDW order and superconductivity and charge order. For this, we analyze the flow of the couplings within parquet renormalization group (pRG) scheme. We show that magnetism wins if all interactions are repulsive and there is little energy space for pRG to develop. However, if system parameters are such that pRG runs over a wide range of energies, the system may develop either superconductivity or an unconventional charge order, which breaks time-reversal symmetry.

Strain-induced phase transition and electron spin-polarization in graphene spirals

PubMed Central

Zhang, Xiaoming; Zhao, Mingwen

2014-01-01

Spin-polarized triangular graphene nanoflakes (t-GNFs) serve as ideal building blocks for the long-desired ferromagnetic graphene superlattices, but they are always assembled to planar structures which reduce its mechanical properties. Here, by joining t-GNFs in a spiral way, we propose one-dimensional graphene spirals (GSs) with superior mechanical properties and tunable electronic structures. We demonstrate theoretically the unique features of electron motion in the spiral lattice by means of first-principles calculations combined with a simple Hubbard model. Within a linear elastic deformation range, the GSs are nonmagnetic metals. When the axial tensile strain exceeds an ultimate strain, however, they convert to magnetic semiconductors with stable ferromagnetic ordering along the edges. Such strain-induced phase transition and tunable electron spin-polarization revealed in the GSs open a new avenue for spintronics devices. PMID:25027550

Strain-induced phase transition and electron spin-polarization in graphene spirals.

PubMed

Zhang, Xiaoming; Zhao, Mingwen

2014-07-16

Spin-polarized triangular graphene nanoflakes (t-GNFs) serve as ideal building blocks for the long-desired ferromagnetic graphene superlattices, but they are always assembled to planar structures which reduce its mechanical properties. Here, by joining t-GNFs in a spiral way, we propose one-dimensional graphene spirals (GSs) with superior mechanical properties and tunable electronic structures. We demonstrate theoretically the unique features of electron motion in the spiral lattice by means of first-principles calculations combined with a simple Hubbard model. Within a linear elastic deformation range, the GSs are nonmagnetic metals. When the axial tensile strain exceeds an ultimate strain, however, they convert to magnetic semiconductors with stable ferromagnetic ordering along the edges. Such strain-induced phase transition and tunable electron spin-polarization revealed in the GSs open a new avenue for spintronics devices.

Epitaxial Growth of Rhenium with Sputtering

DTIC Science & Technology

2016-05-06

corresponds to two atomic Re layers , considering that the c-axis lattice constant of the tri- atomic layered hcp Re unit cell is ~4.5 Å. Frequently, two...Å) corresponds to two Re atomic layers since the c-axis lattice constant of hcp Re, which is composed of three Re atomic layers , is ~4.5 Å...The growth starts in a three dimensional mode but transforms into two dimensional mode as the film gets thicker. With a thin (~2 nm) seed layer

Evidence of benzenoid domains in nanographenes.

PubMed

Baldoni, Matteo; Mercuri, Francesco

2015-01-21

Calculations based on density functional theory demonstrate the occurrence of local deformations of the perfect honeycomb lattice in nanographenes to form arrangements, with triangular symmetry, composed of six-membered ring patterns. The formation of these locally regular superstructures, which can be considered as benzenoid-like domains on the 2D graphene lattice, is ascribed to the gain in resonance energy deriving from aromaticity. The relationship between the atomic morphology of nanographenes and details of the relaxed structure is rationalized in terms of Clar's theory of the aromatic sextet and by extending concepts borrowed from valence bond theory to 2D carbon nanostructures. Namely, two regular arrangements can be evidenced, defined as Clar (fully benzenoid) and Kekulé domains, which correspond to two different regular bond patterns in sets of adjacent six-membered rings. Our findings are compatible with recent experiments and have potentially relevant consequences in the development of novel electronic devices based on graphene materials.

Frustrated magnetism in doped quasi-triangular lattice materials, Cu2(1-x)Zn2x(OH)3NO3/(C7H15COO)

NASA Astrophysics Data System (ADS)

Wu, Jian; Werner, Fletcher; Gangopadhyay, Anup K.; Solin, S. A.

2010-03-01

We have performed DC and AC magnetic susceptibility measurements on the spin S=1/2 quasi-triangular lattice materials Cu2(1-x)Zn2x(OH)3NO3/(C7H15COO). The X-ray diffraction experiments reveal that this class of materials has a crystal structure in P21/m space group, in which Cu^2+ and Zn^2+ ions are arranged on a slightly distorted triangular lattice [1]. Cu2(1-)Zn2x(OH)3NO3 with a short inorganic intercalation NO3 group, have a long-range antiferromagnetic order at low temperature. The Neel temperature TN decreases from 11K to 5.6K while the Curie-Weiss temperature increases from -5.1K to +2.8K as the Zn concentration increases from 0 to 65%. After a longer alkanecarboxylate C7H15COO group was introduced into the interlayer space, a spin-glass like behavior in magnetic properties was observed [2]. The value |θcw /TN| is approximately 20, indicating the materials are in a medium level frustrated state. The onset of a ferromagnetic correlation was found in both DC and AC susceptibility data. The interplay of geometrical frustration and the coexistence of ferromagnetic and antiferromagnetic couplings has driven the materials into a glassy ground state. [1] G. Linder, et al., Journal of Solid State Chemistry (1995) [2] M. A. Girtu et al, Phys Rev B 61,4117(2000).

Dirac cones in isogonal hexagonal metallic structures

NASA Astrophysics Data System (ADS)

Wang, Kang

2018-03-01

A honeycomb hexagonal metallic lattice is equivalent to a triangular atomic one and cannot create Dirac cones in its electromagnetic wave spectrum. We study in this work the low-frequency electromagnetic band structures in isogonal hexagonal metallic lattices that are directly related to the honeycomb one and show that such structures can create Dirac cones. The band formation can be described by a tight-binding model that allows investigating, in terms of correlations between local resonance modes, the condition for the Dirac cones and the consequence of the third structure tile sustaining an extra resonance mode in the unit cell that induces band shifts and thus nonlinear deformation of the Dirac cones following the wave vectors departing from the Dirac points. We show further that, under structure deformation, the deformations of the Dirac cones result from two different correlation mechanisms, both reinforced by the lattice's metallic nature, which directly affects the resonance mode correlations. The isogonal structures provide new degrees of freedom for tuning the Dirac cones, allowing adjustment of the cone shape by modulating the structure tiles at the local scale without modifying the lattice periodicity and symmetry.

Phase transitions and thermodynamic properties of antiferromagnetic Ising model with next-nearest-neighbor interactions on the Kagomé lattice

NASA Astrophysics Data System (ADS)

Ramazanov, M. K.; Murtazaev, A. K.; Magomedov, M. A.; Badiev, M. K.

2018-06-01

We study phase transitions and thermodynamic properties in the two-dimensional antiferromagnetic Ising model with next-nearest-neighbor interaction on a Kagomé lattice by Monte Carlo simulations. A histogram data analysis shows that a second-order transition occurs in the model. From the analysis of obtained data, we can assume that next-nearest-neighbor ferromagnetic interactions in two-dimensional antiferromagnetic Ising model on a Kagomé lattice excite the occurrence of a second-order transition and unusual behavior of thermodynamic properties on the temperature dependence.

Phase transitions in coupled map lattices and in associated probabilistic cellular automata.

PubMed

Just, Wolfram

2006-10-01

Analytical tools are applied to investigate piecewise linear coupled map lattices in terms of probabilistic cellular automata. The so-called disorder condition of probabilistic cellular automata is closely related with attracting sets in coupled map lattices. The importance of this condition for the suppression of phase transitions is illustrated by spatially one-dimensional systems. Invariant densities and temporal correlations are calculated explicitly. Ising type phase transitions are found for one-dimensional coupled map lattices acting on repelling sets and for a spatially two-dimensional Miller-Huse-like system with stable long time dynamics. Critical exponents are calculated within a finite size scaling approach. The relevance of detailed balance of the resulting probabilistic cellular automaton for the critical behavior is pointed out.

The lattice of trumping majorization for 4D probability vectors and 2D catalysts.

PubMed

Bosyk, Gustavo M; Freytes, Hector; Bellomo, Guido; Sergioli, Giuseppe

2018-02-27

The transformation of an initial bipartite pure state into a target one by means of local operations and classical communication and entangled-assisted by a catalyst defines a partial order between probability vectors. This partial order, so-called trumping majorization, is based on tensor products and the majorization relation. Here, we aim to study order properties of trumping majorization. We show that the trumping majorization partial order is indeed a lattice for four dimensional probability vectors and two dimensional catalysts. In addition, we show that the subadditivity and supermodularity of the Shannon entropy on the majorization lattice are inherited by the trumping majorization lattice. Finally, we provide a suitable definition of distance for four dimensional probability vectors.

Strong Cosserat Elasticity in a Transversely Isotropic Polymer Lattice

NASA Astrophysics Data System (ADS)

Rueger, Z.; Lakes, R. S.

2018-02-01

Large size effects are experimentally measured in lattices of triangular unit cells: about a factor of 36 in torsion rigidity and 29 in bending rigidity. This nonclassical phenomenon is consistent with Cosserat elasticity, which allows for the rotation of points and distributed moments in addition to the translation of points and force stress of classical elasticity. The Cosserat characteristic length for torsion is ℓt=9.4 mm ; for bending, it is ℓb=8.8 mm ; these values are comparable to the cell size. Nonclassical effects are much stronger than in stretch-dominated lattices with uniform straight ribs. The lattice structure provides a path to the attainment of arbitrarily large effects.

Recent Topics of Organic Superconductors

NASA Astrophysics Data System (ADS)

Ardavan, Arzhang; Brown, Stuart; Kagoshima, Seiichi; Kanoda, Kazushi; Kuroki, Kazuhiko; Mori, Hatsumi; Ogata, Masao; Uji, Shinya; Wosnitza, Jochen

2012-01-01

Recent developments in research into superconductivity in organic materials are reviewed. In the epoch-defining quasi-one-dimensional TMTSF superconductors with Tc ˜ 1 K, Tc decreases monotonically with increasing pressure, as do signatures of spin fluctuations in the normal state, providing good evidence for magnetically-mediated pairing. Upper critical fields exceed the Zeeman-limiting field by several times, suggesting triplet pairing or a transition to an inhomogeneous superconducting state at high magnetic fields, while triplet pairing is ruled out at low fields by NMR Knight-shift measurements. Evidence for a spatially inhomogeneous superconducting state, Fulde--Ferrel--Larkin--Ovchinnikov state, which has long been sought in various superconducting systems, is now captured by thermodynamic and transport measurements for clean and highly two-dimensional BEDT-TTF and BETS superconductors. Some of the layered superconductors also serve as model systems for Mott physics on anisotropic triangular lattice. For example, the Nernst effect and the pseudo-gap behavior in NMR relaxation are enhanced near to the Mott transition. In the case of increasing spin frustration, the superconducting transition temperature is depressed, and antiferromagnetic ordering is eliminated altogether in the adjacent Mott insulating phase. There is an increasing number of materials exhibiting superconductivity in competition or cooperation with charge order. Theoretical studies shed light on the role of spin and/or charge fluctuations for superconductivity appearing under conditions close to those of correlation-induced insulating phases in the diversity of organic materials.

Softly-confined water cluster between freestanding graphene sheets

NASA Astrophysics Data System (ADS)

Agustian, Rifan; Akaishi, Akira; Nakamura, Jun

2018-01-01

Confined water could adopt new forms not seen in the open air, such as a two-dimensional (2D) square ice trapped between two graphene sheets [Algara-Siller et al., Nature 519, 443-445 (2015)]. In this study, in order to investigate how the flexibility of graphene affects the confined structure of water molecules, we employed classical molecular dynamics simulations with Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential to produce a soft-confining property of graphene. We discovered various solid-like structures of water molecules ranging from two-dimensional to three-dimensional structure encapsulated between two freestanding graphene sheets even at room temperature (300K). A small amount of water encapsulation leads to a layered two-dimensional form with triangular structure. On the other hand, large amounts of water molecules take a three-dimensional flying-saucer-like form with the square ice intra-layer structure. There is also a metastable state where both two-dimensional and three-dimensional structures coexist.

Bandgaps and directional properties of two-dimensional square beam-like zigzag lattices

NASA Astrophysics Data System (ADS)

Wang, Yan-Feng; Wang, Yue-Sheng; Zhang, Chuanzeng

2014-12-01

In this paper we propose four kinds of two-dimensional square beam-like zigzag lattice structures and study their bandgaps and directional propagation of elastic waves. The band structures are calculated by using the finite element method. Both the in-plane and out-of-plane waves are investigated simultaneously via the three-dimensional Euler beam elements. The mechanism of the bandgap generation is analyzed by studying the vibration modes at the bandgap edges. The effects of the geometry parameters of the xy- and z-zigzag lattices on the bandgaps are investigated and discussed. Multiple complete bandgaps are found owing to the separation of the degeneracy by introducing bending arms. The bandgaps are sensitive to the geometry parameters of the periodic systems. The deformed displacement fields of the harmonic responses of a finite lattice structure subjected to harmonic loads at different positions are illustrated to show the directional wave propagation. An extension of the proposed concept to the hexagonal lattices is also presented. The research work in this paper is relevant to the practical design of cellular structures with enhanced vibro-acoustics performance.

Phase transitions in a system of hard Y-shaped particles on the triangular lattice

NASA Astrophysics Data System (ADS)

Mandal, Dipanjan; Nath, Trisha; Rajesh, R.

2018-03-01

We study the different phases and the phase transitions in a system of Y-shaped particles, examples of which include immunoglobulin-G and trinaphthylene molecules, on a triangular lattice interacting exclusively through excluded volume interactions. Each particle consists of a central site and three of its six nearest neighbors chosen alternately, such that there are two types of particles which are mirror images of each other. We study the equilibrium properties of the system using grand canonical Monte Carlo simulations that implement an algorithm with cluster moves that is able to equilibrate the system at densities close to full packing. We show that, with increasing density, the system undergoes two entropy-driven phase transitions with two broken-symmetry phases. At low densities, the system is in a disordered phase. As intermediate phases, there is a solidlike sublattice phase in which one type of particle is preferred over the other and the particles preferentially occupy one of four sublattices, thus breaking both particle symmetry as well as translational invariance. At even higher densities, the phase is a columnar phase, where the particle symmetry is restored, and the particles preferentially occupy even or odd rows along one of the three directions. This phase has translational order in only one direction, and breaks rotational invariance. From finite-size scaling, we demonstrate that both the transitions are first order in nature. We also show that the simpler system with only one type of particle undergoes a single discontinuous phase transition from a disordered phase to a solidlike sublattice phase with an increasing density of particles.

Two-and three-dimensional unsteady lift problems in high-speed flight

NASA Technical Reports Server (NTRS)

Lomax, Harvard; Heaslet, Max A; Fuller, Franklyn B; Sluder, Loma

1952-01-01

The problem of transient lift on two- and three-dimensional wings flying at high speeds is discussed as a boundary-value problem for the classical wave equation. Kirchoff's formula is applied so that the analysis is reduced, just as in the steady state, to an investigation of sources and doublets. The applications include the evaluation of indicial lift and pitching-moment curves for two-dimensional sinking and pitching wings flying at Mach numbers equal to 0, 0.8, 1.0, 1.2 and 2.0. Results for the sinking case are also given for a Mach number of 0.5. In addition, the indicial functions for supersonic-edged triangular wings in both forward and reverse flow are presented and compared with the two-dimensional values.

Laser Fabrication of Two-Dimensional Rotating-Lattice Single Crystal

DOE PAGES

Savytskii, Dmytro; Au-Yeung, Courtney; Dierolf, Volkmar; ...

2017-03-09

A rotating lattice single (RLS) crystal is a unique form of solid, which was fabricated recently as one-dimensional architecture in glass via solid state transformation induced by laser irradiation. In these objects, the lattice rotates gradually and predictably about an axis that lies in the plane of the crystal and is normal to the laser scanning direction. This paper reports on the fabrication of Sb 2S 3 two-dimensional (2D) RLS crystals on the surface of 16SbI 3-84Sb 2S 3 glass, as a model example: individual RLS crystal lines are joined together using "stitching" or "rastering" as two successful protocols. Themore » electron back scattered diffraction mapping and scanning Laue X-ray microdiffraction of the 2D RLS crystals show gradual rotation of lattice comprising of two components, one along the length of each line and another normal to this direction. The former component is determined by the rotation of the first line of the 2D pattern, but the relative contribution of the last component depends on the extent of overlap between two successive lines. By the appropriate choice of initial seed orientation and the direction of scanning, it is possible to control the lattice rotation, and even to reduce it down to 5 for a 50 × 50 μm 2 2D pattern of Sb 2S 3 crystal.« less

Wave Propagation Measurements on Two-Dimensional Lattice.

DTIC Science & Technology

1985-09-15

of boundaries, lattice member connectivities, and structural defects on these parameters. Perhaps, statistical energy analysis or pattern recognition techniques would also be of benefit in such efforts.

Experimental study and modeling of atomic-scale friction in zigzag and armchair lattice orientations of MoS2.

PubMed

Li, Meng; Shi, Jialin; Liu, Lianqing; Yu, Peng; Xi, Ning; Wang, Yuechao

2016-01-01

Physical properties of two-dimensional materials, such as graphene, black phosphorus, molybdenum disulfide (MoS 2 ) and tungsten disulfide, exhibit significant dependence on their lattice orientations, especially for zigzag and armchair lattice orientations. Understanding of the atomic probe motion on surfaces with different orientations helps in the study of anisotropic materials. Unfortunately, there is no comprehensive model that can describe the probe motion mechanism. In this paper, we report a tribological study of MoS 2 in zigzag and armchair orientations. We observed a characteristic power spectrum and friction force values. To explain our results, we developed a modified, two-dimensional, stick-slip Tomlinson model that allows simulation of the probe motion on MoS 2 surfaces by combining the motion in the Mo layer and S layer. Our model fits well with the experimental data and provides a theoretical basis for tribological studies of two-dimensional materials.

Pair correlation functions for identifying spatial correlation in discrete domains

NASA Astrophysics Data System (ADS)

Gavagnin, Enrico; Owen, Jennifer P.; Yates, Christian A.

2018-06-01

Identifying and quantifying spatial correlation are important aspects of studying the collective behavior of multiagent systems. Pair correlation functions (PCFs) are powerful statistical tools that can provide qualitative and quantitative information about correlation between pairs of agents. Despite the numerous PCFs defined for off-lattice domains, only a few recent studies have considered a PCF for discrete domains. Our work extends the study of spatial correlation in discrete domains by defining a new set of PCFs using two natural and intuitive definitions of distance for a square lattice: the taxicab and uniform metric. We show how these PCFs improve upon previous attempts and compare between the quantitative data acquired. We also extend our definitions of the PCF to other types of regular tessellation that have not been studied before, including hexagonal, triangular, and cuboidal. Finally, we provide a comprehensive PCF for any tessellation and metric, allowing investigation of spatial correlation in irregular lattices for which recognizing correlation is less intuitive.

A collection of edge-based elements

NASA Technical Reports Server (NTRS)

Kempel, Leo C.; Volakis, John L.

1992-01-01

Edge-based elements have proved useful in solving electromagnetic problems since they are nondivergent. Previous authors have presented several two and three dimensional elements. Herein, we present four types of elements which are suitable for modeling several types of three dimensional geometries. Distorted brick and triangular prism elements are given in cartesian coordinates as well as the specialized cylindrical shell and pie-shaped prism elements which are suitable for problems best described in polar cylindrical coordinates.

Multigrid for Staggered Lattice Fermions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brower, Richard C.; Clark, M. A.; Strelchenko, Alexei

Critical slowing down in Krylov methods for the Dirac operator presents a major obstacle to further advances in lattice field theory as it approaches the continuum solution. Here we formulate a multi-grid algorithm for the Kogut-Susskind (or staggered) fermion discretization which has proven difficult relative to Wilson multigrid due to its first-order anti-Hermitian structure. The solution is to introduce a novel spectral transformation by the K\\"ahler-Dirac spin structure prior to the Galerkin projection. We present numerical results for the two-dimensional, two-flavor Schwinger model, however, the general formalism is agnostic to dimension and is directly applicable to four-dimensional lattice QCD.

Cooper pair induced frustration and nematicity of two-dimensional magnetic adatom lattices

NASA Astrophysics Data System (ADS)

Schecter, Michael; Syljuâsen, Olav F.; Paaske, Jens

2018-05-01

We propose utilizing the Cooper pair to induce magnetic frustration in systems of two-dimensional (2D) magnetic adatom lattices on s -wave superconducting surfaces. The competition between singlet electron correlations and the RKKY coupling is shown to lead to a variety of hidden-order states that break the point-group symmetry of the 2D adatom lattice at finite temperature. The phase diagram is constructed using a newly developed effective bond theory [M. Schecter et al., Phys. Rev. Lett. 119, 157202 (2017), 10.1103/PhysRevLett.119.157202], and exhibits broad regions of long-range vestigial nematic order.

Terahertz emission from the intrinsic Josephson junctions of high-symmetry thermally-managed Bi2Sr2CaCu2O8+δ microstrip antennas

NASA Astrophysics Data System (ADS)

Klemm, Richard A.; Davis, Andrew E.; Wang, Qing X.; Yamamoto, Takashi; Cerkoney, Daniel P.; Reid, Candy; Koopman, Maximiliaan L.; Minami, Hidetoshi; Kashiwagi, Takanari; Rain, Joseph R.; Doty, Constance M.; Sedlack, Michael A.; Morales, Manuel A.; Watanabe, Chiharu; Tsujimoto, Manabu; Delfanazari, Kaveh; Kadowaki, Kazuo

2017-12-01

We show for high-symmetry disk, square, or equilateral triangular thin microstrip antennas of any composition respectively obeying C ∞v , C 4v , and C 3v point group symmetries, that the transverse magnetic electromagnetic cavity mode wave functions are restricted in form to those that are one-dimensional representations of those point groups. Plots of the common nodal points of the ten lowest-energy non-radiating two-dimensional representations of each of these three symmetries are presented. For comparison with symmetry-broken disk intrinsic Josephson junction microstrip antennas constructed from the highly anisotropic layered superconductor Bi2Sr2CaCu2O8+δ (BSCCO), we present plots of the ten lowest frequency orthonormal wave functions and of their emission power angular distributions. These results are compared with previous results for square and equilateral triangular thin microstrip antennas.

Unstructured viscous grid generation by advancing-front method

NASA Technical Reports Server (NTRS)

Pirzadeh, Shahyar

1993-01-01

A new method of generating unstructured triangular/tetrahedral grids with high-aspect-ratio cells is proposed. The method is based on new grid-marching strategy referred to as 'advancing-layers' for construction of highly stretched cells in the boundary layer and the conventional advancing-front technique for generation of regular, equilateral cells in the inviscid-flow region. Unlike the existing semi-structured viscous grid generation techniques, the new procedure relies on a totally unstructured advancing-front grid strategy resulting in a substantially enhanced grid flexibility and efficiency. The method is conceptually simple but powerful, capable of producing high quality viscous grids for complex configurations with ease. A number of two-dimensional, triangular grids are presented to demonstrate the methodology. The basic elements of the method, however, have been primarily designed with three-dimensional problems in mind, making it extendible for tetrahedral, viscous grid generation.

Bose-Einstein condensate in an optical lattice with Raman-assisted two-dimensional spin-orbit coupling

NASA Astrophysics Data System (ADS)

Pan, Jian-Song; Zhang, Wei; Yi, Wei; Guo, Guang-Can

2016-10-01

In a recent experiment (Z. Wu, L. Zhang, W. Sun, X.-T. Xu, B.-Z. Wang, S.-C. Ji, Y. Deng, S. Chen, X.-J. Liu, and J.-W. Pan, arXiv:1511.08170 [cond-mat.quant-gas]), a Raman-assisted two-dimensional spin-orbit coupling has been realized for a Bose-Einstein condensate in an optical lattice potential. In light of this exciting progress, we study in detail key properties of the system. As the Raman lasers inevitably couple atoms to high-lying bands, the behaviors of the system in both the single- and many-particle sectors are significantly affected. In particular, the high-band effects enhance the plane-wave phase and lead to the emergence of "roton" gaps at low Zeeman fields. Furthermore, we identify high-band-induced topological phase boundaries in both the single-particle and the quasiparticle spectra. We then derive an effective two-band model, which captures the high-band physics in the experimentally relevant regime. Our results not only offer valuable insights into the two-dimensional lattice spin-orbit coupling, but also provide a systematic formalism to model high-band effects in lattice systems with Raman-assisted spin-orbit couplings.

Topological magnon bands in ferromagnetic star lattice.

PubMed

Owerre, S A

2017-05-10

The experimental observation of topological magnon bands and thermal Hall effect in a kagomé lattice ferromagnet Cu(1-3, bdc) has inspired the search for topological magnon effects in various insulating ferromagnets that lack an inversion center allowing a Dzyaloshinskii-Moriya (DM) spin-orbit interaction. The star lattice (also known as the decorated honeycomb lattice) ferromagnet is an ideal candidate for this purpose because it is a variant of the kagomé lattice with additional links that connect the up-pointing and down-pointing triangles. This gives rise to twice the unit cell of the kagomé lattice, and hence more interesting topological magnon effects. In particular, the triangular bridges on the star lattice can be coupled either ferromagnetically or antiferromagnetically which is not possible on the kagomé lattice ferromagnets. Here, we study DM-induced topological magnon bands, chiral edge modes, and thermal magnon Hall effect on the star lattice ferromagnet in different parameter regimes. The star lattice can also be visualized as the parent material from which topological magnon bands can be realized for the kagomé and honeycomb lattices in some limiting cases.

Multiwavelength ultralow-threshold lasing in quantum dot photonic crystal microcavities.

PubMed

Chakravarty, S; Bhattacharya, P; Chakrabarti, S; Mi, Z

2007-05-15

We demonstrate multiwavelength lasing of resonant modes in linear (L3) microcavities in a triangular-lattice 2D photonic crystal (PC) slab. The broad spontaneous emission spectrum from coupled quantum dots, modified by the PC microcavity, is studied as a function of the intensity of incident optical excitation. We observe lasing with an ultralow-threshold power of approximately 600 nW and an output efficiency of approximately 3% at threshold. Two other resonant modes exhibit weaker turnon characteristics and thresholds of approximately 2.5 and 200 microW, respectively.

Image transfer by cascaded stack of photonic crystal and air layers.

PubMed

Shen, C; Michielsen, K; De Raedt, H

2006-01-23

We demonstrate image transfer by a cascaded stack consisting of two and three triangular-lattice photonic crystal slabs separated by air. The quality of the image transfered by the stack is sensitive to the air/photonic crystal interface termination and the frequency. Depending on the frequency and the surface termination, the image can be transfered by the stack with very little deterioration of the resolution, that is the resolution of the final image is approximately the same as the resolution of the image formed behind one single photonic crystal slab.

Bold Diagrammatic Monte Carlo for Fermionic and Fermionized Systems

NASA Astrophysics Data System (ADS)

Svistunov, Boris

2013-03-01

In three different fermionic cases--repulsive Hubbard model, resonant fermions, and fermionized spins-1/2 (on triangular lattice)--we observe the phenomenon of sign blessing: Feynman diagrammatic series features finite convergence radius despite factorial growth of the number of diagrams with diagram order. Bold diagrammatic Monte Carlo technique allows us to sample millions of skeleton Feynman diagrams. With the universal fermionization trick we can fermionize essentially any (bosonic, spin, mixed, etc.) lattice system. The combination of fermionization and Bold diagrammatic Monte Carlo yields a universal first-principle approach to strongly correlated lattice systems, provided the sign blessing is a generic fermionic phenomenon. Supported by NSF and DARPA

Modeling of Triangular Lattice Space Structures with Curved Battens

NASA Technical Reports Server (NTRS)

Chen, Tzikang; Wang, John T.

2005-01-01

Techniques for simulating an assembly process of lattice structures with curved battens were developed. The shape of the curved battens, the tension in the diagonals, and the compression in the battens were predicted for the assembled model. To be able to perform the assembly simulation, a cable-pulley element was implemented, and geometrically nonlinear finite element analyses were performed. Three types of finite element models were created from assembled lattice structures for studying the effects of design and modeling variations on the load carrying capability. Discrepancies in the predictions from these models were discussed. The effects of diagonal constraint failure were also studied.

Exact Solution of the Classical Dimer Model on a Triangular Lattice: Monomer-Monomer Correlations

NASA Astrophysics Data System (ADS)

Basor, Estelle; Bleher, Pavel

2017-12-01

We obtain an asymptotic formula, as {n\\to∞}, for the monomer-monomer correlation function {K_2(n)} in the classical dimer model on a triangular lattice, with the horizontal and vertical weights {w_h=w_v=1} and the diagonal weight {w_d=t > 0}, between two monomers at vertices q and r that are n spaces apart in adjacent rows. We find that {t_c=1/2} is a critical value of t. We prove that in the subcritical case, {0 < t < 1/2}, as {n\\to∞, K_2(n)=K_2(∞)[1-e^{-n/ξ}/n \\Big(C_1+C_2(-1)^n+ O(n^{-1})\\Big) ]}, with explicit formulae for {K_2(∞), ξ, C_1}, and {C_2}. In the supercritical case, {1/2 < t < 1}, we prove that as {n\\to∞, K_2(n)=K_2(∞)\\Bigg[1-e^{-n/ξ}/n \\Big(C_1 cos(ω n+φ_1)+C_2(-1)^n cos(ω n+φ_2)+ C_3+C_4(-1)^n + O(n^{-1})\\Big)\\Bigg]}, with explicit formulae for {K_2(∞), ξ,ω}, and {C_1, C_2, C_3, C_4, φ_1, φ_2}. The proof is based on an extension of the Borodin-Okounkov-Case-Geronimo formula to block Toeplitz determinants and on an asymptotic analysis of the Fredholm determinants in hand.

A discontinuous Galerkin method for the shallow water equations in spherical triangular coordinates

NASA Astrophysics Data System (ADS)

Läuter, Matthias; Giraldo, Francis X.; Handorf, Dörthe; Dethloff, Klaus

2008-12-01

A global model of the atmosphere is presented governed by the shallow water equations and discretized by a Runge-Kutta discontinuous Galerkin method on an unstructured triangular grid. The shallow water equations on the sphere, a two-dimensional surface in R3, are locally represented in terms of spherical triangular coordinates, the appropriate local coordinate mappings on triangles. On every triangular grid element, this leads to a two-dimensional representation of tangential momentum and therefore only two discrete momentum equations. The discontinuous Galerkin method consists of an integral formulation which requires both area (elements) and line (element faces) integrals. Here, we use a Rusanov numerical flux to resolve the discontinuous fluxes at the element faces. A strong stability-preserving third-order Runge-Kutta method is applied for the time discretization. The polynomial space of order k on each curved triangle of the grid is characterized by a Lagrange basis and requires high-order quadature rules for the integration over elements and element faces. For the presented method no mass matrix inversion is necessary, except in a preprocessing step. The validation of the atmospheric model has been done considering standard tests from Williamson et al. [D.L. Williamson, J.B. Drake, J.J. Hack, R. Jakob, P.N. Swarztrauber, A standard test set for numerical approximations to the shallow water equations in spherical geometry, J. Comput. Phys. 102 (1992) 211-224], unsteady analytical solutions of the nonlinear shallow water equations and a barotropic instability caused by an initial perturbation of a jet stream. A convergence rate of O(Δx) was observed in the model experiments. Furthermore, a numerical experiment is presented, for which the third-order time-integration method limits the model error. Thus, the time step Δt is restricted by both the CFL-condition and accuracy demands. Conservation of mass was shown up to machine precision and energy conservation converges for both increasing grid resolution and increasing polynomial order k.

Dirac Fermions in Borophene

NASA Astrophysics Data System (ADS)

Feng, Baojie; Sugino, Osamu; Liu, Ro-Ya; Zhang, Jin; Yukawa, Ryu; Kawamura, Mitsuaki; Iimori, Takushi; Kim, Howon; Hasegawa, Yukio; Li, Hui; Chen, Lan; Wu, Kehui; Kumigashira, Hiroshi; Komori, Fumio; Chiang, Tai-Chang; Meng, Sheng; Matsuda, Iwao

2017-03-01

Honeycomb structures of group IV elements can host massless Dirac fermions with nontrivial Berry phases. Their potential for electronic applications has attracted great interest and spurred a broad search for new Dirac materials especially in monolayer structures. We present a detailed investigation of the β12 sheet, which is a borophene structure that can form spontaneously on a Ag(111) surface. Our tight-binding analysis revealed that the lattice of the β12 sheet could be decomposed into two triangular sublattices in a way similar to that for a honeycomb lattice, thereby hosting Dirac cones. Furthermore, each Dirac cone could be split by introducing periodic perturbations representing overlayer-substrate interactions. These unusual electronic structures were confirmed by angle-resolved photoemission spectroscopy and validated by first-principles calculations. Our results suggest monolayer boron as a new platform for realizing novel high-speed low-dissipation devices.

Surface-assisted DNA self-assembly: An enzyme-free strategy towards formation of branched DNA lattice

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bhanjadeo, Madhabi M.; Academy of Scientific and Innovative Research; Nayak, Ashok K.

DNA based self-assembled nanostructures and DNA origami has proven useful for organizing nanomaterials with firm precision. However, for advanced applications like nanoelectronics and photonics, large-scale organization of self-assembled branched DNA (bDNA) into periodic lattices is desired. In this communication for the first time we report a facile method of self-assembly of Y-shaped bDNA nanostructures on the cationic surface of Aluminum (Al) foil to prepare periodic two dimensional (2D) bDNA lattice. Particularly those Y-shaped bDNA structures having smaller overhangs and unable to self-assemble in solution, they are easily assembled on the surface of Al foil in the absence of ligase. Fieldmore » emission scanning electron microscopy (FESEM) analysis shows homogenous distribution of two-dimensional bDNA lattices across the Al foil. When the assembled bDNA structures were recovered from the Al foil and electrophoresed in nPAGE only higher order polymeric bDNA structures were observed without a trace of monomeric structures which confirms the stability and high yield of the bDNA lattices. Therefore, this enzyme-free economic and efficient strategy for developing bDNA lattices can be utilized in assembling various nanomaterials for functional molecular components towards development of DNA based self-assembled nanodevices. - Highlights: • Al foil surface-assisted self-assembly of monomeric structures into larger branched DNA lattice. • FESEM study confirms the uniform distribution of two-dimensional bDNA lattice structures across the surface of Al foil. • Enzyme-free and economic strategy to prepare higher order structures from simpler DNA nanostructures have been confirmed by recovery assay. • Use of well proven sequences for the preparation of pure Y-shaped monomeric DNA nanostructure with high yield.« less

Quantum electric-dipole liquid on a triangular lattice.

PubMed

Shen, Shi-Peng; Wu, Jia-Chuan; Song, Jun-Da; Sun, Xue-Feng; Yang, Yi-Feng; Chai, Yi-Sheng; Shang, Da-Shan; Wang, Shou-Guo; Scott, James F; Sun, Young

2016-02-04

Geometric frustration and quantum fluctuations may prohibit the formation of long-range ordering even at the lowest temperature, and therefore liquid-like ground states could be expected. A good example is the quantum spin liquid in frustrated magnets. Geometric frustration and quantum fluctuations can happen beyond magnetic systems. Here we propose that quantum electric-dipole liquids, analogues of quantum spin liquids, could emerge in frustrated dielectrics where antiferroelectrically coupled electric dipoles reside on a triangular lattice. The quantum paraelectric hexaferrite BaFe12O19 with geometric frustration represents a promising candidate for the proposed electric-dipole liquid. We present a series of experimental lines of evidence, including dielectric permittivity, heat capacity and thermal conductivity measured down to 66 mK, to reveal the existence of an unusual liquid-like quantum phase in BaFe12O19, characterized by itinerant low-energy excitations with a small gap. The possible quantum liquids of electric dipoles in frustrated dielectrics open up a fresh playground for fundamental physics.

3D printed hierarchical honeycombs with shape integrity under large compressive deformations

DOE PAGES

Chen, Yanyu; Li, Tiantian; Jia, Zian; ...

2017-10-12

Here, we describe the in-plane compressive performance of a new type of hierarchical cellular structure created by replacing cell walls in regular honeycombs with triangular lattice configurations. The fabrication of this relatively complex material architecture with size features spanning from micrometer to centimeter is facilitated by the availability of commercial 3D printers. We apply to these hierarchical honeycombs a thermal treatment that facilitates the shape preservation and structural integrity of the structures under large compressive loading. The proposed hierarchical honeycombs exhibit a progressive failure mode, along with improved stiffness and energy absorption under uniaxial compression. High energy dissipation and shapemore » integrity at large imposed strains (up to 60%) have also been observed in these hierarchical honeycombs under cyclic loading. Experimental and numerical studies suggest that these anomalous mechanical behaviors are attributed to the introduction of a structural hierarchy, intrinsically controlled by the cell wall slenderness of the triangular lattice and by the shape memory effect induced by the thermal and mechanical compressive treatment.« less

3D printed hierarchical honeycombs with shape integrity under large compressive deformations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Yanyu; Li, Tiantian; Jia, Zian

Here, we describe the in-plane compressive performance of a new type of hierarchical cellular structure created by replacing cell walls in regular honeycombs with triangular lattice configurations. The fabrication of this relatively complex material architecture with size features spanning from micrometer to centimeter is facilitated by the availability of commercial 3D printers. We apply to these hierarchical honeycombs a thermal treatment that facilitates the shape preservation and structural integrity of the structures under large compressive loading. The proposed hierarchical honeycombs exhibit a progressive failure mode, along with improved stiffness and energy absorption under uniaxial compression. High energy dissipation and shapemore » integrity at large imposed strains (up to 60%) have also been observed in these hierarchical honeycombs under cyclic loading. Experimental and numerical studies suggest that these anomalous mechanical behaviors are attributed to the introduction of a structural hierarchy, intrinsically controlled by the cell wall slenderness of the triangular lattice and by the shape memory effect induced by the thermal and mechanical compressive treatment.« less

A Firefly-Inspired Method for Protein Structure Prediction in Lattice Models

PubMed Central

Maher, Brian; Albrecht, Andreas A.; Loomes, Martin; Yang, Xin-She; Steinhöfel, Kathleen

2014-01-01

We introduce a Firefly-inspired algorithmic approach for protein structure prediction over two different lattice models in three-dimensional space. In particular, we consider three-dimensional cubic and three-dimensional face-centred-cubic (FCC) lattices. The underlying energy models are the Hydrophobic-Polar (H-P) model, the Miyazawa–Jernigan (M-J) model and a related matrix model. The implementation of our approach is tested on ten H-P benchmark problems of a length of 48 and ten M-J benchmark problems of a length ranging from 48 until 61. The key complexity parameter we investigate is the total number of objective function evaluations required to achieve the optimum energy values for the H-P model or competitive results in comparison to published values for the M-J model. For H-P instances and cubic lattices, where data for comparison are available, we obtain an average speed-up over eight instances of 2.1, leaving out two extreme values (otherwise, 8.8). For six M-J instances, data for comparison are available for cubic lattices and runs with a population size of 100, where, a priori, the minimum free energy is a termination criterion. The average speed-up over four instances is 1.2 (leaving out two extreme values, otherwise 1.1), which is achieved for a population size of only eight instances. The present study is a test case with initial results for ad hoc parameter settings, with the aim of justifying future research on larger instances within lattice model settings, eventually leading to the ultimate goal of implementations for off-lattice models. PMID:24970205

A firefly-inspired method for protein structure prediction in lattice models.

PubMed

Maher, Brian; Albrecht, Andreas A; Loomes, Martin; Yang, Xin-She; Steinhöfel, Kathleen

2014-01-07

We introduce a Firefly-inspired algorithmic approach for protein structure prediction over two different lattice models in three-dimensional space. In particular, we consider three-dimensional cubic and three-dimensional face-centred-cubic (FCC) lattices. The underlying energy models are the Hydrophobic-Polar (H-P) model, the Miyazawa-Jernigan (M-J) model and a related matrix model. The implementation of our approach is tested on ten H-P benchmark problems of a length of 48 and ten M-J benchmark problems of a length ranging from 48 until 61. The key complexity parameter we investigate is the total number of objective function evaluations required to achieve the optimum energy values for the H-P model or competitive results in comparison to published values for the M-J model. For H-P instances and cubic lattices, where data for comparison are available, we obtain an average speed-up over eight instances of 2.1, leaving out two extreme values (otherwise, 8.8). For six M-J instances, data for comparison are available for cubic lattices and runs with a population size of 100, where, a priori, the minimum free energy is a termination criterion. The average speed-up over four instances is 1.2 (leaving out two extreme values, otherwise 1.1), which is achieved for a population size of only eight instances. The present study is a test case with initial results for ad hoc parameter settings, with the aim of justifying future research on larger instances within lattice model settings, eventually leading to the ultimate goal of implementations for off-lattice models.

Transition-metal oxides with triangular lattices: generation of new magnetic and electronic properties.

PubMed

Maignan, A; Kobayashi, W; Hébert, S; Martinet, G; Pelloquin, D; Bellido, N; Simon, Ch

2008-10-06

The search for multifunctional materials as multiferroics to be applied in microelectronic or for new, chemically stable and nontoxic, thermoelectric materials to recover waste heat is showing a common interest in the oxides whose structures contain a triangular network of transition-metal cations. To illustrate this point, two ternary systems, Ba-Co-O and Ca-Co-O, have been chosen. It is shown that new phases with a complex triangular structure can be discovered, for instance, by introduction of Ga (3+) into the Ba-Co-O system to stabilize Ba 6Ga 2Co 11O 26 and Ba 2GaCo 8O 14, which both belong to a large family of compounds with formula [Ba(Co,Ga)O 3-delta] n [BaCo 8O 11]. In the latter, both sublattices contain triangular networks derived from the hexagonal perovskite and the spinel structure. Among the hexagonal perovskite, the Ca 3Co 2O 6 crystals give clear evidence where the coupling of charges and spins is at the origin of a magnetocapacitance effect. In particular, the ferrimagnetic to ferromagnetic transition, with a one-third plateau on the M( H) curve characteristic of triangular magnetism, is accompanied by a peak in the dielectric constant. A second class of cobaltites is the focus of much interest. Their 2D structure, containing CoO 2 planes isostructural to a CdI 2 slice that are stacked in an incommensurate way with rock salt type layers, is referred to misfit cobaltite. The 2D triangular network of edge-shared CoO 6 octahedra is believed to be responsible for large values of the Seebeck coefficient and low electrical resistivity. A clear relationship between the structuresincommensurability ratiosand the electronic properties is evidenced, showing that the charge carrier concentration can be tuned via the control of the ionic radius of the cations in the separating layers.

Hidden-Symmetry-Protected Topological Semimetals on a Square Lattice

NASA Astrophysics Data System (ADS)

Hou, Jing-Min

2013-09-01

We study a two-dimensional fermionic square lattice, which supports the existence of a two-dimensional Weyl semimetal, quantum anomalous Hall effect, and 2π-flux topological semimetal in different parameter ranges. We show that the band degenerate points of the two-dimensional Weyl semimetal and 2π-flux topological semimetal are protected by two distinct novel hidden symmetries, which both correspond to antiunitary composite operations. When these hidden symmetries are broken, a gap opens between the conduction and valence bands, turning the system into a insulator. With appropriate parameters, a quantum anomalous Hall effect emerges. The degenerate point at the boundary between the quantum anomalous Hall insulator and trivial band insulator is also protected by the hidden symmetry.

Lattice gas simulations of dynamical geometry in two dimensions.

PubMed

Klales, Anna; Cianci, Donato; Needell, Zachary; Meyer, David A; Love, Peter J

2010-10-01

We present a hydrodynamic lattice gas model for two-dimensional flows on curved surfaces with dynamical geometry. This model is an extension to two dimensions of the dynamical geometry lattice gas model previously studied in one dimension. We expand upon a variation of the two-dimensional flat space Frisch-Hasslacher-Pomeau (FHP) model created by Frisch [Phys. Rev. Lett. 56, 1505 (1986)] and independently by Wolfram, and modified by Boghosian [Philos. Trans. R. Soc. London, Ser. A 360, 333 (2002)]. We define a hydrodynamic lattice gas model on an arbitrary triangulation whose flat space limit is the FHP model. Rules that change the geometry are constructed using the Pachner moves, which alter the triangulation but not the topology. We present results on the growth of the number of triangles as a function of time. Simulations show that the number of triangles grows with time as t(1/3), in agreement with a mean-field prediction. We also present preliminary results on the distribution of curvature for a typical triangulation in these simulations.

Lie Symmetry Analysis of the Inhomogeneous Toda Lattice Equation via Semi-Discrete Exterior Calculus

NASA Astrophysics Data System (ADS)

Liu, Jiang; Wang, Deng-Shan; Yin, Yan-Bin

2017-06-01

In this work, the Lie point symmetries of the inhomogeneous Toda lattice equation are obtained by semi-discrete exterior calculus, which is a semi-discrete version of Harrison and Estabrook’s geometric approach. A four-dimensional Lie algebra and its one-, two- and three-dimensional subalgebras are given. Two similarity reductions of the inhomogeneous Toda lattice equation are obtained by using the symmetry vectors. Supported by National Natural Science Foundation of China under Grant Nos. 11375030, 11472315, and Department of Science and Technology of Henan Province under Grant No. 162300410223 and Beijing Finance Funds of Natural Science Program for Excellent Talents under Grant No. 2014000026833ZK19

Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices

NASA Astrophysics Data System (ADS)

da Luz, H. L. F.; Abdullaev, F. Kh.; Gammal, A.; Salerno, M.; Tomio, Lauro

2010-10-01

The existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with a linear optical lattice (LOL) in the x direction and a nonlinear optical lattice (NOL) in the y direction, where the NOL can be generated by a periodic spatial modulation of the scattering length using an optically induced Feshbach resonance is demonstrated. In particular, we show that such crossed LOLs and NOLs allow for stabilizing two-dimensional solitons against decay or collapse for both attractive and repulsive interactions. The solutions for the soliton stability are investigated analytically, by using a multi-Gaussian variational approach, with the Vakhitov-Kolokolov necessary criterion for stability; and numerically, by using the relaxation method and direct numerical time integrations of the Gross-Pitaevskii equation. Very good agreement of the results corresponding to both treatments is observed.

Spectral (Finite) Volume Method for Conservation Laws on Unstructured Grids II: Extension to Two Dimensional Scalar Equation

NASA Technical Reports Server (NTRS)

Wang, Z. J.; Liu, Yen; Kwak, Dochan (Technical Monitor)

2002-01-01

The framework for constructing a high-order, conservative Spectral (Finite) Volume (SV) method is presented for two-dimensional scalar hyperbolic conservation laws on unstructured triangular grids. Each triangular grid cell forms a spectral volume (SV), and the SV is further subdivided into polygonal control volumes (CVs) to supported high-order data reconstructions. Cell-averaged solutions from these CVs are used to reconstruct a high order polynomial approximation in the SV. Each CV is then updated independently with a Godunov-type finite volume method and a high-order Runge-Kutta time integration scheme. A universal reconstruction is obtained by partitioning all SVs in a geometrically similar manner. The convergence of the SV method is shown to depend on how a SV is partitioned. A criterion based on the Lebesgue constant has been developed and used successfully to determine the quality of various partitions. Symmetric, stable, and convergent linear, quadratic, and cubic SVs have been obtained, and many different types of partitions have been evaluated. The SV method is tested for both linear and non-linear model problems with and without discontinuities.

Matter-wave solitons supported by quadrupole-quadrupole interactions and anisotropic discrete lattices

NASA Astrophysics Data System (ADS)

Zhong, Rong-Xuan; Huang, Nan; Li, Huang-Wu; He, He-Xiang; Lü, Jian-Tao; Huang, Chun-Qing; Chen, Zhao-Pin

2018-04-01

We numerically and analytically investigate the formations and features of two-dimensional discrete Bose-Einstein condensate solitons, which are constructed by quadrupole-quadrupole interactional particles trapped in the tunable anisotropic discrete optical lattices. The square optical lattices in the model can be formed by two pairs of interfering plane waves with different intensities. Two hopping rates of the particles in the orthogonal directions are different, which gives rise to a linear anisotropic system. We find that if all of the pairs of dipole and anti-dipole are perpendicular to the lattice panel and the line connecting the dipole and anti-dipole which compose the quadrupole is parallel to horizontal direction, both the linear anisotropy and the nonlocal nonlinear one can strongly influence the formations of the solitons. There exist three patterns of stable solitons, namely horizontal elongation quasi-one-dimensional discrete solitons, disk-shape isotropic pattern solitons and vertical elongation quasi-continuous solitons. We systematically demonstrate the relationships of chemical potential, size and shape of the soliton with its total norm and vertical hopping rate and analytically reveal the linear dispersion relation for quasi-one-dimensional discrete solitons.

Ultracold bosons in a one-dimensional optical lattice chain: Newton's cradle and Bose enhancement effect

NASA Astrophysics Data System (ADS)

Wang, Ji-Guo; Yang, Shi-Jie

2017-05-01

We study a model to realize the long-distance correlated tunneling of ultracold bosons in a one-dimensional optical lattice chain. The model reveals the behavior of a quantum Newton's cradle, which is the perfect transfer between two macroscopic quantum states. Due to the Bose enhancement effect, we find that the resonantly tunneling through a Mott domain is greatly enhanced.

Pinning, flux diodes and ratchets for vortices interacting with conformal pinning arrays

DOE PAGES

Olson Reichhardt, C. J.; Wang, Y. L.; Xiao, Z. L.; ...

2016-05-31

A conformal pinning array can be created by conformally transforming a uniform triangular pinning lattice to produce a new structure in which the six-fold ordering of the original lattice is conserved but where there is a spatial gradient in the density of pinning sites. Here we examine several aspects of vortices interacting with conformal pinning arrays and how they can be used to create a flux flow diode effect for driving vortices in different directions across the arrays. Under the application of an ac drive, a pronounced vortex ratchet effect occurs where the vortices flow in the easy direction ofmore » the array asymmetry. When the ac drive is applied perpendicular to the asymmetry direction of the array, it is possible to realize a transverse vortex ratchet effect where there is a generation of a dc flow of vortices perpendicular to the ac drive due to the creation of a noise correlation ratchet by the plastic motion of the vortices. We also examine vortex transport in experiments and compare the pinning effectiveness of conformal arrays to uniform triangular pinning arrays. In conclusion, we find that a triangular array generally pins the vortices more effectively at the first matching field and below, while the conformal array is more effective at higher fields where interstitial vortex flow occurs.« less

Experimental study and modeling of atomic-scale friction in zigzag and armchair lattice orientations of MoS2

PubMed Central

Li, Meng; Shi, Jialin; Liu, Lianqing; Yu, Peng; Xi, Ning; Wang, Yuechao

2016-01-01

Abstract Physical properties of two-dimensional materials, such as graphene, black phosphorus, molybdenum disulfide (MoS2) and tungsten disulfide, exhibit significant dependence on their lattice orientations, especially for zigzag and armchair lattice orientations. Understanding of the atomic probe motion on surfaces with different orientations helps in the study of anisotropic materials. Unfortunately, there is no comprehensive model that can describe the probe motion mechanism. In this paper, we report a tribological study of MoS2 in zigzag and armchair orientations. We observed a characteristic power spectrum and friction force values. To explain our results, we developed a modified, two-dimensional, stick-slip Tomlinson model that allows simulation of the probe motion on MoS2 surfaces by combining the motion in the Mo layer and S layer. Our model fits well with the experimental data and provides a theoretical basis for tribological studies of two-dimensional materials. PMID:27877869

Effective One-Dimensional Coupling in the Highly Frustrated Square-Lattice Itinerant Magnet CaCo2 -yAs2

NASA Astrophysics Data System (ADS)

Sapkota, A.; Ueland, B. G.; Anand, V. K.; Sangeetha, N. S.; Abernathy, D. L.; Stone, M. B.; Niedziela, J. L.; Johnston, D. C.; Kreyssig, A.; Goldman, A. I.; McQueeney, R. J.

2017-10-01

Inelastic neutron scattering measurements on the itinerant antiferromagnet CaCo2 -yAs2 at a temperature of 8 K reveal two orthogonal planes of scattering perpendicular to the Co square lattice in reciprocal space, demonstrating the presence of effective one-dimensional spin interactions. These results are shown to arise from near-perfect bond frustration within the J1-J2 Heisenberg model on a square lattice with ferromagnetic J1 and hence indicate that the extensive previous experimental and theoretical study of the J1-J2 Heisenberg model on local-moment square spin lattices should be expanded to include itinerant spin systems.

Effective One-Dimensional Coupling in the Highly Frustrated Square-Lattice Itinerant Magnet CaCo_{2-y}As_{2}.

PubMed

Sapkota, A; Ueland, B G; Anand, V K; Sangeetha, N S; Abernathy, D L; Stone, M B; Niedziela, J L; Johnston, D C; Kreyssig, A; Goldman, A I; McQueeney, R J

2017-10-06

Inelastic neutron scattering measurements on the itinerant antiferromagnet CaCo_{2-y}As_{2} at a temperature of 8 K reveal two orthogonal planes of scattering perpendicular to the Co square lattice in reciprocal space, demonstrating the presence of effective one-dimensional spin interactions. These results are shown to arise from near-perfect bond frustration within the J_{1}-J_{2} Heisenberg model on a square lattice with ferromagnetic J_{1} and hence indicate that the extensive previous experimental and theoretical study of the J_{1}-J_{2} Heisenberg model on local-moment square spin lattices should be expanded to include itinerant spin systems.

Effective One-Dimensional Coupling in the Highly Frustrated Square-Lattice Itinerant Magnet CaCo 2 - y As 2

DOE PAGES

Sapkota, A.; Ueland, B. G.; Anand, V. K.; ...

2017-10-02

Inelastic neutron scattering measurements on the itinerant antiferromagnet CaCo 2–yAs 2 at a temperature of 8 K reveal two orthogonal planes of scattering perpendicular to the Co square lattice in reciprocal space, demonstrating the presence of effective one-dimensional spin interactions. Here, these results are shown to arise from near-perfect bond frustration within the J 1–J 2 Heisenberg model on a square lattice with ferromagnetic J 1 and hence indicate that the extensive previous experimental and theoretical study of the J 1–J 2 Heisenberg model on local-moment square spin lattices should be expanded to include itinerant spin systems.

Effective One-Dimensional Coupling in the Highly Frustrated Square-Lattice Itinerant Magnet CaCo 2 - y As 2

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sapkota, A.; Ueland, B. G.; Anand, V. K.

Inelastic neutron scattering measurements on the itinerant antiferromagnet CaCo 2–yAs 2 at a temperature of 8 K reveal two orthogonal planes of scattering perpendicular to the Co square lattice in reciprocal space, demonstrating the presence of effective one-dimensional spin interactions. Here, these results are shown to arise from near-perfect bond frustration within the J 1–J 2 Heisenberg model on a square lattice with ferromagnetic J 1 and hence indicate that the extensive previous experimental and theoretical study of the J 1–J 2 Heisenberg model on local-moment square spin lattices should be expanded to include itinerant spin systems.

Geometric stability spectra of dipolar Bose gases in tunable optical lattices

NASA Astrophysics Data System (ADS)

Corson, John P.; Wilson, Ryan M.; Bohn, John L.

2013-07-01

We examine the stability of quasi-two-dimensional dipolar Bose-Einstein condensates in the presence of weak optical lattices of various geometries. We find that when the condensate possesses a roton-maxon quasiparticle dispersion, the conditions for stability exhibit a strong dependence both on the lattice geometry and the polarization tilt. This results in rich structures in the system's stability diagram akin to spectroscopic signatures. We show how these structures originate from the mode matching of rotons to the perturbing lattice. In the case of a one-dimensional lattice, some of the features emerge only when the polarization axis is tilted into the plane of the condensate. Our results suggest that the stability diagram may be used as a novel means to spectroscopically measure rotons in dipolar condensates.

Spatial search on a two-dimensional lattice with long-range interactions

NASA Astrophysics Data System (ADS)

Osada, Tomo; Sanaka, Kaoru; Munro, William J.; Nemoto, Kae

2018-06-01

Quantum-walk-based algorithms that search a marked location among N locations on a d -dimensional lattice succeeds in time O (√{N }) for d >2 , while this is not found to be possible when d =2 . In this paper, we consider a spatial search algorithm using continuous-time quantum walk on a two-dimensional square lattice with the existence of additional long-range edges. We examined such a search on a probabilistic graph model where an edge connecting non-nearest-neighbor lattice points i and j apart by a distance |i -j | is added by probability pi j=|i-j | -α(α ≥0 ) . Through numerical analysis, we found that the search succeeds in time O (√{N }) when α ≤αc=2.4 ±0.1 . For α >2 , the expectation value of the additional long-range edges on each node scales as a constant when N →∞ , which means that search time of O (√{N }) is achieved on a graph with average degree scaling as a constant.

Damping of Bogoliubov excitations in optical lattices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsuchiya, Shunji; Department of Physics, Waseda University, 3-4-1 Okubo, Tokyo 169-8555; Griffin, Allan

2004-08-01

Extending recent work to finite temperatures, we calculate the Landau damping of a Bogoliubov excitation in an optical lattice, due to the coupling to a thermal cloud of such excitations. For simplicity, we consider a one-dimensional Bose-Hubbard model and restrict ourselves to the first energy band. For energy conservation to be satisfied, the excitations in the collision processes must exhibit ''anomalous dispersion,'' analogous to phonons in superfluid {sup 4}He. This leads to the disappearance of all damping processes when Un{sup c0}{>=}6J, where U is the on-site interaction, J is the hopping matrix element, and n{sup c0}(T) is the number ofmore » condensate atoms at a lattice site. This phenomenon also occurs in two-dimensional and three-dimensional optical lattices. The disappearance of Beliaev damping above a threshold wave vector is noted.« less

Tight-Binding Study of Polarons in Two-Dimensional Systems: Implications for Organic Field-Effect Transistor Materials

NASA Astrophysics Data System (ADS)

Lei, Jie

2011-03-01

In order to understand the electronic and transport properties of organic field-effect transistor (FET) materials, we theoretically studied the polarons in two-dimensional systems using a tight-binding model with the Holstein type and Su--Schrieffer--Heeger type electron--lattice couplings. By numerical calculations, it was found that a carrier accepts four kinds of localization, which are named the point polaron, two-dimensional polaron, one-dimensional polaron, and the extended state. The degree of localization is sensitive to the following parameters in the model: the strength and type of electron--lattice couplings, and the signs and relative magnitudes of transfer integrals. When a parameter set for a single-crystal phase of pentacene is applied within the Holstein model, a considerably delocalized hole polaron is found, consistent with the bandlike transport mechanism.

Algebraic Theory of Crystal Vibrations: Localization Properties of Wave Functions in Two-Dimensional Lattices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dietz, Barbara; Iachello, Francesco; Macek, Michal

The localization properties of the wave functions of vibrations in two-dimensional (2D) crystals are studied numerically for square and hexagonal lattices within the framework of an algebraic model. The wave functions of 2D lattices have remarkable localization properties, especially at the van Hove singularities (vHs). Finite-size sheets with a hexagonal lattice (graphene-like materials), in addition, exhibit at zero energy a localization of the wave functions at zigzag edges, so-called edge states. The striped structure of the wave functions at a vHs is particularly noteworthy. We have investigated its stability and that of the edge states with respect to perturbations inmore » the lattice structure, and the effect of the boundary shape on the localization properties. We find that the stripes disappear instantaneously at the vHs in a square lattice when turning on the perturbation, whereas they broaden but persist at the vHss in a hexagonal lattice. For one of them, they eventually merge into edge states with increasing coupling, which, in contrast to the zero-energy edge states, are localized at armchair edges. The results are corroborated based on participation ratios, obtained under various conditions.« less

Algebraic Theory of Crystal Vibrations: Localization Properties of Wave Functions in Two-Dimensional Lattices

DOE PAGES

Dietz, Barbara; Iachello, Francesco; Macek, Michal

2017-08-07

The localization properties of the wave functions of vibrations in two-dimensional (2D) crystals are studied numerically for square and hexagonal lattices within the framework of an algebraic model. The wave functions of 2D lattices have remarkable localization properties, especially at the van Hove singularities (vHs). Finite-size sheets with a hexagonal lattice (graphene-like materials), in addition, exhibit at zero energy a localization of the wave functions at zigzag edges, so-called edge states. The striped structure of the wave functions at a vHs is particularly noteworthy. We have investigated its stability and that of the edge states with respect to perturbations inmore » the lattice structure, and the effect of the boundary shape on the localization properties. We find that the stripes disappear instantaneously at the vHs in a square lattice when turning on the perturbation, whereas they broaden but persist at the vHss in a hexagonal lattice. For one of them, they eventually merge into edge states with increasing coupling, which, in contrast to the zero-energy edge states, are localized at armchair edges. The results are corroborated based on participation ratios, obtained under various conditions.« less

Quantum Statistical Mechanics on a Quantum Computer

NASA Astrophysics Data System (ADS)

Raedt, H. D.; Hams, A. H.; Michielsen, K.; Miyashita, S.; Saito, K.

We describe a quantum algorithm to compute the density of states and thermal equilibrium properties of quantum many-body systems. We present results obtained by running this algorithm on a software implementation of a 21-qubit quantum computer for the case of an antiferromagnetic Heisenberg model on triangular lattices of different size.

Quantum Transport Properties in Two-Dimensional and Low Dimensional Systems

NASA Astrophysics Data System (ADS)

Fang, Hao

1991-02-01

The quantum transport properties in quasi two -dimensional and zero-dimensional systems have been studied at magnetic field of 0 - 8T and low temperatures down to 1.3K. In the (100) Si inversion layer, we investigated the effect of valley splitting on the value of the enhanced effective g factor by the tilted magnetic field measurement. The valley splitting is determined from the beat effect on samples with measurable valley splitting behavior due to misorientation effects. Experimental results illustrate that the effective g factor is enhanced by many body interactions and that the valley splitting has no obvious effect on the g-value. A simulation calculation with a Gaussian distribution of density of states has been carried out and the simulated results are in an excellent agreement with the experimental data. A new and very simple technique has been developed for fabricating two-dimensional periodic submicron structures with feature sizes down to about 300 A. The etching mask is made by coating the material surface with a monolayer of close-packed uniform latex particles. We have demonstrated the formation of a quasi zero-dimensional quantum dot array and performed capacitance measurements on GaAs/AlGaAs heterostructure samples with periodicities ranging from 3000 to 4000 A. A series of nearly equally spaced peaks in a curve of the derivative of capacitance with respect to gate voltage, which corresponds to the energy levels formed by the lateral electric confining potential, is observed. The energy spacings and effective dot widths estimated from a simple parabolic potential model are consistent with the experimental data. Novel magnetoresistance oscillations in a two -dimensional electron gas modulated by a two-dimensional triangular superlattice potential are observed in GaAs/AlGaAs heterostructures. The new oscillations appear at very low magnetic fields and the peak positions are directly determined by the magnetic field and the periodicity of the modulation structure. New oscillation results from the modulation-broadened Landau bandwidth and the induced density of states variation with magnetic field. Physical explanations and theoretical approaches for the commensurability problem in a two-dimensional triangular superlattice potential are presented. The differences in oscillation frequencies and phase factors for two kinds of samples correlate with structures differing in degree of depletion and the resulting geometry.

Magnetic assembly and annealing of colloidal lattices and superlattices.

PubMed

Tierno, Pietro

2014-07-08

The ability to assemble mesoscopic colloidal lattices above a surface is important for fundamental studies related with nucleation and crystallization but also for a variety of technological applications in photonics and microengineering. Current techniques based on particle sedimentation above a lithographic template are limited by a slow deposition process and by the use of static templates, which make difficult to implement fast annealing procedures. Here it is demonstrated a method to realize and anneal a series of colloidal lattices displaying triangular, honeycomb, or kagome-like symmetry above a structure magnetic substrate. By using a binary mixture of particles, superlattices can be realized increasing further the variety and complexity of the colloidal patterns which can be produced.

Spin-orbital quantum liquid on the honeycomb lattice

NASA Astrophysics Data System (ADS)

Corboz, Philippe

2013-03-01

The symmetric Kugel-Khomskii can be seen as a minimal model describing the interactions between spin and orbital degrees of freedom in transition-metal oxides with orbital degeneracy, and it is equivalent to the SU(4) Heisenberg model of four-color fermionic atoms. We present simulation results for this model on various two-dimensional lattices obtained with infinite projected-entangled pair states (iPEPS), an efficient variational tensor-network ansatz for two dimensional wave functions in the thermodynamic limit. This approach can be seen as a two-dimensional generalization of matrix product states - the underlying ansatz of the density matrix renormalization group method. We find a rich variety of exotic phases: while on the square and checkerboard lattices the ground state exhibits dimer-Néel order and plaquette order, respectively, quantum fluctuations on the honeycomb lattice destroy any order, giving rise to a spin-orbital liquid. Our results are supported from flavor-wave theory and exact diagonalization. Furthermore, the properties of the spin-orbital liquid state on the honeycomb lattice are accurately accounted for by a projected variational wave-function based on the pi-flux state of fermions on the honeycomb lattice at 1/4-filling. In that state, correlations are algebraic because of the presence of a Dirac point at the Fermi level, suggesting that the ground state is an algebraic spin-orbital liquid. This model provides a good starting point to understand the recently discovered spin-orbital liquid behavior of Ba3CuSb2O9. The present results also suggest to choose optical lattices with honeycomb geometry in the search for quantum liquids in ultra-cold four-color fermionic atoms. We acknowledge the financial support from the Swiss National Science Foundation.

Lipid-bilayer-assisted two-dimensional self-assembly of DNA origami nanostructures

NASA Astrophysics Data System (ADS)

Suzuki, Yuki; Endo, Masayuki; Sugiyama, Hiroshi

2015-08-01

Self-assembly is a ubiquitous approach to the design and fabrication of novel supermolecular architectures. Here we report a strategy termed `lipid-bilayer-assisted self-assembly' that is used to assemble DNA origami nanostructures into two-dimensional lattices. DNA origami structures are electrostatically adsorbed onto a mica-supported zwitterionic lipid bilayer in the presence of divalent cations. We demonstrate that the bilayer-adsorbed origami units are mobile on the surface and self-assembled into large micrometre-sized lattices in their lateral dimensions. Using high-speed atomic force microscopy imaging, a variety of dynamic processes involved in the formation of the lattice, such as fusion, reorganization and defect filling, are successfully visualized. The surface modifiability of the assembled lattice is also demonstrated by in situ decoration with streptavidin molecules. Our approach provides a new strategy for preparing versatile scaffolds for nanofabrication and paves the way for organizing functional nanodevices in a micrometer space.

Lipid-bilayer-assisted two-dimensional self-assembly of DNA origami nanostructures

PubMed Central

Endo, Masayuki; Sugiyama, Hiroshi

2015-01-01

Self-assembly is a ubiquitous approach to the design and fabrication of novel supermolecular architectures. Here we report a strategy termed ‘lipid-bilayer-assisted self-assembly' that is used to assemble DNA origami nanostructures into two-dimensional lattices. DNA origami structures are electrostatically adsorbed onto a mica-supported zwitterionic lipid bilayer in the presence of divalent cations. We demonstrate that the bilayer-adsorbed origami units are mobile on the surface and self-assembled into large micrometre-sized lattices in their lateral dimensions. Using high-speed atomic force microscopy imaging, a variety of dynamic processes involved in the formation of the lattice, such as fusion, reorganization and defect filling, are successfully visualized. The surface modifiability of the assembled lattice is also demonstrated by in situ decoration with streptavidin molecules. Our approach provides a new strategy for preparing versatile scaffolds for nanofabrication and paves the way for organizing functional nanodevices in a micrometer space. PMID:26310995

Electrostatic modulation of periodic potentials in a two-dimensional electron gas: From antidot lattice to quantum dot lattice

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goswami, Srijit; Aamir, Mohammed Ali; Shamim, Saquib

2013-12-04

We use a dual gated device structure to introduce a gate-tuneable periodic potential in a GaAs/AlGaAs two dimensional electron gas (2DEG). Using only a suitable choice of gate voltages we can controllably alter the potential landscape of the bare 2DEG, inducing either a periodic array of antidots or quantum dots. Antidots are artificial scattering centers, and therefore allow for a study of electron dynamics. In particular, we show that the thermovoltage of an antidot lattice is particularly sensitive to the relative positions of the Fermi level and the antidot potential. A quantum dot lattice, on the other hand, provides themore » opportunity to study correlated electron physics. We find that its current-voltage characteristics display a voltage threshold, as well as a power law scaling, indicative of collective Coulomb blockade in a disordered background.« less

Lattice Boltzmann Equation On a 2D Rectangular Grid

NASA Technical Reports Server (NTRS)

Bouzidi, MHamed; DHumieres, Dominique; Lallemand, Pierre; Luo, Li-Shi; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

We construct a multi-relaxation lattice Boltzmann model on a two-dimensional rectangular grid. The model is partly inspired by a previous work of Koelman to construct a lattice BGK model on a two-dimensional rectangular grid. The linearized dispersion equation is analyzed to obtain the constraints on the isotropy of the transport coefficients and Galilean invariance for various wave propagations in the model. The linear stability of the model is also studied. The model is numerically tested for three cases: (a) a vortex moving with a constant velocity on a mesh periodic boundary conditions; (b) Poiseuille flow with an arbitrasy inclined angle with respect to the lattice orientation: and (c) a cylinder &symmetrically placed in a channel. The numerical results of these tests are compared with either analytic solutions or the results obtained by other methods. Satisfactory results are obtained for the numerical simulations.

Two-dimensional network of atomtronic qubits

NASA Astrophysics Data System (ADS)

Safaei, S.; Grémaud, B.; Dumke, R.; Kwek, L.-C.; Amico, L.; Miniatura, C.

2018-04-01

Through a combination of laser beams, we engineer a two-dimensional optical lattice of Mexican hat potentials able to host atoms in its ring-shaped wells. When tunneling can be ignored (at high laser intensities), we show that a well-defined qubit can be associated with the states of the atoms trapped in each of the rings. Each of these two-level systems can be manipulated by a suitable configuration of Raman laser beams imprinting a synthetic flux onto each Mexican hat cell of the lattice. Overall, we believe that the system has the potential to form a scalable architecture for atomtronic flux qubits.

Tunable spin-orbit coupling for ultracold atoms in two-dimensional optical lattices

NASA Astrophysics Data System (ADS)

Grusdt, Fabian; Li, Tracy; Bloch, Immanuel; Demler, Eugene

2017-06-01

Spin-orbit coupling (SOC) is at the heart of many exotic band structures and can give rise to many-body states with topological order. Here we present a general scheme based on a combination of microwave driving and lattice shaking for the realization of two-dimensional SOC with ultracold atoms in systems with inversion symmetry. We show that the strengths of Rashba and Dresselhaus SOC can be independently tuned in a spin-dependent square lattice. More generally, our method can be used to open gaps between different spin states without breaking time-reversal symmetry. We demonstrate that this allows for the realization of topological insulators with nontrivial spin textures closely related to the Kane-Mele model.

Stable biexcitons in two-dimensional metal-halide perovskites with strong dynamic lattice disorder

NASA Astrophysics Data System (ADS)

Thouin, Félix; Neutzner, Stefanie; Cortecchia, Daniele; Dragomir, Vlad Alexandru; Soci, Cesare; Salim, Teddy; Lam, Yeng Ming; Leonelli, Richard; Petrozza, Annamaria; Kandada, Ajay Ram Srimath; Silva, Carlos

2018-03-01

With strongly bound and stable excitons at room temperature, single-layer, two-dimensional organic-inorganic hybrid perovskites are viable semiconductors for light-emitting quantum optoelectronics applications. In such a technological context, it is imperative to comprehensively explore all the factors—chemical, electronic, and structural—that govern strong multiexciton correlations. Here, by means of two-dimensional coherent spectroscopy, we examine excitonic many-body effects in pure, single-layer (PEA) 2PbI4 (PEA = phenylethylammonium). We determine the binding energy of biexcitons—correlated two-electron, two-hole quasiparticles—to be 44 ±5 meV at room temperature. The extraordinarily high values are similar to those reported in other strongly excitonic two-dimensional materials such as transition-metal dichalcogenides. Importantly, we show that this binding energy increases by ˜25 % upon cooling to 5 K. Our work highlights the importance of multiexciton correlations in this class of technologically promising, solution-processable materials, in spite of the strong effects of lattice fluctuations and dynamic disorder.

Mitigating crack propagation in a highly maneuverable flight vehicle using life extending control logic

NASA Astrophysics Data System (ADS)

Elshabasy, Mohamed Mostafa Yousef Bassyouny

In this research, life extending control logic is proposed to reduce the cost of treating the aging problem of military aircraft structures and to avoid catastrophic failures and fatal accidents due to undetected cracks in the airframe components. The life extending control logic is based on load tailoring to facilitate a desired stress sequence that prolongs the structural life of the cracked airframe components by exploiting certain nonlinear crack retardation phenomena. The load is tailored to include infrequent injections of a single-cycle overload or a single-cycle overload and underload. These irregular loadings have an anti-intuitive but beneficial effect, which has been experimentally validated, on the extension of the operational structural life of the aircraft. A rigid six-degree-of freedom dynamic model of a highly maneuverable air vehicle coupled with an elastic dynamic wing model is used to generate the stress history at the lower skin of the wing. A three-dimensional equivalent plate finite element model is used to calculate the stress in the cracked skin. The plate is chosen to be of uniform chord-wise and span-wise thickness where the mechanical properties are assigned using an ad-hoc approach to mimic the full scale wing model. An in-extensional 3-node triangular element is used as the gridding finite element while the aerodynamic load is calculated using the vortex-lattice method where each lattice is laid upon two triangular finite elements with common hypotenuse. The aerodynamic loads, along with the base-excitation which is due to the motion of the rigid aircraft model, are the driving forces acting on the wing finite element model. An aerodynamic control surface is modulated based on the proposed life extending control logic within an existing flight control system without requiring major modification. One of the main goals of life extending control logic is to enhance the aircraft's service life, without incurring significant loss of vehicle dynamic performance. The value of the control-surface deflection angle is modulated so that the created overstress is sufficiently below the yield stress of the panel material. The results show that extension in crack length was reduced by 40% to 75% with an absence of damage mitigation logic. Moreover, the desired structural integrity is satisfied without affecting the air vehicle dynamic performance.

Phase-space networks of geometrically frustrated systems.

PubMed

Han, Yilong

2009-11-01

We illustrate a network approach to the phase-space study by using two geometrical frustration models: antiferromagnet on triangular lattice and square ice. Their highly degenerated ground states are mapped as discrete networks such that the quantitative network analysis can be applied to phase-space studies. The resulting phase spaces share some comon features and establish a class of complex networks with unique Gaussian spectral densities. Although phase-space networks are heterogeneously connected, the systems are still ergodic due to the random Poisson processes. This network approach can be generalized to phase spaces of some other complex systems.

Optical trapping via guided resonance modes in a Slot-Suzuki-phase photonic crystal lattice.

PubMed

Ma, Jing; Martínez, Luis Javier; Povinelli, Michelle L

2012-03-12

A novel photonic crystal lattice is proposed for trapping a two-dimensional array of particles. The lattice is created by introducing a rectangular slot in each unit cell of the Suzuki-Phase lattice to enhance the light confinement of guided resonance modes. Large quality factors on the order of 10⁵ are predicted in the lattice. A significant decrease of the optical power required for optical trapping can be achieved compared to our previous design.

Minimum mass design of large-scale space trusses subjected to thermal gradients

NASA Technical Reports Server (NTRS)

Williams, R. Brett; Agnes, Gregory S.

2006-01-01

Lightweight, deployable trusses are commonly used to support space-borne instruments including RF reflectors, radar panels, and telescope optics. While in orbit, these support structures are subjected to thermal gradients that vary with altitude, location in orbit, and self-shadowing. Since these instruments have tight dimensional-stability requirements, their truss members are often covered with multi-layer insulation (MLI) blankets to minimize thermal distortions. This paper develops a radiation heat transfer model to predict the thermal gradient experienced by a triangular truss supporting a long, linear radar panel in Medium Earth Orbit (MEO). The influence of self-shadowing effects of the radar panel are included in the analysis, and the influence of both MLI thickness and outer covers/coatings on the magnitude of the thermal gradient are formed into a simple, two-dimensional analysis. This thermal model is then used to size and estimate the structural mass of a triangular truss that meets a given set of structural requirements.

Multicomponent Supramolecular Systems: Self-Organization in Coordination-Driven Self-Assembly

PubMed Central

Zheng, Yao-Rong; Yang, Hai-Bo; Ghosh, Koushik; Zhao, Liang; Stang, Peter J.

2009-01-01

The self-organization of multicomponent supramolecular systems involving a variety of two-dimensional (2-D) polygons and three-dimensional (3-D) cages is presented. Nine self-organizing systems, SS1–SS9, have been studied. Each involving the simultaneous mixing of organoplatinum acceptors and pyridyl donors of varying geometry and their selective self-assembly into three to four specific 2-D (rectangular, triangular, and rhomboid) and/or 3-D (triangular prism and distorted and nondistorted trigonal bipyramidal) supramolecules. The formation of these discrete structures is characterized using NMR spectroscopy and electrospray ionization mass spectrometry (ESI-MS). In all cases, the self-organization process is directed by: (1) the geometric information encoded within the molecular subunits and (2) a thermodynamically driven dynamic self-correction process. The result is the selective self-assembly of multiple discrete products from a randomly formed complex. The influence of key experimental variables – temperature and solvent – on the self-correction process and the fidelity of the resulting self-organization systems is also described. PMID:19544512

Spin-wave energy dispersion of a frustrated spin-½ Heisenberg antiferromagnet on a stacked square lattice.

PubMed

Majumdar, Kingshuk

2011-03-23

The effects of interlayer coupling and spatial anisotropy on the spin-wave excitation spectra of a three-dimensional spatially anisotropic, frustrated spin-½ Heisenberg antiferromagnet (HAFM) are investigated for the two ordered phases using second-order spin-wave expansion. We show that the second-order corrections to the spin-wave energies are significant and find that the energy spectra of the three-dimensional HAFM have similar qualitative features to the energy spectra of the two-dimensional HAFM on a square lattice. We also discuss the features that can provide experimental measures for the strength of the interlayer coupling, spatial anisotropy parameter, and magnetic frustration.

Magnetic dipole interactions in crystals

NASA Astrophysics Data System (ADS)

Johnston, David C.

2016-01-01

The influence of magnetic dipole interactions (MDIs) on the magnetic properties of local-moment Heisenberg spin systems is investigated. A general formulation is presented for calculating the eigenvalues λ and eigenvectors μ ̂ of the MDI tensor of the magnetic dipoles in a line (one dimension, 1D), within a circle (2D) or a sphere (3D) of radius r surrounding a given moment μ⃗i for given magnetic propagation vectors k for collinear and coplanar noncollinear magnetic structures on both Bravais and non-Bravais spin lattices. Results are calculated for collinear ordering on 1D chains, 2D square and simple-hexagonal (triangular) Bravais lattices, 2D honeycomb and kagomé non-Bravais lattices, and 3D cubic Bravais lattices. The λ and μ ̂ values are compared with previously reported results. Calculations for collinear ordering on 3D simple tetragonal, body-centered tetragonal, and stacked triangular and honeycomb lattices are presented for c /a ratios from 0.5 to 3 in both graphical and tabular form to facilitate comparison of experimentally determined easy axes of ordering on these Bravais lattices with the predictions for MDIs. Comparisons with the easy axes measured for several illustrative collinear antiferromagnets (AFMs) are given. The calculations are extended to the cycloidal noncollinear 120∘ AFM ordering on the triangular lattice where λ is found to be the same as for collinear AFM ordering with the same k. The angular orientation of the ordered moments in the noncollinear coplanar AFM structure of GdB4 with a distorted stacked 3D Shastry-Sutherland spin-lattice geometry is calculated and found to be in disagreement with experimental observations, indicating the presence of another source of anisotropy. Similar calculations for the undistorted 2D and stacked 3D Shastry-Sutherland lattices are reported. The thermodynamics of dipolar magnets are calculated using the Weiss molecular field theory for quantum spins, including the magnetic transition temperature Tm and the ordered moment, magnetic heat capacity, and anisotropic magnetic susceptibility χ versus temperature T . The anisotropic Weiss temperature θp in the Curie-Weiss law for T >Tm is calculated. A quantitative study of the competition between FM and AFM ordering on cubic Bravais lattices versus the demagnetization factor in the absence of FM domain effects is presented. The contributions of Heisenberg exchange interactions and of the MDIs to Tm and to θp are found to be additive, which simplifies analysis of experimental data. Some properties in the magnetically-ordered state versus T are presented, including the ordered moment and magnetic heat capacity and, for AFMs, the dipolar anisotropy of the free energy and the perpendicular critical field. The anisotropic χ for dipolar AFMs is calculated both above and below the Néel temperature TN and the results are illustrated for a simple tetragonal lattice with c /a >1 , c /a =1 (cubic), and c /a <1 , where a change in sign of the χ anisotropy is found at c /a =1 . Finally, following the early work of Keffer [Phys. Rev. 87, 608 (1952), 10.1103/PhysRev.87.608], the dipolar anisotropy of χ above TN=69 K of the prototype collinear Heisenberg-exchange-coupled tetragonal compound MnF2 is calculated and found to be in excellent agreement with experimental single-crystal literature data above 130 K, where the smoothly increasing deviation of the experimental data from the theory on cooling from 130 K to TN is deduced to arise from dynamic short-range collinear c -axis AFM ordering in this temperature range driven by the exchange interactions.

Theory of the Lattice Boltzmann Equation: Symmetry properties of Discrete Velocity Sets

NASA Technical Reports Server (NTRS)

Rubinstein, Robert; Luo, Li-Shi

2007-01-01

In the lattice Boltzmann equation, continuous particle velocity space is replaced by a finite dimensional discrete set. The number of linearly independent velocity moments in a lattice Boltzmann model cannot exceed the number of discrete velocities. Thus, finite dimensionality introduces linear dependencies among the moments that do not exist in the exact continuous theory. Given a discrete velocity set, it is important to know to exactly what order moments are free of these dependencies. Elementary group theory is applied to the solution of this problem. It is found that by decomposing the velocity set into subsets that transform among themselves under an appropriate symmetry group, it becomes relatively straightforward to assess the behavior of moments in the theory. The construction of some standard two- and three-dimensional models is reviewed from this viewpoint, and procedures for constructing some new higher dimensional models are suggested.

Higher-n triangular dilatonic black holes

NASA Astrophysics Data System (ADS)

Zadora, Anton; Gal'tsov, Dmitri V.; Chen, Chiang-Mei

2018-04-01

Dilaton gravity with the form fields is known to possess dyon solutions with two horizons for the discrete "triangular" values of the dilaton coupling constant a =√{ n (n + 1) / 2 }. This sequence first obtained numerically and then explained analytically as consequence of the regularity of the dilaton, should have some higher-dimensional and/or group theoretical origin. Meanwhile, this origin was explained earlier only for n = 1 , 2 in which cases the solutions were known analytically. We extend this explanation to n = 3 , 5 presenting analytical triangular solutions for the theory with different dilaton couplings a , b in electric and magnetic sectors in which case the quantization condition reads ab = n (n + 1) / 2. The solutions are derived via the Toda chains for B2 and G2 Lie algebras. They are found in the closed form in general D space-time dimensions. Solutions satisfy the entropy product rules indicating on the microscopic origin of their entropy and have negative binding energy in the extremal case.

Hidden-Symmetry-Protected Topological Semimetals on a Square Lattice

NASA Astrophysics Data System (ADS)

Hou, Jing-Min

2014-03-01

We study a two-dimensional fermionic square lattice, which supports the existence of two-dimensional Weyl semimetal, quantum anomalous Hall effect, and 2 π -flux topological semimetal in different parameter ranges. We show that the band degenerate points of the two-dimensional Weyl semimetal and 2 π -flux topological semimetal are protected by two distinct novel hidden symmetries, which both corresponds to antiunitary composite operations. When these hidden symmetries are broken, a gap opens between the conduction and valence bands, turning the system into a insulator. With appropriate parameters, a quantum anomalous Hall effect emerges. The degenerate point at the boundary between the quantum anomalous Hall insulator and trivial band insulator is also protected by the hidden symmetry. [PRL 111, 130403(2013)] This work was supported by the National Natural Science Foundation of China under Grants No. 11004028 and No. 11274061.

Modified spin-wave theory with ordering vector optimization: spatially anisotropic triangular lattice and J1J2J3 model with Heisenberg interactions

NASA Astrophysics Data System (ADS)

Hauke, Philipp; Roscilde, Tommaso; Murg, Valentin; Cirac, J. Ignacio; Schmied, Roman

2011-07-01

We study the ground-state phases of the S=1/2 Heisenberg quantum antiferromagnet on the spatially anisotropic triangular lattice (SATL) and on the square lattice with up to next-next-nearest-neighbor coupling (the J1J2J3 model), making use of Takahashi's modified spin-wave (MSW) theory supplemented by ordering vector optimization. We compare the MSW results with exact diagonalization and projected-entangled-pair-states calculations, demonstrating their qualitative and quantitative reliability. We find that the MSW theory correctly accounts for strong quantum effects on the ordering vector of the magnetic phases of the models under investigation: in particular, collinear magnetic order is promoted at the expense of non-collinear (spiral) order, and several spiral states that are stable at the classical level disappear from the quantum phase diagram. Moreover, collinear states and non-collinear ones are never connected continuously, but they are separated by parameter regions in which the MSW theory breaks down, signaling the possible appearance of a non-magnetic ground state. In the case of the SATL, a large breakdown region appears also for weak couplings between the chains composing the lattice, suggesting the possible occurrence of a large non-magnetic region continuously connected with the spin-liquid state of the uncoupled chains. This shows that the MSW theory is—despite its apparent simplicity—a versatile tool for finding candidate regions in the case of spin-liquid phases, which are among prime targets for relevant quantum simulations.

Integrable Seven-Point Discrete Equations and Second-Order Evolution Chains

NASA Astrophysics Data System (ADS)

Adler, V. E.

2018-04-01

We consider differential-difference equations defining continuous symmetries for discrete equations on a triangular lattice. We show that a certain combination of continuous flows can be represented as a secondorder scalar evolution chain. We illustrate the general construction with a set of examples including an analogue of the elliptic Yamilov chain.

Uniaxial compression on the superconductivity of β-BDA-TTP salts

NASA Astrophysics Data System (ADS)

Ito, Hiroshi; Ishihara, Tetsuo; Tanaka, Hisaaki; Kuroda, Shin-ichi; Yamada, Jun-ichi

2008-10-01

The β-type BDA-TTP superconductors attract attention due to the high transition temperature Tc at ambient pressure for organic superconductors. In order to get insight into the superconductivity in terms of the dimerized anisotropic triangular lattice model, Tc of β-(BDA-TTP)2X [X = SbF6, X = AsF6] is studied under uniaxial compression by resistivity measurements. Under compression parallel to the donor stack, Tc increases gradually up to 3 (X = SbF6), 5 (X = AsF6) kbar, and decreases under further piston pressure. Under compression perpendicular to the donor stack, Tc decreases gradually up to 2.5 (X = SbF6), 4 (X = AsF6) kbar and then decreases rapidly under further pressure. Only for X = AsF6, a Tc minimum at 3 kbar is found for both direction. These trends in Tc are understood as an interplay between the enhancement of antiferromagnetic spin fluctuation and frustration on the triangular lattice. By the interplane compression, Tc increased by 0.5 K up to 2 kbar for both salts, demonstrating the importance of the interlayer interaction.

Consequences of Spatial Antisymmetry on Light

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mascarenhas, Angelo; Fluegel, Brian

2016-12-21

Light propagation in two and three dimensional lattices for which the index of refraction exhibits spatial antisymmetry is investigated in the ray and photonic crystal regimes. In these regimes, all the two dimensional antisymmetry groups for which light fails to propagate are identified. In the ray-regime, it is observed that in tilings described by 7 of the 46 two dimensional antisymmetric groups, light is localized within a fundamental domain and does not propagate through the tiling, in contrast to the behavior in the other 39 groups. To understand the above phenomenon, a rule based on the number of anti-mirror planesmore » passing through a single Bravais lattice point is derived. In the wave regime for photonic crystals, it is observed that there are no propagating eigensolutions for the same 7 tilings as above, whereas propagating solutions and energy pass band dispersion curves can be obtained for the other 39 groups. The reasons underlying this peculiar behavior are analyzed using the topological approach for modeling flow in dynamical billiards to shed light on the applicability of Bloch's theorem for these periodic antisymmetric lattices.« less

Logarithmic Superdiffusion in Two Dimensional Driven Lattice Gases

NASA Astrophysics Data System (ADS)

Krug, J.; Neiss, R. A.; Schadschneider, A.; Schmidt, J.

2018-03-01

The spreading of density fluctuations in two-dimensional driven diffusive systems is marginally anomalous. Mode coupling theory predicts that the diffusivity in the direction of the drive diverges with time as (ln t)^{2/3} with a prefactor depending on the macroscopic current-density relation and the diffusion tensor of the fluctuating hydrodynamic field equation. Here we present the first numerical verification of this behavior for a particular version of the two-dimensional asymmetric exclusion process. Particles jump strictly asymmetrically along one of the lattice directions and symmetrically along the other, and an anisotropy parameter p governs the ratio between the two rates. Using a novel massively parallel coupling algorithm that strongly reduces the fluctuations in the numerical estimate of the two-point correlation function, we are able to accurately determine the exponent of the logarithmic correction. In addition, the variation of the prefactor with p provides a stringent test of mode coupling theory.

Model of chiral spin liquids with Abelian and non-Abelian topological phases

NASA Astrophysics Data System (ADS)

Chen, Jyong-Hao; Mudry, Christopher; Chamon, Claudio; Tsvelik, A. M.

2017-12-01

We present a two-dimensional lattice model for quantum spin-1/2 for which the low-energy limit is governed by four flavors of strongly interacting Majorana fermions. We study this low-energy effective theory using two alternative approaches. The first consists of a mean-field approximation. The second consists of a random phase approximation (RPA) for the single-particle Green's functions of the Majorana fermions built from their exact forms in a certain one-dimensional limit. The resulting phase diagram consists of two competing chiral phases, one with Abelian and the other with non-Abelian topological order, separated by a continuous phase transition. Remarkably, the Majorana fermions propagate in the two-dimensional bulk, as in the Kitaev model for a spin liquid on the honeycomb lattice. We identify the vison fields, which are mobile (they are static in the Kitaev model) domain walls propagating along only one of the two space directions.

Effects of hydrostatic pressure on spin-lattice coupling in two-dimensional ferromagnetic Cr2Ge2Te6

NASA Astrophysics Data System (ADS)

Sun, Y.; Xiao, R. C.; Lin, G. T.; Zhang, R. R.; Ling, L. S.; Ma, Z. W.; Luo, X.; Lu, W. J.; Sun, Y. P.; Sheng, Z. G.

2018-02-01

Spin-lattice coupling plays an important role in both formation and understanding of the magnetism in two-dimensional magnetic semiconductors (2DMS). In this paper, the steady pressure effects on the lattice structure, Raman resonances, and magnetization of a 2DMS Cr2Ge2Te6 have been studied by both experiments and first principles calculations. It is found that the bond length of Cr-Cr decreases, the angle of Cr-Te-Cr diverges from 90°, and the Raman modes Eg3 and Ag1 show an increase with the application of external pressure. Consequently, the magnetic phase transition temperature TC decreases from 66.6 K to 60.6 K (˜9%) as the pressure increases from 0 to 1 GPa. These pressure effects not only confirm the existence of strong spin-lattice coupling but also reveal the detailed information about the lattice deformation effect on the magnetic properties in such 2DMS, which would be a benefit for the further understanding and manipulation of the magnetism in 2D materials.

Singular ferromagnetic susceptibility of the transverse-field Ising antiferromagnet on the triangular lattice

NASA Astrophysics Data System (ADS)

Biswas, Sounak; Damle, Kedar

2018-02-01

A transverse magnetic field Γ is known to induce antiferromagnetic three-sublattice order of the Ising spins σz in the triangular lattice Ising antiferromagnet at low enough temperature. This low-temperature order is known to melt on heating in a two-step manner, with a power-law ordered intermediate temperature phase characterized by power-law correlations at the three-sublattice wave vector Q : <σz(R ⃗) σz(0 ) > ˜cos(Q .R ⃗) /|R⃗| η (T ) with the temperature-dependent power-law exponent η (T )∈(1 /9 ,1 /4 ) . Here, we use a quantum cluster algorithm to study the ferromagnetic easy-axis susceptibility χu(L ) of an L ×L sample in this power-law ordered phase. Our numerical results are consistent with a recent prediction of a singular L dependence χu(L ) ˜L2 -9 η when η (T ) is in the range (1 /9 ,2 /9 ) . This finite-size result implies, via standard scaling arguments, that the ferromagnetic susceptibility χu(B ) to a uniform field B along the easy axis is singular at intermediate temperatures in the small B limit, χu(B ) ˜|B| -4/-18 η 4 -9 η for η (T )∈(1 /9 ,2 /9 ) , although there is no ferromagnetic long-range order in the low temperature state. Additionally we establish similar two-step melting behavior (via a study of the order parameter susceptibility χQ) in the case of the ferrimagnetic three-sublattice ordered phase which is stabilized by ferromagnetic next-neighbor couplings (J2) and confirm that the ferromagnetic susceptibility obeys the predicted singular form in the associated power-law ordered phase.

Critical exponents of the disorder-driven superfluid-insulator transition in one-dimensional Bose-Einstein condensates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cestari, J. C. C.; Foerster, A.; Gusmao, M. A.

2011-11-15

We investigate the nature of the superfluid-insulator quantum phase transition driven by disorder for noninteracting ultracold atoms on one-dimensional lattices. We consider two different cases: Anderson-type disorder, with local energies randomly distributed, and pseudodisorder due to a potential incommensurate with the lattice, which is usually called the Aubry-Andre model. A scaling analysis of numerical data for the superfluid fraction for different lattice sizes allows us to determine quantum critical exponents characterizing the disorder-driven superfluid-insulator transition. We also briefly discuss the effect of interactions close to the noninteracting quantum critical point of the Aubry-Andre model.

Edge-Controlled Growth and Etching of Two-Dimensional GaSe Monolayers

DOE PAGES

Li, Xufan; Dong, Jichen; Idrobo, Juan C.; ...

2016-12-07

Understanding the atomistic mechanisms governing the growth of two-dimensional (2D) materials is of great importance in guiding the synthesis of wafer-sized, single-crystalline, high-quality 2D crystals and heterostructures. Etching, in many cases regarded as the reverse process of material growth, has been used to study the growth kinetics of graphene. In this paper, we explore a growth–etching–regrowth process of monolayer GaSe crystals, including single-crystalline triangles and irregularly shaped domains formed by merged triangles. We show that the etching begins at a slow rate, creating triangular, truncated triangular, or hexagonally shaped holes that eventually evolve to exclusively triangles that are rotated 60°more » with respect to the crystalline orientation of the monolayer triangular crystals. The regrowth occurs much faster than etching, reversibly filling the etched holes and then enlarging the size of the monolayer crystals. A theoretical model developed based on kinetic Wulff construction (KWC) theory and density functional theory (DFT) calculations accurately describe the observed morphology evolution of the monolayer GaSe crystals and etched holes during the growth and etching processes, showing that they are governed by the probability of atom attachment/detachment to/from different types of edges with different formation energies of nucleus/dents mediated by chemical potential difference Δμ between Ga and Se. Finally, our growth–etching–regrowth study provides not only guidance to understand the growth mechanisms of 2D binary crystals but also a potential method for the synthesis of large, shape-controllable, high-quality single-crystalline 2D crystals and their lateral heterostructures.« less

Modal Ring Method for the Scattering of Electromagnetic Waves

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.; Kreider, Kevin L.

1993-01-01

The modal ring method for electromagnetic scattering from perfectly electric conducting (PEC) symmetrical bodies is presented. The scattering body is represented by a line of finite elements (triangular) on its outer surface. The infinite computational region surrounding the body is represented analytically by an eigenfunction expansion. The modal ring method effectively reduces the two dimensional scattering problem to a one-dimensional problem similar to the method of moments. The modal element method is capable of handling very high frequency scattering because it has a highly banded solution matrix.

Geometric magnetic frustration in RE{sub 2}O{sub 2}S oxysulfides (RE = Sm, Eu and Gd)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Biondo, V.; Sarvezuk, P.W.C.; Ivashita, F.F.

2014-06-01

Graphical abstract: Stacked planes in the <001> direction of an oxysulfide structure, showing the triangular nets formed by rare earth cations, which moments present geometric magnetic frustration. - Highlights: • We prepared monophasic RE{sub 2}O{sub 2}S Oxysulfides (RE = Sm, Eu and Gd). • RE{sub 2}O{sub 2}S compounds were characterized regarding structural and magnetic properties. • Mössbauer spectra were obtained for Eu{sub 2}O{sub 2}S and Gd{sub 2}O{sub 2}S at different temperatures. • Oxysulfides present geometric magnetic frustration of the rare-earth sublattice. - Abstract: RE{sub 2}O{sub 2}S oxysulfides (with RE = Sm, Eu and Gd) were prepared and characterized regarding theirmore » structural and magnetic properties. The compounds crystallized in the trigonal symmetry (space group P-3m/D{sub 3}{sup 3}d), with the lattice parameter varying linearly with the ionic radius of the RE cation. All these oxysulfides are magnetically frustrated and only the gadolinium sample showed magnetic order down to 3 K. The magnetic frustration is attributed to the spatial distribution of cations over the lattice, where the RE’s magnetic moments occupy the sites forming a triangular plane lattice, perpendicular to the direction. This geometric magnetic frustration was firstly recognized for these oxysulfides.« less

Studies on unsteady pressure fields in the region of separating and reattaching flows

NASA Astrophysics Data System (ADS)

Govinda Ram, H. S.; Arakeri, V. H.

1990-12-01

Experimental studies on the measurement of pressure fields in the region of separating and reattaching flows behind several two-dimensional fore-bodies and one axisymmetric body are reported. In particular, extensive measurements of mean pressure, surface pressure fluctuation, and pressure fluctuation within the flow were made for a series of two-dimensional fore-body shapes consisting of triangular nose with varying included angle. The measurements from different bodies are compared and one of the important findings is that the maximum values of rms pressure fluctuation levels in the shear layer approaching reattachment are almost equal to the maximum value of the surface fluctuation levels.

Signatures of two-step impurity mediated vortex lattice melting in Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Dey, Bishwajyoti

2017-04-01

We study impurity mediated vortex lattice melting in a rotating two-dimensional Bose-Einstein condensate (BEC). Impurities are introduced either through a protocol in which vortex lattice is produced in an impurity potential or first creating the vortex lattice in the absence of random pinning and then cranking up the impurity potential. These two protocols have obvious relation with the two commonly known protocols of creating vortex lattice in a type-II superconductor: zero field cooling protocol and the field cooling protocol respectively. Time-splitting Crank-Nicolson method has been used to numerically simulate the vortex lattice dynamics. It is shown that the vortex lattice follows a two-step melting via loss of positional and orientational order. This vortex lattice melting process in BEC closely mimics the recently observed two-step melting of vortex matter in weakly pinned type-II superconductor Co-intercalated NbSe2. Also, using numerical perturbation analysis, we compare between the states obtained in two protocols and show that the vortex lattice states are metastable and more disordered when impurities are introduced after the formation of an ordered vortex lattice. The author would like to thank SERB, Govt. of India and BCUD-SPPU for financial support through research Grants.

Generalized hydrodynamic transport in lattice-gas automata

NASA Technical Reports Server (NTRS)

Luo, Li-Shi; Chen, Hudong; Chen, Shiyi; Doolen, Gary D.; Lee, Yee-Chun

1991-01-01

The generalized hydrodynamics of two-dimensional lattice-gas automata is solved analytically in the linearized Boltzmann approximation. The dependence of the transport coefficients (kinematic viscosity, bulk viscosity, and sound speed) upon wave number k is obtained analytically. Anisotropy of these coefficients due to the lattice symmetry is studied for the entire range of wave number, k. Boundary effects due to a finite mean free path (Knudsen layer) are analyzed, and accurate comparisons are made with lattice-gas simulations.

Nonautonomous ultradiscrete hungry Toda lattice and a generalized box-ball system

NASA Astrophysics Data System (ADS)

Maeda, Kazuki

2017-09-01

A nonautonomous version of the ultradiscrete hungry Toda lattice with a finite lattice boundary condition is derived by applying reduction and ultradiscretization to a nonautonomous two-dimensional discrete Toda lattice. It is shown that the derived ultradiscrete system has a direct connection to the box-ball system with many kinds of balls and finite carrier capacity. Particular solutions to the ultradiscrete system are constructed by using the theory of some sort of discrete biorthogonal polynomials.

Application of the control volume mixed finite element method to a triangular discretization

USGS Publications Warehouse

Naff, R.L.

2012-01-01

A two-dimensional control volume mixed finite element method is applied to the elliptic equation. Discretization of the computational domain is based in triangular elements. Shape functions and test functions are formulated on the basis of an equilateral reference triangle with unit edges. A pressure support based on the linear interpolation of elemental edge pressures is used in this formulation. Comparisons are made between results from the standard mixed finite element method and this control volume mixed finite element method. Published 2011. This article is a US Government work and is in the public domain in the USA. ?? 2012 John Wiley & Sons, Ltd. This article is a US Government work and is in the public domain in the USA.

Conical wave propagation and diffraction in two-dimensional hexagonally packed granular lattices

DOE PAGES

Chong, C.; Kevrekidis, P. G.; Ablowitz, M. J.; ...

2016-01-25

We explore linear and nonlinear mechanisms for conical wave propagation in two-dimensional lattices in the realm of phononic crystals. As a prototypical example, a statically compressed granular lattice of spherical particles arranged in a hexagonal packing configuration is analyzed. Upon identifying the dispersion relation of the underlying linear problem, the resulting diffraction properties are considered. Analysis both via a heuristic argument for the linear propagation of a wave packet and via asymptotic analysis leading to the derivation of a Dirac system suggests the occurrence of conical diffraction. This analysis is valid for strong precompression, i.e., near the linear regime. Formore » weak precompression, conical wave propagation is still possible, but the resulting expanding circular wave front is of a nonoscillatory nature, resulting from the complex interplay among the discreteness, nonlinearity, and geometry of the packing. Lastly, the transition between these two types of propagation is explored.« less

Parallel Implementation of Triangular Cellular Automata for Computing Two-Dimensional Elastodynamic Response on Arbitrary Domains

NASA Astrophysics Data System (ADS)

Leamy, Michael J.; Springer, Adam C.

In this research we report parallel implementation of a Cellular Automata-based simulation tool for computing elastodynamic response on complex, two-dimensional domains. Elastodynamic simulation using Cellular Automata (CA) has recently been presented as an alternative, inherently object-oriented technique for accurately and efficiently computing linear and nonlinear wave propagation in arbitrarily-shaped geometries. The local, autonomous nature of the method should lead to straight-forward and efficient parallelization. We address this notion on symmetric multiprocessor (SMP) hardware using a Java-based object-oriented CA code implementing triangular state machines (i.e., automata) and the MPI bindings written in Java (MPJ Express). We use MPJ Express to reconfigure our existing CA code to distribute a domain's automata to cores present on a dual quad-core shared-memory system (eight total processors). We note that this message passing parallelization strategy is directly applicable to computer clustered computing, which will be the focus of follow-on research. Results on the shared memory platform indicate nearly-ideal, linear speed-up. We conclude that the CA-based elastodynamic simulator is easily configured to run in parallel, and yields excellent speed-up on SMP hardware.

Heavy fermion behavior in the quasi-one-dimensional Kondo lattice CeCo 2Ga 8

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Le; Fu, Zhaoming; Sun, Jianping

Dimensionality plays an essential role in determining the anomalous non-Fermi liquid properties in heavy fermion systems. So far most heavy fermion compounds are quasi-two-dimensional or three-dimensional. Here we report the synthesis and systematic investigations of the single crystals of the quasi-one-dimensional Kondo lattice CeCo 2Ga 8. Resistivity measurements at ambient pressure reveal the onset of coherence at T * ≈ 20 K and non-Fermi liquid behavior with linear temperature dependence over a decade in temperature from 2 to 0.1 K. The specific heat increases logarithmically with lowering temperature between 10 and 2 K and reaches 800 mJ/mol K 2 atmore » 1 K, suggesting that CeCo 2Ga 8 is a heavy fermion compound in the close vicinity of a quantum critical point. Resistivity measurements under pressure further confirm the non-Fermi liquid behavior in a large temperature–pressure range. The magnetic susceptibility is found to follow the typical behavior for a one-dimensional spin chain from 300 K down to T *, and first-principles calculations predict flat Fermi surfaces for the itinerant f-electron bands. These suggest that CeCo 2Ga 8 is a rare example of the quasi-one-dimensional Kondo lattice, but its non-Fermi liquid behaviors resemble those of the quasi-two-dimensional YbRh 2Si 2 family. The study of the quasi-one-dimensional CeCo 2Ga 8 family may therefore help us to understand the role of dimensionality on heavy fermion physics and quantum criticality.« less

Heavy fermion behavior in the quasi-one-dimensional Kondo lattice CeCo2Ga8

NASA Astrophysics Data System (ADS)

Wang, Le; Fu, Zhaoming; Sun, Jianping; Liu, Min; Yi, Wei; Yi, Changjiang; Luo, Yongkang; Dai, Yaomin; Liu, Guangtong; Matsushita, Yoshitaka; Yamaura, Kazunari; Lu, Li; Cheng, Jin-Guang; Yang, Yi-feng; Shi, Youguo; Luo, Jianlin

2017-07-01

Dimensionality plays an essential role in determining the anomalous non-Fermi liquid properties in heavy fermion systems. So far most heavy fermion compounds are quasi-two-dimensional or three-dimensional. Here we report the synthesis and systematic investigations of the single crystals of the quasi-one-dimensional Kondo lattice CeCo2Ga8. Resistivity measurements at ambient pressure reveal the onset of coherence at T * ≈ 20 K and non-Fermi liquid behavior with linear temperature dependence over a decade in temperature from 2 to 0.1 K. The specific heat increases logarithmically with lowering temperature between 10 and 2 K and reaches 800 mJ/mol K2 at 1 K, suggesting that CeCo2Ga8 is a heavy fermion compound in the close vicinity of a quantum critical point. Resistivity measurements under pressure further confirm the non-Fermi liquid behavior in a large temperature-pressure range. The magnetic susceptibility is found to follow the typical behavior for a one-dimensional spin chain from 300 K down to T *, and first-principles calculations predict flat Fermi surfaces for the itinerant f-electron bands. These suggest that CeCo2Ga8 is a rare example of the quasi-one-dimensional Kondo lattice, but its non-Fermi liquid behaviors resemble those of the quasi-two-dimensional YbRh2Si2 family. The study of the quasi-one-dimensional CeCo2Ga8 family may therefore help us to understand the role of dimensionality on heavy fermion physics and quantum criticality.

Heavy fermion behavior in the quasi-one-dimensional Kondo lattice CeCo 2Ga 8

DOE PAGES

Wang, Le; Fu, Zhaoming; Sun, Jianping; ...

2017-07-04

Dimensionality plays an essential role in determining the anomalous non-Fermi liquid properties in heavy fermion systems. So far most heavy fermion compounds are quasi-two-dimensional or three-dimensional. Here we report the synthesis and systematic investigations of the single crystals of the quasi-one-dimensional Kondo lattice CeCo 2Ga 8. Resistivity measurements at ambient pressure reveal the onset of coherence at T * ≈ 20 K and non-Fermi liquid behavior with linear temperature dependence over a decade in temperature from 2 to 0.1 K. The specific heat increases logarithmically with lowering temperature between 10 and 2 K and reaches 800 mJ/mol K 2 atmore » 1 K, suggesting that CeCo 2Ga 8 is a heavy fermion compound in the close vicinity of a quantum critical point. Resistivity measurements under pressure further confirm the non-Fermi liquid behavior in a large temperature–pressure range. The magnetic susceptibility is found to follow the typical behavior for a one-dimensional spin chain from 300 K down to T *, and first-principles calculations predict flat Fermi surfaces for the itinerant f-electron bands. These suggest that CeCo 2Ga 8 is a rare example of the quasi-one-dimensional Kondo lattice, but its non-Fermi liquid behaviors resemble those of the quasi-two-dimensional YbRh 2Si 2 family. The study of the quasi-one-dimensional CeCo 2Ga 8 family may therefore help us to understand the role of dimensionality on heavy fermion physics and quantum criticality.« less

Quantum search algorithms on a regular lattice

NASA Astrophysics Data System (ADS)

Hein, Birgit; Tanner, Gregor

2010-07-01

Quantum algorithms for searching for one or more marked items on a d-dimensional lattice provide an extension of Grover’s search algorithm including a spatial component. We demonstrate that these lattice search algorithms can be viewed in terms of the level dynamics near an avoided crossing of a one-parameter family of quantum random walks. We give approximations for both the level splitting at the avoided crossing and the effectively two-dimensional subspace of the full Hilbert space spanning the level crossing. This makes it possible to give the leading order behavior for the search time and the localization probability in the limit of large lattice size including the leading order coefficients. For d=2 and d=3, these coefficients are calculated explicitly. Closed form expressions are given for higher dimensions.

Two-dimensional chiral topological superconductivity in Shiba lattices

PubMed Central

Li, Jian; Neupert, Titus; Wang, Zhijun; MacDonald, A. H.; Yazdani, A.; Bernevig, B. Andrei

2016-01-01

The chiral p-wave superconductor is the archetypal example of a state of matter that supports non-Abelian anyons, a highly desired type of exotic quasiparticle. With this, it is foundational for the distant goal of building a topological quantum computer. While some candidate materials for bulk chiral superconductors exist, they are subject of an ongoing debate about their actual paring state. Here we propose an alternative route to chiral superconductivity, consisting of the surface of an ordinary superconductor decorated with a two-dimensional lattice of magnetic impurities. We furthermore identify a promising experimental platform to realize this proposal. PMID:27465127

Upon Generating Discrete Expanding Integrable Models of the Toda Lattice Systems and Infinite Conservation Laws

NASA Astrophysics Data System (ADS)

Zhang, Yufeng; Zhang, Xiangzhi; Wang, Yan; Liu, Jiangen

2017-01-01

With the help of R-matrix approach, we present the Toda lattice systems that have extensive applications in statistical physics and quantum physics. By constructing a new discrete integrable formula by R-matrix, the discrete expanding integrable models of the Toda lattice systems and their Lax pairs are generated, respectively. By following the constructing formula again, we obtain the corresponding (2+1)-dimensional Toda lattice systems and their Lax pairs, as well as their (2+1)-dimensional discrete expanding integrable models. Finally, some conservation laws of a (1+1)-dimensional generalised Toda lattice system and a new (2+1)-dimensional lattice system are generated, respectively.

Testing holography using lattice super-Yang-Mills theory on a 2-torus

NASA Astrophysics Data System (ADS)

Catterall, Simon; Jha, Raghav G.; Schaich, David; Wiseman, Toby

2018-04-01

We consider maximally supersymmetric SU (N ) Yang-Mills theory in Euclidean signature compactified on a flat two-dimensional torus with antiperiodic ("thermal") fermion boundary conditions imposed on one cycle. At large N , holography predicts that this theory describes certain black hole solutions in type IIA and IIB supergravity, and we use lattice gauge theory to test this. Unlike the one-dimensional quantum mechanics case where there is only the dimensionless temperature to vary, here we emphasize there are two more parameters which determine the shape of the flat torus. While a rectangular Euclidean torus yields a thermal interpretation, allowing for skewed tori modifies the holographic dual black hole predictions and results in another direction to test holography. Our lattice calculations are based on a supersymmetric formulation naturally adapted to a particular skewing. Using this we perform simulations up to N =16 with several lattice spacings for both skewed and rectangular tori. We observe the two expected black hole phases with their predicted behavior, with a transition between them that is consistent with the gravity prediction based on the Gregory-Laflamme transition.

Development of a finite volume two-dimensional model and its application in a bay with two inlets: Mobile Bay, Alabama

NASA Astrophysics Data System (ADS)

Lee, Jun; Lee, Jungwoo; Yun, Sang-Leen; Oh, Hye-Cheol

2017-08-01

The purpose of this study was to develop a two-dimensional shallow water flow model using the finite volume method on a combined unstructured triangular and quadrilateral grid system to simulate coastal, estuarine and river flows. The intercell numerical fluxes were calculated using the classical Osher-Solomon's approximate Riemann solver for the governing conservation laws to be able to handle wetting and drying processes and to capture a tidal bore like phenomenon. The developed model was validated with several benchmark test problems including the two-dimensional dam-break problem. The model results were well agreed with results of other models and experimental results in literature. The unstructured triangular and quadrilateral combined grid system was successfully implemented in the model, thus the developed model would be more flexible when applying in an estuarine system, which includes narrow channels. Then, the model was tested in Mobile Bay, Alabama, USA. The developed model reproduced water surface elevation well as having overall Predictive Skill of 0.98. We found that the primary inlet, Main Pass, only covered 35% of the fresh water exchange while it covered 89% of the total water exchange between the ocean and Mobile Bay. There were also discharge phase difference between MP and the secondary inlet, Pass aux Herons, and this phase difference in flows would act as a critical role in substances' exchange between the eastern Mississippi Sound and the northern Gulf of Mexico through Main Pass and Pass aux Herons in Mobile Bay.

Observation of Two-Dimensional Localized Jones-Roberts Solitons in Bose-Einstein Condensates

NASA Astrophysics Data System (ADS)

Meyer, Nadine; Proud, Harry; Perea-Ortiz, Marisa; O'Neale, Charlotte; Baumert, Mathis; Holynski, Michael; Kronjäger, Jochen; Barontini, Giovanni; Bongs, Kai

2017-10-01

Jones-Roberts solitons are the only known class of stable dark solitonic solutions of the nonlinear Schrödinger equation in two and three dimensions. They feature a distinctive elongated elliptical shape that allows them to travel without change of form. By imprinting a triangular phase pattern, we experimentally generate two-dimensional Jones-Roberts solitons in a three-dimensional atomic Bose-Einstein condensate. We monitor their dynamics, observing that this kind of soliton is indeed not affected by dynamic (snaking) or thermodynamic instabilities, that instead make other classes of dark solitons unstable in dimensions higher than one. Our results confirm the prediction that Jones-Roberts solitons are stable solutions of the nonlinear Schrödinger equation and promote them for applications beyond matter wave physics, like energy and information transport in noisy and inhomogeneous environments.

Partial entropic stabilization of lattice Boltzmann magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Flint, Christopher; Vahala, George

2018-01-01

The entropic lattice Boltzmann algorithm of Karlin et al. [Phys. Rev. E 90, 031302 (2014), 10.1103/PhysRevE.90.031302] is partially extended to magnetohydrodynamics, based on the Dellar model of introducing a vector distribution for the magnetic field. This entropic ansatz is now applied only to the scalar particle distribution function so as to permit the many problems entailing magnetic field reversal. A 9-bit lattice is employed for both particle and magnetic distributions for our two-dimensional simulations. The entropic ansatz is benchmarked against our earlier multiple relaxation lattice-Boltzmann model for the Kelvin-Helmholtz instability in a magnetized jet. Other two-dimensional simulations are performed and compared to results determined by more standard direct algorithms: in particular the switch over between the Kelvin-Helmholtz or tearing mode instability of Chen et al. [J. Geophys. Res.: Space Phys. 102, 151 (1997), 10.1029/96JA03144], and the generalized Orszag-Tang vortex model of Biskamp-Welter [Phys. Fluids B 1, 1964 (1989), 10.1063/1.859060]. Very good results are achieved.

Atom-Dependent Edge-Enhanced Second-Harmonic Generation on MoS2 Monolayers.

PubMed

Lin, Kuang-I; Ho, Yen-Hung; Liu, Shu-Bai; Ciou, Jian-Jhih; Huang, Bo-Ting; Chen, Christopher; Chang, Han-Ching; Tu, Chien-Liang; Chen, Chang-Hsiao

2018-02-14

Edge morphology and lattice orientation of single-crystal molybdenum disulfide (MoS 2 ) monolayers, a transition metal dichalcogenide (TMD), possessing a triangular shape with different edges grown by chemical vapor deposition are characterized by atomic force microscopy and transmission electron microscopy. Multiphoton laser scanning microscopy is utilized to study one-dimensional atomic edges of MoS 2 monolayers with localized midgap electronic states, which result in greatly enhanced optical second-harmonic generation (SHG). Microscopic S-zigzag edge and S-Mo Klein edge (bare Mo atoms protruding from a S-zigzag edge) terminations and the edge-atom dependent resonance energies can therefore be deduced based on SHG images. Theoretical calculations based on density functional theory clearly explain the lower energy of the S-zigzag edge states compared to the corresponding S-Mo Klein edge states. Characterization of the atomic-scale variation of edge-enhanced SHG is a step forward in this full-optical and high-yield technique of atomic-layer TMDs.

Numerical analysis of light extraction enhancement of GaN-based thin-film flip-chip light-emitting diodes with high-refractive-index buckling nanostructures

NASA Astrophysics Data System (ADS)

Yue, Qing-Yang; Yang, Yang; Cheng, Zhen-Jia; Guo, Cheng-Shan

2018-06-01

In this work, the light extraction efficiency enhancement of GaN-based thin-film flip-chip (TFFC) light-emitting diodes (LEDs) with high-refractive-index (TiO2) buckling nanostructures was studied using the three-dimensional finite difference time domain method. Compared with 2-D photonic crystals, the buckling structures have the advantages of a random directionality and a broad distribution in periodicity, which can effectively extract the guided light propagating in all azimuthal directions over a wide spectrum. Numerical studies revealed that the light extraction efficiency of buckling-structured LEDs reaches 1.1 times that of triangular lattice photonic crystals. The effects of the buckling structure feature sizes and the thickness of the N-GaN layer on the light extraction efficiency for TFFC LEDs were also investigated systematically. With optimized structural parameters, a significant light extraction enhancement of about 2.6 times was achieved for TiO2 buckling-structured TFFC LEDs compared with planar LEDs.

Metallic Borides, La 2 Re 3 B 7 and La 3 Re 2 B 5 , Featuring Extensive Boron–Boron Bonding

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bugaris, Daniel E.; Malliakas, Christos D.; Chung, Duck Young

We synthesized La 2Re 3B 7 and La 3Re 2B 5 in single-crystalline form from a molten La/Ni eutectic at 1000°C, in the first example of the flux crystal growth of ternary rare-earth rhenium borides. Both compounds crystallize in their own orthorhombic structure types, with La 2Re 3B 7 (space group Pcca) having lattice parameters a = 7.657(2) Å, b = 6.755(1) Å, and c = 11.617(2) Å, and La 3Re 2B 5 (space group Pmma) having lattice parameters a = 10.809(2) Å, b = 5.287(1) Å, and c = 5.747(1) Å. Furthermore, the compounds possess three-dimensional framework structures thatmore » are built up from rhenium boride polyhedra and boron-boron bonding. La 3Re 2B 5 features fairly common B 2 dumbbells, whereas La 2Re 3B 7 has unique one-dimensional subunits composed of alternating triangular B3 and trans-B4 zigzag chain fragments. Also observed in La 3Re 2B 5 is an unusual coordination of B by an octahedron of La atoms. Electronic band structure calculations predict that La 2Re 3B 7 is a semimetal, which is observed in the electrical resistivity data as measured on single crystals, with behavior obeying the Bloch-Grüneisen model and a room-temperature resistivity ρ300K of ~ 375 μΩ cm. The electronic band structure calculations also suggest that La 3Re 2B 5 is a regular metal.« less

Metallic Borides, La 2 Re 3 B 7 and La 3 Re 2 B 5 , Featuring Extensive Boron–Boron Bonding

DOE PAGES

Bugaris, Daniel E.; Malliakas, Christos D.; Chung, Duck Young; ...

2016-01-26

We synthesized La 2Re 3B 7 and La 3Re 2B 5 in single-crystalline form from a molten La/Ni eutectic at 1000°C, in the first example of the flux crystal growth of ternary rare-earth rhenium borides. Both compounds crystallize in their own orthorhombic structure types, with La 2Re 3B 7 (space group Pcca) having lattice parameters a = 7.657(2) Å, b = 6.755(1) Å, and c = 11.617(2) Å, and La 3Re 2B 5 (space group Pmma) having lattice parameters a = 10.809(2) Å, b = 5.287(1) Å, and c = 5.747(1) Å. Furthermore, the compounds possess three-dimensional framework structures thatmore » are built up from rhenium boride polyhedra and boron-boron bonding. La 3Re 2B 5 features fairly common B 2 dumbbells, whereas La 2Re 3B 7 has unique one-dimensional subunits composed of alternating triangular B3 and trans-B4 zigzag chain fragments. Also observed in La 3Re 2B 5 is an unusual coordination of B by an octahedron of La atoms. Electronic band structure calculations predict that La 2Re 3B 7 is a semimetal, which is observed in the electrical resistivity data as measured on single crystals, with behavior obeying the Bloch-Grüneisen model and a room-temperature resistivity ρ300K of ~ 375 μΩ cm. The electronic band structure calculations also suggest that La 3Re 2B 5 is a regular metal.« less

Band warping, band non-parabolicity, and Dirac points in electronic and lattice structures

NASA Astrophysics Data System (ADS)

Resca, Lorenzo; Mecholsky, Nicholas A.; Pegg, Ian L.

2017-10-01

We illustrate at a fundamental level the physical and mathematical origins of band warping and band non-parabolicity in electronic and vibrational structures. We point out a robust presence of pairs of topologically induced Dirac points in a primitive-rectangular lattice using a p-type tight-binding approximation. We analyze two-dimensional primitive-rectangular and square Bravais lattices with implications that are expected to generalize to more complex structures. Band warping is shown to arise at the onset of a singular transition to a crystal lattice with a larger symmetry group, which allows the possibility of irreducible representations of higher dimensions, hence band degeneracy, at special symmetry points in reciprocal space. Band warping is incompatible with a multi-dimensional Taylor series expansion, whereas band non-parabolicities are associated with multi-dimensional Taylor series expansions to all orders. Still band non-parabolicities may merge into band warping at the onset of a larger symmetry group. Remarkably, while still maintaining a clear connection with that merging, band non-parabolicities may produce pairs of conical intersections at relatively low-symmetry points. Apparently, such conical intersections are robustly maintained by global topology requirements, rather than any local symmetry protection. For two p-type tight-binding bands, we find such pairs of conical intersections drifting along the edges of restricted Brillouin zones of primitive-rectangular Bravais lattices as lattice constants vary relatively to each other, until these conical intersections merge into degenerate warped bands at high-symmetry points at the onset of a square lattice. The conical intersections that we found appear to have similar topological characteristics as Dirac points extensively studied in graphene and other topological insulators, even though our conical intersections have none of the symmetry complexity and protection afforded by the latter more complex structures.

Semi-analytical solution for the generalized absorbing boundary condition in molecular dynamics simulations

NASA Astrophysics Data System (ADS)

Lee, Chung-Shuo; Chen, Yan-Yu; Yu, Chi-Hua; Hsu, Yu-Chuan; Chen, Chuin-Shan

2017-07-01

We present a semi-analytical solution of a time-history kernel for the generalized absorbing boundary condition in molecular dynamics (MD) simulations. To facilitate the kernel derivation, the concept of virtual atoms in real space that can conform with an arbitrary boundary in an arbitrary lattice is adopted. The generalized Langevin equation is regularized using eigenvalue decomposition and, consequently, an analytical expression of an inverse Laplace transform is obtained. With construction of dynamical matrices in the virtual domain, a semi-analytical form of the time-history kernel functions for an arbitrary boundary in an arbitrary lattice can be found. The time-history kernel functions for different crystal lattices are derived to show the generality of the proposed method. Non-equilibrium MD simulations in a triangular lattice with and without the absorbing boundary condition are conducted to demonstrate the validity of the solution.

Frustrated Magnetism of Dipolar Molecules on a Square Optical Lattice: Prediction of a Quantum Paramagnetic Ground State

NASA Astrophysics Data System (ADS)

Zou, Haiyuan; Zhao, Erhai; Liu, W. Vincent

2017-08-01

Motivated by the experimental realization of quantum spin models of polar molecule KRb in optical lattices, we analyze the spin 1 /2 dipolar Heisenberg model with competing anisotropic, long-range exchange interactions. We show that, by tilting the orientation of dipoles using an external electric field, the dipolar spin system on square lattice comes close to a maximally frustrated region similar, but not identical, to that of the J1-J2 model. This provides a simple yet powerful route to potentially realize a quantum spin liquid without the need for a triangular or kagome lattice. The ground state phase diagrams obtained from Schwinger-boson and spin-wave theories consistently show a spin disordered region between the Néel, stripe, and spiral phase. The existence of a finite quantum paramagnetic region is further confirmed by an unbiased variational ansatz based on tensor network states and a tensor renormalization group.

Striped, honeycomb, and twisted moiré patterns in surface adsorption systems with highly degenerate commensurate ground states

NASA Astrophysics Data System (ADS)

Elder, K. R.; Achim, C. V.; Granato, E.; Ying, S. C.; Ala-Nissila, T.

2017-11-01

Atomistically thin adsorbate layers on surfaces with a lattice mismatch display complex spatial patterns and ordering due to strain-driven self-organization. In this work, a general formalism to model such ultrathin adsorption layers that properly takes into account the competition between strain and adhesion energy of the layers is presented. The model is based on the amplitude expansion of the two-dimensional phase field crystal (PFC) model, which retains atomistic length scales but allows relaxation of the layers at diffusive time scales. The specific systems considered here include cases where both the film and the adsorption potential can have either honeycomb (H) or triangular (T) symmetry. These systems include the so-called (1 ×1 ) , (√{3 }×√{3 }) R 30∘ , (2 ×2 ) , (√{7 }×√{7 }) R 19 .1∘ , and other higher order states that can contain a multitude of degenerate commensurate ground states. The relevant phase diagrams for many combinations of the H and T systems are mapped out as a function of adhesion strength and misfit strain. The coarsening patterns in some of these systems is also examined. The predictions are in good agreement with existing experimental data for selected strained ultrathin adsorption layers.

Exotic Quantum Phases and Phase Transitions of Strongly Interacting Electrons in Low-Dimensional Systems

NASA Astrophysics Data System (ADS)

Mishmash, Ryan V.

Experiments on strongly correlated quasi-two-dimensional electronic materials---for example, the high-temperature cuprate superconductors and the putative quantum spin liquids kappa-(BEDT-TTF)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2---routinely reveal highly mysterious quantum behavior which cannot be explained in terms of weakly interacting degrees of freedom. Theoretical progress thus requires the introduction of completely new concepts and machinery beyond the traditional framework of the band theory of solids and its interacting counterpart, Landau's Fermi liquid theory. In full two dimensions, controlled and reliable analytical approaches to such problems are severely lacking, as are numerical simulations of even the simplest of model Hamiltonians due to the infamous fermionic sign problem. Here, we attempt to circumvent some of these difficulties by studying analogous problems in quasi-one dimension. In this lower dimensional setting, theoretical and numerical tractability are on much stronger footing due to the methods of bosonization and the density matrix renormalization group, respectively. Using these techniques, we attack two problems: (1) the Mott transition between a Fermi liquid metal and a quantum spin liquid as potentially directly relevant to the organic compounds kappa-(BEDT-TTF)2Cu 2(CN)3 and EtMe3Sb[Pd(dmit)2] 2 and (2) non-Fermi liquid metals as strongly motivated by the strange metal phase observed in the cuprates. In both cases, we are able to realize highly exotic quantum phases as ground states of reasonable microscopic models. This lends strong credence to respective underlying slave-particle descriptions of the low-energy physics, which are inherently strongly interacting and also unconventional in comparison to weakly interacting alternatives. Finally, working in two dimensions directly, we propose a new slave-particle theory which explains in a universal way many of the intriguing experimental results of the triangular lattice organic spin liquid candidates kappa-(BEDT-TTF) 2Cu2(CN)3 and EtMe3Sb[Pd(dmit) 2]2. With use of large-scale variational Monte Carlo calculations, we show that this new state has very competitive trial energy in an effective spin model thought to describe the essential features of the real materials.

Mach Cones in a Coulomb Lattice and a Dusty Plasma

NASA Astrophysics Data System (ADS)

Samsonov, D.; Goree, J.; Ma, Z. W.; Bhattacharjee, A.; Thomas, H. M.; Morfill, G. E.

1999-11-01

Mach cones, or V-shaped disturbances created by supersonic objects, have been detected in a two-dimensional Coulomb crystal. Electrically charged microspheres levitated in a glow-discharge plasma formed a dusty plasma, with particles arranged in a hexagonal lattice in a horizontal plane. Beneath this lattice plane, a sphere moved faster than the lattice sound speed. Mach cones were double, first compressive then rarefactive, due to the strongly coupled crystalline state. Molecular dynamics simulations using a Yukawa potential also show multiple Mach cones.

Parallel CARLOS-3D code development

DOE Office of Scientific and Technical Information (OSTI.GOV)

Putnam, J.M.; Kotulski, J.D.

1996-02-01

CARLOS-3D is a three-dimensional scattering code which was developed under the sponsorship of the Electromagnetic Code Consortium, and is currently used by over 80 aerospace companies and government agencies. The code has been extensively validated and runs on both serial workstations and parallel super computers such as the Intel Paragon. CARLOS-3D is a three-dimensional surface integral equation scattering code based on a Galerkin method of moments formulation employing Rao- Wilton-Glisson roof-top basis for triangular faceted surfaces. Fully arbitrary 3D geometries composed of multiple conducting and homogeneous bulk dielectric materials can be modeled. This presentation describes some of the extensions tomore » the CARLOS-3D code, and how the operator structure of the code facilitated these improvements. Body of revolution (BOR) and two-dimensional geometries were incorporated by simply including new input routines, and the appropriate Galerkin matrix operator routines. Some additional modifications were required in the combined field integral equation matrix generation routine due to the symmetric nature of the BOR and 2D operators. Quadrilateral patched surfaces with linear roof-top basis functions were also implemented in the same manner. Quadrilateral facets and triangular facets can be used in combination to more efficiently model geometries with both large smooth surfaces and surfaces with fine detail such as gaps and cracks. Since the parallel implementation in CARLOS-3D is at high level, these changes were independent of the computer platform being used. This approach minimizes code maintenance, while providing capabilities with little additional effort. Results are presented showing the performance and accuracy of the code for some large scattering problems. Comparisons between triangular faceted and quadrilateral faceted geometry representations will be shown for some complex scatterers.« less

Exotic superfluidity and pairing phenomena in atomic Fermi gases in mixed dimensions.

PubMed

Zhang, Leifeng; Che, Yanming; Wang, Jibiao; Chen, Qijin

2017-10-11

Atomic Fermi gases have been an ideal platform for simulating conventional and engineering exotic physical systems owing to their multiple tunable control parameters. Here we investigate the effects of mixed dimensionality on the superfluid and pairing phenomena of a two-component ultracold atomic Fermi gas with a short-range pairing interaction, while one component is confined on a one-dimensional (1D) optical lattice whereas the other is in a homogeneous 3D continuum. We study the phase diagram and the pseudogap phenomena throughout the entire BCS-BEC crossover, using a pairing fluctuation theory. We find that the effective dimensionality of the non-interacting lattice component can evolve from quasi-3D to quasi-1D, leading to strong Fermi surface mismatch. Upon pairing, the system becomes effectively quasi-two dimensional in the BEC regime. The behavior of T c bears similarity to that of a regular 3D population imbalanced Fermi gas, but with a more drastic departure from the regular 3D balanced case, featuring both intermediate temperature superfluidity and possible pair density wave ground state. Unlike a simple 1D optical lattice case, T c in the mixed dimensions has a constant BEC asymptote.

Flipping Triangles!

ERIC Educational Resources Information Center

Zucker, Marc

2009-01-01

We introduce a simple game made up of a board of coins on a triangular lattice. We then study the possibility of turning the board from one pattern of heads and tails to some other pattern. Given that a solution exists we find a precise answer to the number of solutions possible. We then generalize this to more complex boards with coins of many…

Continuous-variable gate decomposition for the Bose-Hubbard model

NASA Astrophysics Data System (ADS)

Kalajdzievski, Timjan; Weedbrook, Christian; Rebentrost, Patrick

2018-06-01

In this work, we decompose the time evolution of the Bose-Hubbard model into a sequence of logic gates that can be implemented on a continuous-variable photonic quantum computer. We examine the structure of the circuit that represents this time evolution for one-dimensional and two-dimensional lattices. The elementary gates needed for the implementation are counted as a function of lattice size. We also include the contribution of the leading dipole interaction term which may be added to the Hamiltonian and its corresponding circuit.

DNA denaturation through a model of the partition points on a one-dimensional lattice

NASA Astrophysics Data System (ADS)

Mejdani, R.; Huseini, H.

1994-08-01

We have shown that by using a model of the partition points gas on a one-dimensional lattice, we can study, besides the saturation curves obtained before for the enzyme kinetics, also the denaturation process, i.e. the breaking of the hydrogen bonds connecting the two strands, under treatment by heat of DNA. We think that this model, as a very simple model and mathematically transparent, can be advantageous for pedagogic goals or other theoretical investigations in chemistry or modern biology.

Phase stability in the two-dimensional anisotropic boson Hubbard Hamiltonian

DOE PAGES

Ying, T.; Batrouni, G. G.; Rousseau, V. G.; ...

2013-05-15

The two dimensional square lattice hard-core boson Hubbard model with near neighbor interactions has a ‘checkerboard’ charge density wave insulating phase at half-filling and sufficiently large intersite repulsion. When doped, rather than forming a supersolid phase in which long range charge density wave correlations coexist with a condensation of superfluid defects, the system instead phase separates. However, it is known that there are other lattice geometries and interaction patterns for which such coexistence takes place. In this paper we explore the possibility that anisotropic hopping or anisotropic near neighbor repulsion might similarly stabilize the square lattice supersolid. Lastly, by consideringmore » the charge density wave structure factor and superfluid density for different ratios of interaction strength and hybridization in the ˆx and ˆy directions, we conclude that phase separation still occurs.« less

Metal-insulator-superconductor transition of spin-3/2 atoms on optical lattices

NASA Astrophysics Data System (ADS)

De Silva, Theja N.

2018-01-01

We use a slave-rotor approach within a mean-field theory to study the competition of metallic, Mott-insulating, and superconducting phases of spin-3/2 fermions subjected to a periodic optical lattice potential. In addition to the metallic, the Mott-insulating, and the superconducting phases that are associated with the gauge symmetry breaking of the spinon field, we identify an emerging superconducting phase that breaks both roton and spinon field gauge symmetries. This superconducting phase emerges as a result of the competition between spin-0 singlet and spin-2 quintet interaction channels naturally available for spin-3/2 systems. The two superconducting phases can be distinguished from each other by quasiparticle weight. We further discuss the properties of these phases for both two-dimensional square and three-dimensional cubic lattices at zero and finite temperatures.

Dynamics of a bilayer membrane coupled to a two-dimensional cytoskeleton: Scale transfers of membrane deformations

NASA Astrophysics Data System (ADS)

Okamoto, Ryuichi; Komura, Shigeyuki; Fournier, Jean-Baptiste

2017-07-01

We theoretically investigate the dynamics of a floating lipid bilayer membrane coupled with a two-dimensional cytoskeleton network, taking into account explicitly the intermonolayer friction, the discrete lattice structure of the cytoskeleton, and its prestress. The lattice structure breaks lateral continuous translational symmetry and couples Fourier modes with different wave vectors. It is shown that within a short time interval a long-wavelength deformation excites a collection of modes with wavelengths shorter than the lattice spacing. These modes relax slowly with a common renormalized rate originating from the long-wavelength mode. As a result, and because of the prestress, the slowest relaxation is governed by the intermonolayer friction. Conversely, and most interestingly, forces applied at the scale of the cytoskeleton for a sufficiently long time can cooperatively excite large-scale modes.

Lattice Three-Species Models of the Spatial Spread of Rabies among FOXES

NASA Astrophysics Data System (ADS)

Benyoussef, A.; Boccara, N.; Chakib, H.; Ez-Zahraouy, H.

Lattice models describing the spatial spread of rabies among foxes are studied. In these models, the fox population is divided into three-species: susceptible (S), infected or incubating (I), and infectious or rabid (R). They are based on the fact that susceptible and incubating foxes are territorial while rabid foxes have lost their sense of direction and move erratically. Two different models are investigated: a one-dimensional coupled-map lattice model, and a two-dimensional automata network model. Both models take into account the short-range character of the infection process and the diffusive motion of rabid foxes. Numerical simulations show how the spatial distribution of rabies, and the speed of propagation of the epizootic front depend upon the carrying capacity of the environment and diffusion of rabid foxes out of their territory.

The Game of Life Rules on Penrose Tilings: Still Life and Oscillators

NASA Astrophysics Data System (ADS)

Owens, Nick; Stepney, Susan

John Horton Conway's Game of Life is a simple two-dimensional, two state cellular automaton (CA), remarkable for its complex behaviour. That behaviour is known to be very sensitive to a change in the CA rules. Here we continue our investigations into its sensitivity to changes in the lattice, by the use of an aperiodic Penrose tiling lattice.

Phase diagrams for an evolutionary prisoner's dilemma game on two-dimensional lattices

NASA Astrophysics Data System (ADS)

Szabó, György; Vukov, Jeromos; Szolnoki, Attila

2005-10-01

The effects of payoffs and noise on the maintenance of cooperative behavior are studied in an evolutionary prisoner’s dilemma game with players located on the sites of different two-dimensional lattices. This system exhibits a phase transition from a mixed state of cooperators and defectors to a homogeneous one where only the defectors remain alive. Using Monte Carlo simulations and the generalized mean-field approximations we have determined the phase boundaries (critical points) separating the two phases on the plane of the temperature (noise) and temptation to choose defection. In the zero temperature limit the cooperation can be sustained only for those connectivity structures where three-site clique percolation occurs.

"Building" 3D visualization skills in mineralogy

NASA Astrophysics Data System (ADS)

Gaudio, S. J.; Ajoku, C. N.; McCarthy, B. S.; Lambart, S.

2016-12-01

Studying mineralogy is fundamental for understanding the composition and physical behavior of natural materials in terrestrial and extraterrestrial environments. However, some students struggle and ultimately get discouraged with mineralogy course material because they lack well-developed spatial visualization skills that are needed to deal with three-dimensional (3D) objects, such as crystal forms or atomic-scale structures, typically represented in two-dimensional (2D) space. Fortunately, spatial visualization can improve with practice. Our presentation demonstrates a set of experiential learning activities designed to support the development and improvement of spatial visualization skills in mineralogy using commercially available magnetic building tiles, rods, and spheres. These instructional support activities guide students in the creation of 3D models that replicate macroscopic crystal forms and atomic-scale structures in a low-pressure learning environment and at low cost. Students physically manipulate square and triangularly shaped magnetic tiles to build 3D open and closed crystal forms (platonic solids, prisms, pyramids and pinacoids). Prismatic shapes with different closing forms are used to demonstrate the relationship between crystal faces and Miller Indices. Silica tetrahedra and octahedra are constructed out of magnetic rods (bonds) and spheres (oxygen atoms) to illustrate polymerization, connectivity, and the consequences for mineral formulae. In another activity, students practice the identification of symmetry elements and plane lattice types by laying magnetic rods and spheres over wallpaper patterns. The spatial visualization skills developed and improved through our experiential learning activities are critical to the study of mineralogy and many other geology sub-disciplines. We will also present pre- and post- activity assessments that are aligned with explicit learning outcomes.

Electron counting and a large family of two-dimensional semiconductors

NASA Astrophysics Data System (ADS)

Miao, Maosheng; Botana, Jorge; Zurek, Eva; Liu, Jingyao; Yang, Wen

Two-dimensional semiconductors (2DSC) are currently the focus of many studies, thanks to their novel and superior transport properties that may greatly influence future electronic devices. The potential applications of 2DSCs range from low-dimensional electronics, topological insulators and vallytronics all the way to novel photolysis. However, compared with the conventional semiconductors that are comprised of main group elements and cover a large range of band gaps and lattice constants, the choice of 2D materials is very limited. In this work, we propose and demonstrate a large family of 2DSCs, all adopting the same structure and consisting of only main group elements. Using advanced density functional calculations, we demonstrate the attainability of these materials, and show that they cover a large range of lattice constants, band gaps and band edge states, making them good candidate materials for heterojunctions. This family of two dimensional materials may be instrumental in the fabrication of 2DSC devices that may rival the currently employed 3D semiconductors.

Surface-assisted DNA self-assembly: An enzyme-free strategy towards formation of branched DNA lattice.

PubMed

Bhanjadeo, Madhabi M; Nayak, Ashok K; Subudhi, Umakanta

2017-04-01

DNA based self-assembled nanostructures and DNA origami has proven useful for organizing nanomaterials with firm precision. However, for advanced applications like nanoelectronics and photonics, large-scale organization of self-assembled branched DNA (bDNA) into periodic lattices is desired. In this communication for the first time we report a facile method of self-assembly of Y-shaped bDNA nanostructures on the cationic surface of Aluminum (Al) foil to prepare periodic two dimensional (2D) bDNA lattice. Particularly those Y-shaped bDNA structures having smaller overhangs and unable to self-assemble in solution, they are easily assembled on the surface of Al foil in the absence of ligase. Field emission scanning electron microscopy (FESEM) analysis shows homogenous distribution of two-dimensional bDNA lattices across the Al foil. When the assembled bDNA structures were recovered from the Al foil and electrophoresed in nPAGE only higher order polymeric bDNA structures were observed without a trace of monomeric structures which confirms the stability and high yield of the bDNA lattices. Therefore, this enzyme-free economic and efficient strategy for developing bDNA lattices can be utilized in assembling various nanomaterials for functional molecular components towards development of DNA based self-assembled nanodevices. Copyright © 2017 Elsevier Inc. All rights reserved.

Coherent, atomically thin transition-metal dichalcogenide superlattices with engineered strain

NASA Astrophysics Data System (ADS)

Xie, Saien; Tu, Lijie; Han, Yimo; Huang, Lujie; Kang, Kibum; Lao, Ka Un; Poddar, Preeti; Park, Chibeom; Muller, David A.; DiStasio, Robert A.; Park, Jiwoong

2018-03-01

Epitaxy forms the basis of modern electronics and optoelectronics. We report coherent atomically thin superlattices in which different transition metal dichalcogenide monolayers—despite large lattice mismatches—are repeated and laterally integrated without dislocations within the monolayer plane. Grown by an omnidirectional epitaxy, these superlattices display fully matched lattice constants across heterointerfaces while maintaining an isotropic lattice structure and triangular symmetry. This strong epitaxial strain is precisely engineered via the nanoscale supercell dimensions, thereby enabling broad tuning of the optical properties and producing photoluminescence peak shifts as large as 250 millielectron volts. We present theoretical models to explain this coherent growth and the energetic interplay governing the ripple formation in these strained monolayers. Such coherent superlattices provide building blocks with targeted functionalities at the atomically thin limit.

Topological modes bound to dislocations in mechanical metamaterials

NASA Astrophysics Data System (ADS)

Paulose, Jayson; Chen, Bryan Gin-Ge; Vitelli, Vincenzo

2015-02-01

Mechanical metamaterials are artificial structures with unusual properties, such as negative Poisson ratio, bistability or tunable vibrational properties, that originate in the geometry of their unit cell. Often at the heart of such unusual behaviour is a soft mode: a motion that does not significantly stretch or compress the links between constituent elements. When activated by motors or external fields, soft modes become the building blocks of robots and smart materials. Here, we demonstrate the existence of topological soft modes that can be positioned at desired locations in a metamaterial while being robust against a wide range of structural deformations or changes in material parameters. These protected modes, localized at dislocations in deformed kagome and square lattices, are the mechanical analogue of topological states bound to defects in electronic systems. We create physical realizations of the topological modes in prototypes of kagome lattices built out of rigid triangular plates. We show mathematically that they originate from the interplay between two Berry phases: the Burgers vector of the dislocation and the topological polarization of the lattice. Our work paves the way towards engineering topologically protected nanomechanical structures for molecular robotics or information storage and read-out.

GPU surface extraction using the closest point embedding

NASA Astrophysics Data System (ADS)

Kim, Mark; Hansen, Charles

2015-01-01

Isosurface extraction is a fundamental technique used for both surface reconstruction and mesh generation. One method to extract well-formed isosurfaces is a particle system; unfortunately, particle systems can be slow. In this paper, we introduce an enhanced parallel particle system that uses the closest point embedding as the surface representation to speedup the particle system for isosurface extraction. The closest point embedding is used in the Closest Point Method (CPM), a technique that uses a standard three dimensional numerical PDE solver on two dimensional embedded surfaces. To fully take advantage of the closest point embedding, it is coupled with a Barnes-Hut tree code on the GPU. This new technique produces well-formed, conformal unstructured triangular and tetrahedral meshes from labeled multi-material volume datasets. Further, this new parallel implementation of the particle system is faster than any known methods for conformal multi-material mesh extraction. The resulting speed-ups gained in this implementation can reduce the time from labeled data to mesh from hours to minutes and benefits users, such as bioengineers, who employ triangular and tetrahedral meshes

Two-dimensional, phase modulated lattice sums with application to the Helmholtz Green’s function

DOE Office of Scientific and Technical Information (OSTI.GOV)

Linton, C. M., E-mail: C.M.Linton@lboro.ac.uk

2015-01-15

A class of two-dimensional phase modulated lattice sums in which the denominator is an indefinite quadratic polynomial Q is expressed in terms of a single, exponentially convergent series of elementary functions. This expression provides an extremely efficient method for the computation of the quasi-periodic Green’s function for the Helmholtz equation that arises in a number of physical contexts when studying wave propagation through a doubly periodic medium. For a class of sums in which Q is positive definite, our new result can be used to generate representations in terms of θ-functions which are significant generalisations of known results.

Finite-size scaling of clique percolation on two-dimensional Moore lattices

NASA Astrophysics Data System (ADS)

Dong, Jia-Qi; Shen, Zhou; Zhang, Yongwen; Huang, Zi-Gang; Huang, Liang; Chen, Xiaosong

2018-05-01

Clique percolation has attracted much attention due to its significance in understanding topological overlap among communities and dynamical instability of structured systems. Rich critical behavior has been observed in clique percolation on Erdős-Rényi (ER) random graphs, but few works have discussed clique percolation on finite dimensional systems. In this paper, we have defined a series of characteristic events, i.e., the historically largest size jumps of the clusters, in the percolating process of adding bonds and developed a new finite-size scaling scheme based on the interval of the characteristic events. Through the finite-size scaling analysis, we have found, interestingly, that, in contrast to the clique percolation on an ER graph where the critical exponents are parameter dependent, the two-dimensional (2D) clique percolation simply shares the same critical exponents with traditional site or bond percolation, independent of the clique percolation parameters. This has been corroborated by bridging two special types of clique percolation to site percolation on 2D lattices. Mechanisms for the difference of the critical behaviors between clique percolation on ER graphs and on 2D lattices are also discussed.

Exploration properties of biased evanescent random walkers on a one-dimensional lattice

NASA Astrophysics Data System (ADS)

Esguerra, Jose Perico; Reyes, Jelian

2017-08-01

We investigate the combined effects of bias and evanescence on the characteristics of random walks on a one-dimensional lattice. We calculate the time-dependent return probability, eventual return probability, conditional mean return time, and the time-dependent mean number of visited sites of biased immortal and evanescent discrete-time random walkers on a one-dimensional lattice. We then extend the calculations to the case of a continuous-time step-coupled biased evanescent random walk on a one-dimensional lattice with an exponential waiting time distribution.

Discrete breathers in a two-dimensional hexagonal Fermi Pasta Ulam lattice

NASA Astrophysics Data System (ADS)

Butt, Imran A.; Wattis, Jonathan A. D.

2007-02-01

We consider a two-dimensional Fermi-Pasta-Ulam (FPU) lattice with hexagonal symmetry. Using asymptotic methods based on small amplitude ansatz, at third order we obtain a reduction to a cubic nonlinear Schrödinger equation (NLS) for the breather envelope. However, this does not support stable soliton solutions, so we pursue a higher order analysis yielding a generalized NLS, which includes known stabilizing terms. We present numerical results which suggest that long-lived stationary and moving breathers are supported by the lattice. We find breather solutions which move in an arbitrary direction, an ellipticity criterion for the wavenumbers of the carrier wave, asymptotic estimates for the breather energy, and a minimum threshold energy below which breathers cannot be found. This energy threshold is maximized for stationary breathers and becomes vanishingly small near the boundary of the elliptic domain where breathers attain a maximum speed. Several of the results obtained are similar to those obtained for the square FPU lattice (Butt and Wattis 2006 J. Phys. A: Math. Gen. 39 4955), though we find that the square and hexagonal lattices exhibit different properties in regard to the generation of harmonics, and the isotropy of the generalized NLS equation.

An upwind multigrid method for solving viscous flows on unstructured triangular meshes. M.S. Thesis

NASA Technical Reports Server (NTRS)

Bonhaus, Daryl Lawrence

1993-01-01

A multigrid algorithm is combined with an upwind scheme for solving the two dimensional Reynolds averaged Navier-Stokes equations on triangular meshes resulting in an efficient, accurate code for solving complex flows around multiple bodies. The relaxation scheme uses a backward-Euler time difference and relaxes the resulting linear system using a red-black procedure. Roe's flux-splitting scheme is used to discretize convective and pressure terms, while a central difference is used for the diffusive terms. The multigrid scheme is demonstrated for several flows around single and multi-element airfoils, including inviscid, laminar, and turbulent flows. The results show an appreciable speed up of the scheme for inviscid and laminar flows, and dramatic increases in efficiency for turbulent cases, especially those on increasingly refined grids.

Nuclear core and fuel assemblies

DOEpatents

Downs, Robert E.

1981-01-01

A fast flux nuclear core of a plurality of rodded, open-lattice assemblies having a rod pattern rotated relative to a rod support structure pattern. Elongated fuel rods are oriented on a triangular array and laterally supported by grid structures positioned along the length of the assembly. Initial inter-assembly contact is through strongbacks at the corners of the support pattern and peripheral fuel rods between adjacent assemblies are nested so as to maintain a triangular pitch across a clearance gap between the other portions of adjacent assemblies. The rod pattern is rotated relative to the strongback support pattern by an angle .alpha. equal to sin .sup.-1 (p/2c), where p is the intra-assembly rod pitch and c is the center-to-center spacing among adjacent assemblies.

On the Wiener Polarity Index of Lattice Networks.

PubMed

Chen, Lin; Li, Tao; Liu, Jinfeng; Shi, Yongtang; Wang, Hua

2016-01-01

Network structures are everywhere, including but not limited to applications in biological, physical and social sciences, information technology, and optimization. Network robustness is of crucial importance in all such applications. Research on this topic relies on finding a suitable measure and use this measure to quantify network robustness. A number of distance-based graph invariants, also known as topological indices, have recently been incorporated as descriptors of complex networks. Among them the Wiener type indices are the most well known and commonly used such descriptors. As one of the fundamental variants of the original Wiener index, the Wiener polarity index has been introduced for a long time and known to be related to the cluster coefficient of networks. In this paper, we consider the value of the Wiener polarity index of lattice networks, a common network structure known for its simplicity and symmetric structure. We first present a simple general formula for computing the Wiener polarity index of any graph. Using this formula, together with the symmetric and recursive topology of lattice networks, we provide explicit formulas of the Wiener polarity index of the square lattices, the hexagonal lattices, the triangular lattices, and the 33 ⋅ 42 lattices. We also comment on potential future research topics.

Correlation strength, Lifshitz transition, and the emergence of a two-dimensional to three-dimensional crossover in FeSe under pressure

NASA Astrophysics Data System (ADS)

Skornyakov, S. L.; Anisimov, V. I.; Vollhardt, D.; Leonov, I.

2018-03-01

We report a detailed theoretical study of the electronic structure, spectral properties, and lattice parameters of bulk FeSe under pressure using a fully charge self-consistent implementation of the density functional theory plus dynamical mean-field theory method (DFT+DMFT). In particular, we perform a structural optimization and compute the evolution of the lattice parameters (volume, c /a ratio, and the internal z position of Se) and the electronic structure of the tetragonal (space group P 4 /n m m ) unit cell of paramagnetic FeSe. Our results for the lattice parameters obtained by structural optimization using DFT+DMFT are in good quantitative agreement with experiment, implying a crucial importance of electron correlations in determining the correct lattice properties of FeSe. Most importantly, upon compression to 10 GPa our results reveal a topological change in the Fermi surface (Lifshitz transition) which is accompanied by a two- to three-dimensional crossover and a small reduction of the quasiparticle mass renormalization compared to ambient pressure. The behavior of the momentum-resolved magnetic susceptibility χ (q ) shows no topological changes of magnetic correlations under pressure but demonstrates a reduction of the degree of the in-plane (π ,π ) stripe-type nesting. Our results for the electronic structure and lattice parameters of FeSe are in good qualitative agreement with recent experiments on its isoelectronic counterpart FeSe1 -xSx .

Connector design in a long-span-fixed dental prosthesis: a three-dimensional finite element analysis.

PubMed

Harshitha Gowda, B H; Satish Babu, C L

2013-01-01

The goal of every prosthetic management is to simulate nature and be in harmony with nature within the physiological limits. The occlusal forces on a fixed dental prosthesis are transmitted to the surrounding structures through pontics, connectors and retainers and more stresses are seen at the connector region. To analyze the stress patterns in cast and soldered connectors between the two pontics and between the retainer and pontic of a four unit fixed dental prosthesis on axial and non axial loading and also to observe and ascertain the need to modify the design of the rigid connectors. Subsequently four models each of cast and soldered connectors with cylindrical and triangular design, of dimension 3 × 4 mm and thickness 0.5 mm was designed for the study. The first premolar and second molar were considered as the abutments and 2 nd premolar and 1 st molar as the pontics. The analysis was done using ANSYS version 8.0 software and by placing axial and non-axial load of 40 Newtons each. Von Misses stresses were observed at the connector region between the two pontics, especially in the cervical region. The cylindrical cast connectors showed less stress in comparison to triangular design and the difference in the stress distribution of cast and soldered connectors were marginal. The occlusal forces on a fixed dental prosthesis are transmitted to the surrounding structures through pontics, connectors and retainers with maximum stresses concentrated at the connectors. Hence this three-dimensional finite element analysis study investigated stress distribution in a four unit posterior fixed dental prosthesis, having cylindrical and triangular connector designs.

Quantum anomalous Hall phase in a one-dimensional optical lattice

NASA Astrophysics Data System (ADS)

Liu, Sheng; Shao, L. B.; Hou, Qi-Zhe; Xue, Zheng-Yuan

2018-03-01

We propose to simulate and detect quantum anomalous Hall phase with ultracold atoms in a one-dimensional optical lattice, with the other synthetic dimension being realized by modulating spin-orbit coupling. We show that the system manifests a topologically nontrivial phase with two chiral edge states which can be readily detected in this synthetic two-dimensional system. Moreover, it is interesting that at the phase transition point there is a flat energy band and this system can also be in a topologically nontrivial phase with two Fermi zero modes existing at the boundaries by considering the synthetic dimension as a modulated parameter. We also show how to measure these topological phases experimentally in ultracold atoms. Another model with a random Rashba and Dresselhaus spin-orbit coupling strength is also found to exhibit topological nontrivial phase, and the impact of the disorder to the system is revealed.

High-resolution three-dimensional structural microscopy by single-angle Bragg ptychography

DOE PAGES

Hruszkewycz, S. O.; Allain, M.; Holt, M. V.; ...

2016-11-21

Coherent X-ray microscopy by phase retrieval of Bragg diffraction intensities enables lattice distortions within a crystal to be imaged at nanometre-scale spatial resolutions in three dimensions. While this capability can be used to resolve structure–property relationships at the nanoscale under working conditions, strict data measurement requirements can limit the application of current approaches. Here, in this work, we introduce an efficient method of imaging three-dimensional (3D) nanoscale lattice behaviour and strain fields in crystalline materials with a methodology that we call 3D Bragg projection ptychography (3DBPP). This method enables 3D image reconstruction of a crystal volume from a series ofmore » two-dimensional X-ray Bragg coherent intensity diffraction patterns measured at a single incident beam angle. Structural information about the sample is encoded along two reciprocal-space directions normal to the Bragg diffracted exit beam, and along the third dimension in real space by the scanning beam. Finally, we present our approach with an analytical derivation, a numerical demonstration, and an experimental reconstruction of lattice distortions in a component of a nanoelectronic prototype device.« less

Balanced Central Schemes for the Shallow Water Equations on Unstructured Grids

NASA Technical Reports Server (NTRS)

Bryson, Steve; Levy, Doron

2004-01-01

We present a two-dimensional, well-balanced, central-upwind scheme for approximating solutions of the shallow water equations in the presence of a stationary bottom topography on triangular meshes. Our starting point is the recent central scheme of Kurganov and Petrova (KP) for approximating solutions of conservation laws on triangular meshes. In order to extend this scheme from systems of conservation laws to systems of balance laws one has to find an appropriate discretization of the source terms. We first show that for general triangulations there is no discretization of the source terms that corresponds to a well-balanced form of the KP scheme. We then derive a new variant of a central scheme that can be balanced on triangular meshes. We note in passing that it is straightforward to extend the KP scheme to general unstructured conformal meshes. This extension allows us to recover our previous well-balanced scheme on Cartesian grids. We conclude with several simulations, verifying the second-order accuracy of our scheme as well as its well-balanced properties.

Model of chiral spin liquids with Abelian and non-Abelian topological phases

DOE PAGES

Chen, Jyong-Hao; Mudry, Christopher; Chamon, Claudio; ...

2017-12-15

In this article, we present a two-dimensional lattice model for quantum spin-1/2 for which the low-energy limit is governed by four flavors of strongly interacting Majorana fermions. We study this low-energy effective theory using two alternative approaches. The first consists of a mean-field approximation. The second consists of a random phase approximation (RPA) for the single-particle Green's functions of the Majorana fermions built from their exact forms in a certain one-dimensional limit. The resulting phase diagram consists of two competing chiral phases, one with Abelian and the other with non-Abelian topological order, separated by a continuous phase transition. Remarkably, themore » Majorana fermions propagate in the two-dimensional bulk, as in the Kitaev model for a spin liquid on the honeycomb lattice. We identify the vison fields, which are mobile (they are static in the Kitaev model) domain walls propagating along only one of the two space directions.« less

Model of chiral spin liquids with Abelian and non-Abelian topological phases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Jyong-Hao; Mudry, Christopher; Chamon, Claudio

In this article, we present a two-dimensional lattice model for quantum spin-1/2 for which the low-energy limit is governed by four flavors of strongly interacting Majorana fermions. We study this low-energy effective theory using two alternative approaches. The first consists of a mean-field approximation. The second consists of a random phase approximation (RPA) for the single-particle Green's functions of the Majorana fermions built from their exact forms in a certain one-dimensional limit. The resulting phase diagram consists of two competing chiral phases, one with Abelian and the other with non-Abelian topological order, separated by a continuous phase transition. Remarkably, themore » Majorana fermions propagate in the two-dimensional bulk, as in the Kitaev model for a spin liquid on the honeycomb lattice. We identify the vison fields, which are mobile (they are static in the Kitaev model) domain walls propagating along only one of the two space directions.« less

One-loop calculations in Supersymmetric Lattice QCD

NASA Astrophysics Data System (ADS)

Costa, M.; Panagopoulos, H.

2017-03-01

We study the self energies of all particles which appear in a lattice regularization of supersymmetric QCD (N = 1). We compute, perturbatively to one-loop, the relevant two-point Green's functions using both the dimensional and the lattice regularizations. Our lattice formulation employs the Wilson fermion acrion for the gluino and quark fields. The gauge group that we consider is SU(Nc) while the number of colors, Nc and the number of flavors, Nf , are kept as generic parameters. We have also searched for relations among the propagators which are computed from our one-loop results. We have obtained analytic expressions for the renormalization functions of the quark field (Zψ), gluon field (Zu), gluino field (Zλ) and squark field (ZA±). We present here results from dimensional regularization, relegating to a forthcoming publication [1] our results along with a more complete list of references. Part of the lattice study regards also the renormalization of quark bilinear operators which, unlike the nonsupersymmetric case, exhibit a rich pattern of operator mixing at the quantum level.

Biased and greedy random walks on two-dimensional lattices with quenched randomness: The greedy ant within a disordered environment

NASA Astrophysics Data System (ADS)

Mitran, T. L.; Melchert, O.; Hartmann, A. K.

2013-12-01

The main characteristics of biased greedy random walks (BGRWs) on two-dimensional lattices with real-valued quenched disorder on the lattice edges are studied. Here the disorder allows for negative edge weights. In previous studies, considering the negative-weight percolation (NWP) problem, this was shown to change the universality class of the existing, static percolation transition. In the presented study, four different types of BGRWs and an algorithm based on the ant colony optimization heuristic were considered. Regarding the BGRWs, the precise configurations of the lattice walks constructed during the numerical simulations were influenced by two parameters: a disorder parameter ρ that controls the amount of negative edge weights on the lattice and a bias strength B that governs the drift of the walkers along a certain lattice direction. The random walks are “greedy” in the sense that the local optimal choice of the walker is to preferentially traverse edges with a negative weight (associated with a net gain of “energy” for the walker). Here, the pivotal observable is the probability that, after termination, a lattice walk exhibits a total negative weight, which is here considered as percolating. The behavior of this observable as function of ρ for different bias strengths B is put under scrutiny. Upon tuning ρ, the probability to find such a feasible lattice walk increases from zero to 1. This is the key feature of the percolation transition in the NWP model. Here, we address the question how well the transition point ρc, resulting from numerically exact and “static” simulations in terms of the NWP model, can be resolved using simple dynamic algorithms that have only local information available, one of the basic questions in the physics of glassy systems.

Cross-circularly polarized two-exciton states in one to three dimensions

NASA Astrophysics Data System (ADS)

Ajiki, Hiroshi

2015-03-01

Biexciton and two-exciton dissociated states of Frenkel-type excitons are studied theoretically using an exciton tight-binding (TB) model including a polarization degree of freedom. Because the biexciton consists of two cross-circularly polarized excitons, an on-site interaction (V) between the two excitons should be considered in addition to a nearest-neighbor two-exciton attractive interaction (δ). Although there are an infinitely large number of combinations of V and δ providing the observed binding energy of a biexciton, the wave function of the biexciton and two-exciton dissociated states is nearly independent of these parameter sets. This means that all the two-exciton states are uniquely determined from the exciton TB model. There are a spatially symmetric and an antisymmetric biexciton state for a one-dimensional (1D) lattice and two symmetric and one antisymmetric biexciton states at most for two- (2D) and three-dimensional (3D) lattices. In contrast, when the polarization degree of freedom is ignored, there is one biexciton state for 1D, 2D, and 3D lattices. For this study, a rapid and memory-saving calculation method for two-exciton states is extended to include the polarization degree of freedom.

Cross-circularly polarized two-exciton states in one to three dimensions.

PubMed

Ajiki, Hiroshi

2015-03-14

Biexciton and two-exciton dissociated states of Frenkel-type excitons are studied theoretically using an exciton tight-binding (TB) model including a polarization degree of freedom. Because the biexciton consists of two cross-circularly polarized excitons, an on-site interaction (V) between the two excitons should be considered in addition to a nearest-neighbor two-exciton attractive interaction (δ). Although there are an infinitely large number of combinations of V and δ providing the observed binding energy of a biexciton, the wave function of the biexciton and two-exciton dissociated states is nearly independent of these parameter sets. This means that all the two-exciton states are uniquely determined from the exciton TB model. There are a spatially symmetric and an antisymmetric biexciton state for a one-dimensional (1D) lattice and two symmetric and one antisymmetric biexciton states at most for two- (2D) and three-dimensional (3D) lattices. In contrast, when the polarization degree of freedom is ignored, there is one biexciton state for 1D, 2D, and 3D lattices. For this study, a rapid and memory-saving calculation method for two-exciton states is extended to include the polarization degree of freedom.

Quasi-two-dimensional Bose-Einstein condensation of lattice bosons in the spin-1/2 XXZ ferromagnet K2CuF4

NASA Astrophysics Data System (ADS)

Hirata, Satoshi; Kurita, Nobuyuki; Yamada, Motoki; Tanaka, Hidekazu

2017-05-01

K2CuF4 is magnetically described as a spin-1/2 , quasi-two-dimensional (2D), square-lattice XXZ ferromagnet with weak easy-plane anisotropy. The magnetic ordering for an applied magnetic field H parallel to the c axis is equivalent to the Bose-Einstein condensation (BEC) of lattice bosons, as discussed by Matsubara and Matsuda [T. Matsubara and H. Matsuda, Prog. Theor. Phys. 16, 569 (1956), 10.1143/PTP.16.569]. Magnetization and specific-heat measurements were performed to obtain the temperature versus magnetic field phase diagram for H ∥c . The phase boundary between polarized and ordered phases was found to be expressed by the power law Hc(T ) -Hc(0 ) ∝Tϕ with exponent ϕ ≈1.0 in a wide temperature range, in agreement with the theory of quasi-2D BEC.

Transition from two-dimensional photonic crystals to dielectric metasurfaces in the optical diffraction with a fine structure

PubMed Central

Rybin, Mikhail V.; Samusev, Kirill B.; Lukashenko, Stanislav Yu.; Kivshar, Yuri S.; Limonov, Mikhail F.

2016-01-01

We study experimentally a fine structure of the optical Laue diffraction from two-dimensional periodic photonic lattices. The periodic photonic lattices with the C4v square symmetry, orthogonal C2v symmetry, and hexagonal C6v symmetry are composed of submicron dielectric elements fabricated by the direct laser writing technique. We observe surprisingly strong optical diffraction from a finite number of elements that provides an excellent tool to determine not only the symmetry but also exact number of particles in the finite-length structure and the sample shape. Using different samples with orthogonal C2v symmetry and varying the lattice spacing, we observe experimentally a transition between the regime of multi-order diffraction, being typical for photonic crystals to the regime where only the zero-order diffraction can be observed, being is a clear fingerprint of dielectric metasurfaces characterized by effective parameters. PMID:27491952

Wavelength-scale Microlasers based on VCSEL-Photonic Crystal Architecture

DTIC Science & Technology

2015-01-20

molecular beam epitaxy , MBE). We will also assume the triangular lattice of air...Abbreviations, and Acronyms InP: indium phosphide InGaAsP: indium gallium arsenide phosphide MBE: molecular beam epiitaxy VCSEL : vertical cavity...substrates and were grown by MBE. Electron beam lithography and reactive ion etching was used to deep‐etch the holes of the PhC‐ VCSELS ,

Tunable all-angle negative refraction and photonic band gaps in two-dimensional plasma photonic crystals with square-like Archimedean lattices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Hai-Feng, E-mail: hanlor@163.com, E-mail: lsb@nuaa.edu.cn; Nanjing Artillery Academy, Nanjing 211132; Liu, Shao-Bin, E-mail: hanlor@163.com, E-mail: lsb@nuaa.edu.cn

In this paper, the tunable all-angle negative refraction and photonic band gaps (PBGs) in two types of two-dimensional (2D) plasma photonic crystals (PPCs) composed of homogeneous plasma and dielectric (GaAs) with square-like Archimedean lattices (ladybug and bathroom lattices) for TM wave are theoretically investigated based on a modified plane wave expansion method. The type-1 structure is dielectric rods immersed in the plasma background, and the complementary structure is named as type-2 PPCs. Theoretical simulations demonstrate that the both types of PPCs with square-like Archimedean lattices have some advantages in obtaining the higher cut-off frequency, the larger PBGs, more number ofmore » PBGs, and the relative bandwidths compared to the conventional square lattices as the filling factor or radius of inserted rods is same. The influences of plasma frequency and radius of inserted rod on the properties of PBGs for both types of PPCs also are discussed in detail. The calculated results show that PBGs can be manipulated by the parameters as mentioned above. The possibilities of all-angle negative refraction in such two types of PPCs at low bands also are discussed. Our calculations reveal that the all-angle negative phenomena can be observed in the first two TM bands, and the frequency range of all-angle negative refraction can be tuned by changing plasma frequency. Those properties can be used to design the optical switching and sensor.« less

Realization of a Hole-Doped Mott Insulator on a Triangular Silicon Lattice

NASA Astrophysics Data System (ADS)

Ming, Fangfei; Johnston, Steve; Mulugeta, Daniel; Smith, Tyler S.; Vilmercati, Paolo; Lee, Geunseop; Maier, Thomas A.; Snijders, Paul C.; Weitering, Hanno H.

2017-12-01

The physics of doped Mott insulators is at the heart of some of the most exotic physical phenomena in materials research including insulator-metal transitions, colossal magnetoresistance, and high-temperature superconductivity in layered perovskite compounds. Advances in this field would greatly benefit from the availability of new material systems with a similar richness of physical phenomena but with fewer chemical and structural complications in comparison to oxides. Using scanning tunneling microscopy and spectroscopy, we show that such a system can be realized on a silicon platform. The adsorption of one-third monolayer of Sn atoms on a Si(111) surface produces a triangular surface lattice with half filled dangling bond orbitals. Modulation hole doping of these dangling bonds unveils clear hallmarks of Mott physics, such as spectral weight transfer and the formation of quasiparticle states at the Fermi level, well-defined Fermi contour segments, and a sharp singularity in the density of states. These observations are remarkably similar to those made in complex oxide materials, including high-temperature superconductors, but highly extraordinary within the realm of conventional s p -bonded semiconductor materials. It suggests that exotic quantum matter phases can be realized and engineered on silicon-based materials platforms.

A scalable PC-based parallel computer for lattice QCD

NASA Astrophysics Data System (ADS)

Fodor, Z.; Katz, S. D.; Pappa, G.

2003-05-01

A PC-based parallel computer for medium/large scale lattice QCD simulations is suggested. The Eo¨tvo¨s Univ., Inst. Theor. Phys. cluster consists of 137 Intel P4-1.7GHz nodes. Gigabit Ethernet cards are used for nearest neighbor communication in a two-dimensional mesh. The sustained performance for dynamical staggered (wilson) quarks on large lattices is around 70(110) GFlops. The exceptional price/performance ratio is below $1/Mflop.

Growth, Characterization and Device Development in Monocrystalline Diamond Films

DTIC Science & Technology

1988-06-01

ABSTRACT (ContMut on reverse,*i nauar and .dnr,A, A. W, -,,,I !Cu single crystals have been grown and prepared for use as a lattice matched substrate. A...literature survey of potential substrates which are both lattice and energy matched with diamond to promote two-dimensional growth has also been...first reported high resolution lattice imaging of CVD diamond. Diamond power MESFET devices have been theoretically evaluated and found to be capable

A VERSATILE SHARP INTERFACE IMMERSED BOUNDARY METHOD FOR INCOMPRESSIBLE FLOWS WITH COMPLEX BOUNDARIES

PubMed Central

Mittal, R.; Dong, H.; Bozkurttas, M.; Najjar, F.M.; Vargas, A.; von Loebbecke, A.

2010-01-01

A sharp interface immersed boundary method for simulating incompressible viscous flow past three-dimensional immersed bodies is described. The method employs a multi-dimensional ghost-cell methodology to satisfy the boundary conditions on the immersed boundary and the method is designed to handle highly complex three-dimensional, stationary, moving and/or deforming bodies. The complex immersed surfaces are represented by grids consisting of unstructured triangular elements; while the flow is computed on non-uniform Cartesian grids. The paper describes the salient features of the methodology with special emphasis on the immersed boundary treatment for stationary and moving boundaries. Simulations of a number of canonical two- and three-dimensional flows are used to verify the accuracy and fidelity of the solver over a range of Reynolds numbers. Flow past suddenly accelerated bodies are used to validate the solver for moving boundary problems. Finally two cases inspired from biology with highly complex three-dimensional bodies are simulated in order to demonstrate the versatility of the method. PMID:20216919

High-rotational symmetry lattices fabricated by moiré nanolithography.

PubMed

Lubin, Steven M; Zhou, Wei; Hryn, Alexander J; Huntington, Mark D; Odom, Teri W

2012-09-12

This paper describes a new nanofabrication method, moiré nanolithography, that can fabricate subwavelength lattices with high-rotational symmetries. By exposing elastomeric photomasks sequentially at multiple offset angles, we created arrays with rotational symmetries as high as 36-fold, which is three times higher than quasiperiodic lattices (≤12-fold) and six times higher than two-dimensional periodic lattices (≤6-fold). Because these moiré nanopatterns can be generated over wafer-scale areas, they are promising for a range of photonic applications, especially those that require broadband, omnidirectional absorption of visible light.

O (a) improvement of 2D N = (2 , 2) lattice SYM theory

NASA Astrophysics Data System (ADS)

Hanada, Masanori; Kadoh, Daisuke; Matsuura, So; Sugino, Fumihiko

2018-04-01

We perform a tree-level O (a) improvement of two-dimensional N = (2 , 2) supersymmetric Yang-Mills theory on the lattice, motivated by the fast convergence in numerical simulations. The improvement respects an exact supersymmetry Q which is needed for obtaining the correct continuum limit without a parameter fine tuning. The improved lattice action is given within a milder locality condition in which the interactions are decaying as the exponential of the distance on the lattice. We also prove that the path-integral measure is invariant under the improved Q-transformation.

3d Abelian dualities with boundaries

NASA Astrophysics Data System (ADS)

Aitken, Kyle; Baumgartner, Andrew; Karch, Andreas; Robinson, Brandon

2018-03-01

We establish the action of three-dimensional bosonization and particle-vortex duality in the presence of a boundary, which supports a non-anomalous two-dimensional theory. We confirm our prescription using a microscopic realization of the duality in terms of a Euclidean lattice.

Identifying the genes of unconventional high temperature superconductors.

PubMed

Hu, Jiangping

We elucidate a recently emergent framework in unifying the two families of high temperature (high [Formula: see text]) superconductors, cuprates and iron-based superconductors. The unification suggests that the latter is simply the counterpart of the former to realize robust extended s-wave pairing symmetries in a square lattice. The unification identifies that the key ingredients (gene) of high [Formula: see text] superconductors is a quasi two dimensional electronic environment in which the d -orbitals of cations that participate in strong in-plane couplings to the p -orbitals of anions are isolated near Fermi energy. With this gene, the superexchange magnetic interactions mediated by anions could maximize their contributions to superconductivity. Creating the gene requires special arrangements between local electronic structures and crystal lattice structures. The speciality explains why high [Formula: see text] superconductors are so rare. An explicit prediction is made to realize high [Formula: see text] superconductivity in Co/Ni-based materials with a quasi two dimensional hexagonal lattice structure formed by trigonal bipyramidal complexes.

Percolation of spatially constraint networks

NASA Astrophysics Data System (ADS)

Li, Daqing; Li, Guanliang; Kosmidis, Kosmas; Stanley, H. E.; Bunde, Armin; Havlin, Shlomo

2011-03-01

We study how spatial constraints are reflected in the percolation properties of networks embedded in one-dimensional chains and two-dimensional lattices. We assume long-range connections between sites on the lattice where two sites at distance r are chosen to be linked with probability p(r)~r-δ. Similar distributions have been found in spatially embedded real networks such as social and airline networks. We find that for networks embedded in two dimensions, with 2<δ<4, the percolation properties show new intermediate behavior different from mean field, with critical exponents that depend on δ. For δ<2, the percolation transition belongs to the universality class of percolation in Erdös-Rényi networks (mean field), while for δ>4 it belongs to the universality class of percolation in regular lattices. For networks embedded in one dimension, we find that, for δ<1, the percolation transition is mean field. For 1<δ<2, the critical exponents depend on δ, while for δ>2 there is no percolation transition as in regular linear chains.

Emergent pseudospin-1 Maxwell fermions with a threefold degeneracy in optical lattices

NASA Astrophysics Data System (ADS)

Zhu, Yan-Qing; Zhang, Dan-Wei; Yan, Hui; Xing, Ding-Yu; Zhu, Shi-Liang

2017-09-01

The discovery of relativistic spin-1/2 fermions such as Dirac and Weyl fermions in condensed-matter or artificial systems opens a new era in modern physics. An interesting but rarely explored question is whether other relativistic spinal excitations could be realized with artificial systems. Here, we construct two- and three-dimensional tight-binding models realizable with cold fermionic atoms in optical lattices, where the low energy excitations are effectively described by the spin-1 Maxwell equations in the Hamiltonian form. These relativistic (linear dispersion) excitations with unconventional integer pseudospin, beyond the Dirac-Weyl-Majorana fermions, are an exotic kind of fermions named as Maxwell fermions. We demonstrate that the systems have rich topological features. For instance, the threefold degenerate points called Maxwell points may have quantized Berry phases and anomalous quantum Hall effects with spin-momentum locking may appear in topological Maxwell insulators in the two-dimensional lattices. In three dimensions, Maxwell points may have nontrivial monopole charges of ±2 with two Fermi arcs connecting them, and the merging of the Maxwell points leads to topological phase transitions. Finally, we propose realistic schemes for realizing the model Hamiltonians and detecting the topological properties of the emergent Maxwell quasiparticles in optical lattices.

Microwave (EPR) measurements of the penetration depth measurements of high-Tc superconductors

NASA Technical Reports Server (NTRS)

Dalal, N. S.; Rakvin, B.; Mahl, T. A.; Bhalla, A. S.; Sheng, Z. Z.

1991-01-01

The use is discussed of electron paramagnetic resonance (EPR) as a quick and easily accessible method for measuring the London penetration depth, lambda for the high T sub c superconductors. The method uses the broadening of the EPR signal, due to the emergence of the magnetic flux lattice, of a free radical adsorbed on the surface of the sample. The second moment, of the EPR signal below T sub c is fitted to the Brandt equation for a simple triangular lattice. The precision of this method compares quite favorably with those of the more standard methods such as micro sup(+)SR, neutron scattering, and magnetic susceptibility.

An EPR methodology for measuring the London penetration depth for the ceramic superconductors

NASA Technical Reports Server (NTRS)

Rakvin, B.; Mahl, T. A.; Dalal, N. S.

1990-01-01

The use is discussed of electron paramagnetic resonance (EPR) as a quick and easily accessible method for measuring the London penetration depth, lambda for the high T(sub c) superconductors. The method utilizes the broadening of the EPR signal, due to the emergence of the magnetic flux lattice, of a free radical adsorbed on the surface of the sample. The second moment, of the EPR signal below T(sub c) is fitted to the Brandt equation for a simple triangular lattice. The precision of this method compares quite favorably with those of the more standard methods such as micro sup(+)SR, Neutron scattering, and magnetic susceptibility.

From the S U (2 ) quantum link model on the honeycomb lattice to the quantum dimer model on the kagome lattice: Phase transition and fractionalized flux strings

NASA Astrophysics Data System (ADS)

Banerjee, D.; Jiang, F.-J.; Olesen, T. Z.; Orland, P.; Wiese, U.-J.

2018-05-01

We consider the (2 +1 ) -dimensional S U (2 ) quantum link model on the honeycomb lattice and show that it is equivalent to a quantum dimer model on the kagome lattice. The model has crystalline confined phases with spontaneously broken translation invariance associated with pinwheel order, which is investigated with either a Metropolis or an efficient cluster algorithm. External half-integer non-Abelian charges [which transform nontrivially under the Z (2 ) center of the S U (2 ) gauge group] are confined to each other by fractionalized strings with a delocalized Z (2 ) flux. The strands of the fractionalized flux strings are domain walls that separate distinct pinwheel phases. A second-order phase transition in the three-dimensional Ising universality class separates two confining phases: one with correlated pinwheel orientations, and the other with uncorrelated pinwheel orientations.

Imaging galectin-3 dependent endocytosis with lattice light-sheet microscopy

NASA Astrophysics Data System (ADS)

Baek, Jongho; Lou, Jieqiong; Coelho, Simao; Lim, Yean Jin; Seidlitz, Silvia; Nicovich, Philip R.; Wunder, Christian; Johannes, Ludger; Gaus, Katharina

2017-04-01

Lattice light-sheet (LLS) microscopy provides ultrathin light sheets of a two-dimensional optical lattice that allows us imaging three-dimensional (3D) objects for hundreds of time points at sub-second intervals and at or below the diffraction limit. Galectin-3 (Gal3), a carbohydrate-binding protein, triggers glycosphingolipid (GSL)-dependent biogenesis of morphologically distinct endocytic vesicles that are cargo specific and clathrin independent. In this study, we apply LLS microscopy to study the dynamics of Gal3 dependent endocytosis in live T cells. This will allow us to observe Gal3-mediated endocytosis at high temporal and excellent 3D spatial resolution, which may shed light on our understanding of the mechanism and physiological function of Gal3-induced endocytosis.

Development of axisymmetric lattice Boltzmann flux solver for complex multiphase flows

NASA Astrophysics Data System (ADS)

Wang, Yan; Shu, Chang; Yang, Li-Ming; Yuan, Hai-Zhuan

2018-05-01

This paper presents an axisymmetric lattice Boltzmann flux solver (LBFS) for simulating axisymmetric multiphase flows. In the solver, the two-dimensional (2D) multiphase LBFS is applied to reconstruct macroscopic fluxes excluding axisymmetric effects. Source terms accounting for axisymmetric effects are introduced directly into the governing equations. As compared to conventional axisymmetric multiphase lattice Boltzmann (LB) method, the present solver has the kinetic feature for flux evaluation and avoids complex derivations of external forcing terms. In addition, the present solver also saves considerable computational efforts in comparison with three-dimensional (3D) computations. The capability of the proposed solver in simulating complex multiphase flows is demonstrated by studying single bubble rising in a circular tube. The obtained results compare well with the published data.

Polymer photonic crystal slab waveguides

NASA Astrophysics Data System (ADS)

Liguda, C.; Böttger, G.; Kuligk, A.; Blum, R.; Eich, M.; Roth, H.; Kunert, J.; Morgenroth, W.; Elsner, H.; Meyer, H. G.

2001-04-01

We present details of the fabrication, calculations, and transmission measurements for finite two-dimensional (2D) polymer photonic crystal (PC) slab waveguides, which were fabricated from a benzocyclobutene polymer on a low refractive index substrate from Teflon. A square air hole lattice (500 nm lattice constant, 300 nm hole diameter) was realized by electron beam lithography and reactive ion etching. Polarization and wavelength dependent transmission results show TE-like and TM-like stop gaps at 1.3 μm excitation wavelengths and are in good agreement with the calculated data obtained by 2D and three-dimensional finite difference time domain methods. Transmission was suppressed by 15 dB in the center of the TE-like stop gap for a PC length of ten lattice constants.

Probing the exchange statistics of one-dimensional anyon models

NASA Astrophysics Data System (ADS)

Greschner, Sebastian; Cardarelli, Lorenzo; Santos, Luis

2018-05-01

We propose feasible scenarios for revealing the modified exchange statistics in one-dimensional anyon models in optical lattices based on an extension of the multicolor lattice-depth modulation scheme introduced in [Phys. Rev. A 94, 023615 (2016), 10.1103/PhysRevA.94.023615]. We show that the fast modulation of a two-component fermionic lattice gas in the presence a magnetic field gradient, in combination with additional resonant microwave fields, allows for the quantum simulation of hardcore anyon models with periodic boundary conditions. Such a semisynthetic ring setup allows for realizing an interferometric arrangement sensitive to the anyonic statistics. Moreover, we show as well that simple expansion experiments may reveal the formation of anomalously bound pairs resulting from the anyonic exchange.

Applications of the Lattice Boltzmann Method to Complex and Turbulent Flows

NASA Technical Reports Server (NTRS)

Luo, Li-Shi; Qi, Dewei; Wang, Lian-Ping; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

We briefly review the method of the lattice Boltzmann equation (LBE). We show the three-dimensional LBE simulation results for a non-spherical particle in Couette flow and 16 particles in sedimentation in fluid. We compare the LBE simulation of the three-dimensional homogeneous isotropic turbulence flow in a periodic cubic box of the size 1283 with the pseudo-spectral simulation, and find that the two results agree well with each other but the LBE method is more dissipative than the pseudo-spectral method in small scales, as expected.

An extended approach for computing the critical properties in the two-and three-dimensional lattices within the effective-field renormalization group method

NASA Astrophysics Data System (ADS)

de Albuquerque, Douglas F.; Santos-Silva, Edimilson; Moreno, N. O.

2009-10-01

In this letter we employing the effective-field renormalization group (EFRG) to study the Ising model with nearest neighbors to obtain the reduced critical temperature and exponents ν for bi- and three-dimensional lattices by increasing cluster scheme by extending recent works. The technique follows up the same strategy of the mean field renormalization group (MFRG) by introducing an alternative way for constructing classical effective-field equations of state takes on rigorous Ising spin identities.

Realization of discrete quantum billiards in a two-dimensional optical lattice

DOE Office of Scientific and Technical Information (OSTI.GOV)

Krimer, Dmitry O.; Max-Planck Institute for the Physics of Complex Systems, Noethnitzer Strasse 38, D-01187 Dresden; Khomeriki, Ramaz

2011-10-15

We propose a method for optical visualization of the Bose-Hubbard model with two interacting bosons in the form of two-dimensional (2D) optical lattices consisting of optical waveguides, where the waveguides at the diagonal are characterized by different refractive indices than others elsewhere, modeling the boson-boson interaction. We study the light intensity distribution function averaged over the direction of propagation for both ordered and disordered cases, exploring the sensitivity of the averaged picture with respect to the beam injection position. For our finite systems, the resulting patterns are reminiscent the ones set in billiards, and therefore we introduce a definition ofmore » discrete quantum billiards and discuss the possible relevance to its well-established continuous counterpart.« less

Polymorphism in the nitrate salt of the [Mn(acetylacetonate)2(H2O)2]+ ion.

PubMed

Biju, A R; Rajasekharan, M V

2010-06-01

The crystallization of [Mn(acac)(2)(H(2)O)(2)](+) from solutions containing excess nitrate leads to the formation of four polymorphs. All polymorphs contain two different types of complex ions, one containing essentially coplanar acac ligands and the other in which the two acac ligands together assume a chair conformation. Molecular modelling using DFT (density-functional theory) calculations shows that the coplanar conformation is the electronically stable one. The hydrogen bonding between the trans-water molecules and the nitrate ion produces a one-dimensional chain of 12-membered rings, which are further organized into a two-dimensional network via a lattice water molecule. Lattice-energy calculations have been carried out to compare the stabilities of the four polymorphs.

Structural stability and electronic properties of an octagonal allotrope of two dimensional boron nitride.

PubMed

Takahashi, Lauren; Takahashi, Keisuke

2017-03-27

An octagonal allotrope of two dimensional boron nitride is explored through first principles calculations. Calculations show that two dimensional octagonal boron nitride can be formed with a binding energy comparable to two dimensional hexagonal boron nitride. In addition, two dimensional octagonal boron nitride is found to have a band gap smaller than two dimensional hexagonal boron nitride, suggesting the possibility of semiconductive attributes. Two dimensional octagonal boron nitride also has the ability to layer through physisorption. Defects present within two dimensional octagonal boron nitride also lead toward the introduction of a magnetic moment through the absence of boron atoms. The presence of defects is also found to render both hexagonal and octagonal boron nitrides reactive against hydrogen, where greater reactivity is seen in the presence of nitrogen. Thus, two dimensional octagonal boron nitride is confirmed with potential to tailor properties and reactivity through lattice shape and purposeful introduction of defects.

Asymptotics of the monomer-dimer model on two-dimensional semi-infinite lattices

NASA Astrophysics Data System (ADS)

Kong, Yong

2007-05-01

By using the asymptotic theory of Pemantle and Wilson [R. Pemantle and M. C. Wilson, J. Comb. Theory, Ser. AJCBTA70097-316510.1006/jcta.2001.3201 97, 129 (2002)], asymptotic expansions of the free energy of the monomer-dimer model on two-dimensional semi-infinite ∞×n lattices in terms of dimer density are obtained for small values of n , at both high- and low-dimer-density limits. In the high-dimer-density limit, the theoretical results confirm the dependence of the free energy on the parity of n , a result obtained previously by computational methods by Y. Kong [Y. Kong, Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.74.061102 74, 061102 (2006); Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.73.016106 73, 016106 (2006);Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.74.011102 74, 011102 (2006)]. In the low-dimer-density limit, the free energy on a cylinder ∞×n lattice strip has exactly the same first n terms in the series expansion as that of an infinite ∞×∞ lattice.

Topologically protected bound states in one-dimensional Floquet acoustic waveguide systems

NASA Astrophysics Data System (ADS)

Peng, Yu-Gui; Geng, Zhi-Guo; Zhu, Xue-Feng

2018-03-01

Topological manipulation of sound has recently been a hot spot in acoustics due to the fascinating property of defect immune transport. To the best of our knowledge, the studies on one-dimensional (1D) topological acoustic systems hitherto mainly focus on the case of the Su-Schrieffer-Heeger model. Here, we show that topologically protected bound states may also exist in 1D periodically modulated acoustic waveguide systems, viz., 1D Floquet topological insulators. The results show that tuning the coupling strength in a waveguide lattice could trigger topological phase transition, which gives rise to topologically protected interface states as we put together two waveguide lattices featured with different topological phases or winding numbers. However, for the combined lattice, input at the waveguides other than the interfacial ones will excite bulk states. We have further verified the robustness of interface bound states against the variation of coupling strengths between the two distinct waveguide lattices. This work extends the scope of topological acoustics and may promote potential applications for acoustic devices with topological functionalities.

Lattice surgery on the Raussendorf lattice

NASA Astrophysics Data System (ADS)

Herr, Daniel; Paler, Alexandru; Devitt, Simon J.; Nori, Franco

2018-07-01

Lattice surgery is a method to perform quantum computation fault-tolerantly by using operations on boundary qubits between different patches of the planar code. This technique allows for universal planar code computation without eliminating the intrinsic two-dimensional nearest-neighbor properties of the surface code that eases physical hardware implementations. Lattice surgery approaches to algorithmic compilation and optimization have been demonstrated to be more resource efficient for resource-intensive components of a fault-tolerant algorithm, and consequently may be preferable over braid-based logic. Lattice surgery can be extended to the Raussendorf lattice, providing a measurement-based approach to the surface code. In this paper we describe how lattice surgery can be performed on the Raussendorf lattice and therefore give a viable alternative to computation using braiding in measurement-based implementations of topological codes.

Directed Abelian algebras and their application to stochastic models.

PubMed

Alcaraz, F C; Rittenberg, V

2008-10-01

With each directed acyclic graph (this includes some D-dimensional lattices) one can associate some Abelian algebras that we call directed Abelian algebras (DAAs). On each site of the graph one attaches a generator of the algebra. These algebras depend on several parameters and are semisimple. Using any DAA, one can define a family of Hamiltonians which give the continuous time evolution of a stochastic process. The calculation of the spectra and ground-state wave functions (stationary state probability distributions) is an easy algebraic exercise. If one considers D-dimensional lattices and chooses Hamiltonians linear in the generators, in finite-size scaling the Hamiltonian spectrum is gapless with a critical dynamic exponent z=D. One possible application of the DAA is to sandpile models. In the paper we present this application, considering one- and two-dimensional lattices. In the one-dimensional case, when the DAA conserves the number of particles, the avalanches belong to the random walker universality class (critical exponent sigma_(tau)=32 ). We study the local density of particles inside large avalanches, showing a depletion of particles at the source of the avalanche and an enrichment at its end. In two dimensions we did extensive Monte-Carlo simulations and found sigma_(tau)=1.780+/-0.005 .

Magnetic dipole interactions in crystals

DOE PAGES

Johnston, David

2016-01-13

The influence of magnetic dipole interactions (MDIs) on the magnetic properties of local-moment Heisenberg spin systems is investigated. A general formulation is presented for calculating the eigenvalues λ and eigenvectors μ ˆ of the MDI tensor of the magnetic dipoles in a line (one dimension, 1D), within a circle (2D) or a sphere (3D) of radius r surrounding a given moment μ → i for given magnetic propagation vectors k for collinear and coplanar noncollinear magnetic structures on both Bravais and non-Bravais spin lattices. Results are calculated for collinear ordering on 1D chains, 2D square and simple-hexagonal (triangular) Bravaismore » lattices, 2D honeycomb and kagomé non-Bravais lattices, and 3D cubic Bravais lattices. The λ and μ ˆ values are compared with previously reported results. Calculations for collinear ordering on 3D simple tetragonal, body-centered tetragonal, and stacked triangular and honeycomb lattices are presented for c/a ratios from 0.5 to 3 in both graphical and tabular form to facilitate comparison of experimentally determined easy axes of ordering on these Bravais lattices with the predictions for MDIs. Comparisons with the easy axes measured for several illustrative collinear antiferromagnets (AFMs) are given. The calculations are extended to the cycloidal noncollinear 120 ° AFM ordering on the triangular lattice where λ is found to be the same as for collinear AFM ordering with the same k. The angular orientation of the ordered moments in the noncollinear coplanar AFM structure of GdB 4 with a distorted stacked 3D Shastry-Sutherland spin-lattice geometry is calculated and found to be in disagreement with experimental observations, indicating the presence of another source of anisotropy. Similar calculations for the undistorted 2D and stacked 3D Shastry-Sutherland lattices are reported. The thermodynamics of dipolar magnets are calculated using the Weiss molecular field theory for quantum spins, including the magnetic transition temperature T m and the ordered moment, magnetic heat capacity, and anisotropic magnetic susceptibility χ versus temperature T . The anisotropic Weiss temperature θ p in the Curie-Weiss law for T>T m is calculated. A quantitative study of the competition between FM and AFM ordering on cubic Bravais lattices versus the demagnetization factor in the absence of FM domain effects is presented. The contributions of Heisenberg exchange interactions and of the MDIs to T m and to θ p are found to be additive, which simplifies analysis of experimental data. Some properties in the magnetically-ordered state versus T are presented, including the ordered moment and magnetic heat capacity and, for AFMs, the dipolar anisotropy of the free energy and the perpendicular critical field. The anisotropic χ for dipolar AFMs is calculated both above and below the Néel temperature T N and the results are illustrated for a simple tetragonal lattice with c/a>1, c/a=1 (cubic), and c/a<1 , where a change in sign of the χ anisotropy is found at c/a=1 . Finally, following the early work of Keffer [Phys. Rev. 87, 608 (1952)], the dipolar anisotropy of χ above T N =69 K of the prototype collinear Heisenberg-exchange-coupled tetragonal compound MnF 2 is calculated and found to be in excellent agreement with experimental single-crystal literature data above 130 K, where the smoothly increasing deviation of the experimental data from the theory on cooling from 130 K to T N is deduced to arise from dynamic short-range collinear c -axis AFM ordering in this temperature range driven by the exchange interactions.« less

Molecular Dynamics Simulation Studies of Fracture in Two Dimensions

DTIC Science & Technology

1980-05-01

reversibility of trajectories. The microscopic elastic constants, dispersion relation and phonon spectrum of the system were determined by lattice dynamics. These... linear elasticity theory of a two-dimensional crack embedded in an infinite medium. System con- sists of 436 particles arranged in a tri- angular lattice ...satisfying these demands. In evaluating the mechanical energy of his model, Griffith used a result from linear elasticity theory, namely that for any body

Twelve inequivalent Dirac cones in two-dimensional ZrB2

NASA Astrophysics Data System (ADS)

Lopez-Bezanilla, Alejandro

2018-01-01

Theoretical evidence of the existence of 12 inequivalent Dirac cones at the vicinity of the Fermi energy in monolayered ZrB2 is presented. Two-dimensional ZrB2 is a mechanically stable d - and p -orbital compound exhibiting a unique electronic structure with two Dirac cones out of high-symmetry points in the irreducible Brillouin zone with a small electron-pocket compensation. First-principles calculations demonstrate that while one of the cones is insensitive to lattice expansion, the second cone vanishes for small perturbation of the vertical Zr position. Internal symmetry breaking with external physical stimuli, along with the relativistic effect of spin-orbit coupling, is able to remove selectively the Dirac cones. A rational explanation in terms of d - and p -orbital mixing is provided to elucidate the origin of the infrequent Dirac cones in a flat structure. The versatility of transition-metal d orbitals combined with the honeycomb lattice provided by the B atoms yields particular features in a two-dimensional material.

Twelve inequivalent Dirac cones in two-dimensional ZrB 2

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lopez-Bezanilla, Alejandro

Theoretical evidence of the existence of 12 inequivalent Dirac cones at the vicinity of the Fermi energy in monolayered ZrB 2 is presented. Two-dimensional ZrB 2 is a mechanically stable d- and p-orbital compound exhibiting a unique electronic structure with two Dirac cones out of high-symmetry points in the irreducible Brillouin zone with a small electron-pocket compensation. First-principles calculations demonstrate that while one of the cones is insensitive to lattice expansion, the second cone vanishes for small perturbation of the vertical Zr position. Internal symmetry breaking with external physical stimuli, along with the relativistic effect of spin-orbit coupling, is ablemore » to remove selectively the Dirac cones. A rational explanation in terms of d- and p-orbital mixing is provided to elucidate the origin of the infrequent Dirac cones in a flat structure. In conclusion, the versatility of transition-metal d orbitals combined with the honeycomb lattice provided by the B atoms yields particular features in a two-dimensional material.« less

Twelve inequivalent Dirac cones in two-dimensional ZrB 2

DOE PAGES

Lopez-Bezanilla, Alejandro

2018-01-29

Theoretical evidence of the existence of 12 inequivalent Dirac cones at the vicinity of the Fermi energy in monolayered ZrB 2 is presented. Two-dimensional ZrB 2 is a mechanically stable d- and p-orbital compound exhibiting a unique electronic structure with two Dirac cones out of high-symmetry points in the irreducible Brillouin zone with a small electron-pocket compensation. First-principles calculations demonstrate that while one of the cones is insensitive to lattice expansion, the second cone vanishes for small perturbation of the vertical Zr position. Internal symmetry breaking with external physical stimuli, along with the relativistic effect of spin-orbit coupling, is ablemore » to remove selectively the Dirac cones. A rational explanation in terms of d- and p-orbital mixing is provided to elucidate the origin of the infrequent Dirac cones in a flat structure. In conclusion, the versatility of transition-metal d orbitals combined with the honeycomb lattice provided by the B atoms yields particular features in a two-dimensional material.« less

Critical behavior of dissipative two-dimensional spin lattices

NASA Astrophysics Data System (ADS)

Rota, R.; Storme, F.; Bartolo, N.; Fazio, R.; Ciuti, C.

2017-04-01

We explore critical properties of two-dimensional lattices of spins interacting via an anisotropic Heisenberg Hamiltonian that are subject to incoherent spin flips. We determine the steady-state solution of the master equation for the density matrix via the corner-space renormalization method. We investigate the finite-size scaling and critical exponent of the magnetic linear susceptibility associated with a dissipative ferromagnetic transition. We show that the von Neumann entropy increases across the critical point, revealing a strongly mixed character of the ferromagnetic phase. Entanglement is witnessed by the quantum Fisher information, which exhibits a critical behavior at the transition point, showing that quantum correlations play a crucial role in the transition.

Similarity between the superconductivity in the graphene with the spin transport in the two-dimensional antiferromagnet in the honeycomb lattice

NASA Astrophysics Data System (ADS)

Lima, L. S.

2017-02-01

We have used the Dirac's massless quasi-particles together with the Kubo's formula to study the spin transport by electrons in the graphene monolayer. We have calculated the electric conductivity and verified the behavior of the AC and DC currents of this system, that is a relativistic electron plasma. Our results show that the AC conductivity tends to infinity in the limit ω → 0 , similar to the behavior obtained for the spin transport in the two-dimensional frustrated antiferromagnet in the honeycomb lattice. We have made a diagrammatic expansion for the Green's function and we have not gotten significative change in the results.

Hidden symmetries of the extended Kitaev-Heisenberg model: Implications for the honeycomb-lattice iridates A2IrO3

NASA Astrophysics Data System (ADS)

Chaloupka, Jiří; Khaliullin, Giniyat

2015-07-01

We have explored the hidden symmetries of a generic four-parameter nearest-neighbor spin model, allowed in honeycomb-lattice compounds under trigonal compression. Our method utilizes a systematic algorithm to identify all dual transformations of the model that map the Hamiltonian on itself, changing the parameters and providing exact links between different points in its parameter space. We have found the complete set of points of hidden SU(2) symmetry at which a seemingly highly anisotropic model can be mapped back on the Heisenberg model and inherits therefore its properties such as the presence of gapless Goldstone modes. The procedure used to search for the hidden symmetries is quite general and may be extended to other bond-anisotropic spin models and other lattices, such as the triangular, kagome, hyperhoneycomb, or harmonic-honeycomb lattices. We apply our findings to the honeycomb-lattice iridates Na2IrO3 and Li2IrO3 , and illustrate how they help to identify plausible values of the model parameters that are compatible with the available experimental data.

Design of a compact polarizing beam splitter based on a photonic crystal ring resonator with a triangular lattice.

PubMed

Yu, Tianbao; Huang, Jiehui; Liu, Nianhua; Yang, Jianyi; Liao, Qinghua; Jiang, Xiaoqing

2010-04-10

We propose and simulate a new kind of compact polarizing beam splitter (PBS) based on a photonic crystal ring resonator (PCRR) with complete photonic bandgaps. The two polarized states are separated far enough by resonant and nonresonant coupling between the waveguide modes and the microring modes. Some defect holes are utilized to control the beam propagation. The simulated results obtained by the finite-difference time-domain method show that high transmission (over 95%) is obtained and the polarization separation is realized with a length as short as 3.1 microm. The design of the proposed PBS can be flexible, thanks to the advantages of PCRRs.

Entropic multirelaxation-time lattice Boltzmann method for moving and deforming geometries in three dimensions

NASA Astrophysics Data System (ADS)

Dorschner, B.; Chikatamarla, S. S.; Karlin, I. V.

2017-06-01

Entropic lattice Boltzmann methods have been developed to alleviate intrinsic stability issues of lattice Boltzmann models for under-resolved simulations. Its reliability in combination with moving objects was established for various laminar benchmark flows in two dimensions in our previous work [B. Dorschner, S. Chikatamarla, F. Bösch, and I. Karlin, J. Comput. Phys. 295, 340 (2015), 10.1016/j.jcp.2015.04.017] as well as for three-dimensional one-way coupled simulations of engine-type geometries in B . Dorschner, F. Bösch, S. Chikatamarla, K. Boulouchos, and I. Karlin [J. Fluid Mech. 801, 623 (2016), 10.1017/jfm.2016.448] for flat moving walls. The present contribution aims to fully exploit the advantages of entropic lattice Boltzmann models in terms of stability and accuracy and extends the methodology to three-dimensional cases, including two-way coupling between fluid and structure and then turbulence and deforming geometries. To cover this wide range of applications, the classical benchmark of a sedimenting sphere is chosen first to validate the general two-way coupling algorithm. Increasing the complexity, we subsequently consider the simulation of a plunging SD7003 airfoil in the transitional regime at a Reynolds number of Re =40 000 and, finally, to access the model's performance for deforming geometries, we conduct a two-way coupled simulation of a self-propelled anguilliform swimmer. These simulations confirm the viability of the new fluid-structure interaction lattice Boltzmann algorithm to simulate flows of engineering relevance.

Chiral liquid phase of simple quantum magnets

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Zhentao; Feiguin, Adrian E.; Zhu, Wei

2017-11-07

We study a T=0 quantum phase transition between a quantum paramagnetic state and a magnetically ordered state for a spin S=1 XXZ Heisenberg antiferromagnet on a two-dimensional triangular lattice. The transition is induced by an easy-plane single-ion anisotropy D. At the mean-field level, the system undergoes a direct transition at a critical D=D c between a paramagnetic state at D>D c and an ordered state with broken U(1) symmetry at Dc. We show that beyond mean field the phase diagram is very different and includes an intermediate, partially ordered chiral liquid phase. Specifically, we find that inside the paramagnetic phasemore » the Ising (J z) component of the Heisenberg exchange binds magnons into a two-particle bound state with zero total momentum and spin. This bound state condenses at D>D c, before single-particle excitations become unstable, and gives rise to a chiral liquid phase, which spontaneously breaks spatial inversion symmetry, but leaves the spin-rotational U(1) and time-reversal symmetries intact. This chiral liquid phase is characterized by a finite vector chirality without long-range dipolar magnetic order. In our analytical treatment, the chiral phase appears for arbitrarily small J z because the magnon-magnon attraction becomes singular near the single-magnon condensation transition. This phase exists in a finite range of D and transforms into the magnetically ordered state at some Dc. In conclusion, we corroborate our analytic treatment with numerical density matrix renormalization group calculations.« less

Chip-based microtrap arrays for cold polar molecules

NASA Astrophysics Data System (ADS)

Hou, Shunyong; Wei, Bin; Deng, Lianzhong; Yin, Jianping

2017-12-01

Compared to the atomic chip, which has been a powerful platform to perform an astonishing range of applications from rapid Bose-Einstein condensate (BEC) production to the atomic clock, the molecular chip is only in its infant stages. Recently a one-dimensional electric lattice was demonstrated to trap polar molecules on a chip. This excellent work opens up the way to building a molecular chip laboratory. Here we propose a two-dimensional (2D) electric lattice on a chip with concise and robust structure, which is formed by arrays of squared gold wires. Arrays of microtraps that originate in the microsize electrodes offer a steep gradient and thus allow for confining both light and heavy polar molecules. Theoretical analysis and numerical calculations are performed using two types of sample molecules, N D3 and SrF, to justify the possibility of our proposal. The height of the minima of the potential wells is about 10 μm above the surface of the chip and can be easily adjusted in a wide range by changing the voltages applied on the electrodes. These microtraps offer intriguing perspectives for investigating cold molecules in periodic potentials, such as quantum computing science, low-dimensional physics, and some other possible applications amenable to magnetic or optical lattice. The 2D adjustable electric lattice is expected to act as a building block for a future gas-phase molecular chip laboratory.

Emergent reduced dimensionality by vertex frustration in artificial spin ice

NASA Astrophysics Data System (ADS)

Gilbert, Ian; Lao, Yuyang; Carrasquillo, Isaac; O'Brien, Liam; Watts, Justin D.; Manno, Michael; Leighton, Chris; Scholl, Andreas; Nisoli, Cristiano; Schiffer, Peter

2016-02-01

Reducing the dimensionality of a physical system can have a profound effect on its properties, as in the ordering of low-dimensional magnetic materials, phonon dispersion in mercury chain salts, sliding phases, and the electronic states of graphene. Here we explore the emergence of quasi-one-dimensional behaviour in two-dimensional artificial spin ice, a class of lithographically fabricated nanomagnet arrays used to study geometrical frustration. We extend the implementation of artificial spin ice by fabricating a new array geometry, the so-called tetris lattice. We demonstrate that the ground state of the tetris lattice consists of alternating ordered and disordered bands of nanomagnetic moments. The disordered bands can be mapped onto an emergent thermal one-dimensional Ising model. Furthermore, we show that the level of degeneracy associated with these bands dictates the susceptibility of island moments to thermally induced reversals, thus establishing that vertex frustration can reduce the relevant dimensionality of physical behaviour in a magnetic system.

Emergent reduced dimensionality by vertex frustration in artificial spin ice

DOE PAGES

Gilbert, Ian; Lao, Yuyang; Carrasquillo, Isaac; ...

2015-10-26

Reducing the dimensionality of a physical system can have a profound effect on its properties, as in the ordering of low-dimensional magnetic materials, phonon dispersion in mercury chain salts, sliding phases, and the electronic states of graphene. Here we explore the emergence of quasi-one-dimensional behaviour in two-dimensional artificial spin ice, a class of lithographically fabricated nanomagnet arrays used to study geometrical frustration. We extend the implementation of artificial spin ice by fabricating a new array geometry, the so-called tetris lattice. We demonstrate that the ground state of the tetris lattice consists of alternating ordered and disordered bands of nanomagnetic moments.more » The disordered bands can be mapped onto an emergent thermal one-dimensional Ising model. Furthermore, we show that the level of degeneracy associated with these bands dictates the susceptibility of island moments to thermally induced reversals, thus establishing that vertex frustration can reduce the relevant dimensionality of physical behaviour in a magnetic system.« less

Method to estimate center of rigidity using vibration recordings

USGS Publications Warehouse

Safak, Erdal; Çelebi, Mehmet

1990-01-01

A method to estimate the center of rigidity of buildings by using vibration recordings is presented. The method is based on the criterion that the coherence of translational motions with the rotational motion is minimum at the center of rigidity. Since the coherence is a function of frequency, a gross but frequency-independent measure of the coherency is defined as the integral of the coherence function over the frequency. The center of rigidity is determined by minimizing this integral. The formulation is given for two-dimensional motions. Two examples are presented for the method; a rectangular building with ambient-vibration recordings, and a triangular building with earthquake-vibration recordings. Although the examples given are for buildings, the method can be applied to any structure with two-dimensional motions.

A simulator for discrete quantum walks on lattices

NASA Astrophysics Data System (ADS)

Rodrigues, J.; Paunković, N.; Mateus, P.

In this paper, we present a simulator for two-particle quantum walks on the line and one-particle on a two-dimensional squared lattice. It can be used to investigate the equivalence between the two cases (one- and two-particle walks) for various boundary conditions (open, circular, reflecting, absorbing and their combinations). For the case of a single walker on a two-dimensional lattice, the simulator can also implement the Möbius strip. Furthermore, other topologies for the walker are also simulated by the proposed tool, like certain types of planar graphs with degree up to 4, by considering missing links over the lattice. The main purpose of the simulator is to study the genuinely quantum effects on the global properties of the two-particle joint probability distribution on the entanglement between the walkers/axis. For that purpose, the simulator is designed to compute various quantities such as: the entanglement and classical correlations, (classical and quantum) mutual information, the average distance between the two walkers, different hitting times and quantum discord. These quantities are of vital importance in designing possible algorithmic applications of quantum walks, namely in search, 3-SAT problems, etc. The simulator can also implement the static partial measurements of particle(s) positions and dynamic breaking of the links between certain nodes, both of which can be used to investigate the effects of decoherence on the walker(s). Finally, the simulator can be used to investigate the dynamic Anderson-like particle localization by varying the coin operators of certain nodes on the line/lattice. We also present some illustrative and relevant examples of one- and two-particle quantum walks in various scenarios. The tool was implemented in C and is available on-line at http://qwsim.weebly.com/.

ACOSS Eleven (Active Control of Space Structures). Volume 1

DTIC Science & Technology

1983-12-01

Influence Function ................. 19 3.4 Mirror Deformations. ........................... o............. 23 3.5 Selection of Point Objects...to simulate errors in the knowledge of influence function . 5) The influence function for edge actuators may be different from that for interior... Influence Function Each of the three mirrors has 37 actuators distributed on an equi- lateral triangular lattice as shown in Figure 3-3. In consultation with

Dynamics of the Spin Liquid Phase of Cs2CuCl4

NASA Astrophysics Data System (ADS)

Ma, Ookie; Vachon, Marc-Andre; Mitrovi{Ć}, Vesna F.; Marston, Brad

2008-03-01

The dynamics of a spin-liquid phase of an antiferromagnet on the anisotropic triangular lattice and in a magnetic field are studied with a combination of Gutzwiller-projected wavefunctions and mean-field theory. Candidate ground states that support fermionic gapless spinon excitations include four different U(1) spin liquidsootnotetextY. Zhou, X. G. Wen, cond-mat/0210662 (2003).. The lattice and the states interpolate between limiting cases of 1D decoupled chains (J/J^' = 0) and the isotropic 2D square lattice (J/J^'= ∞). Parameters of the mean field theory are chosen to minimize the ground state energy of the corresponding Gutzwiller-projected wavefunction. The spin-lattice relaxation rate 1/T1, calculated within the mean-field approximation, is compared to NMR measurementsootnotetextM. A. Vachon, O. Ma, J. B. Marston, V. F. Mitrovi'c, unpublished (2007). in the spin liquid phase of Cs2CuCl4ootnotetextY. Tokiwa, T. Radu, R. Coldea, H. Wilhelm, Z. Tylczynski, F. Steglich, PRB 73, 134414 (2006)..

Quantum transport in d-dimensional lattices

DOE PAGES

Manzano, Daniel; Chuang, Chern; Cao, Jianshu

2016-04-28

We show that both fermionic and bosonic uniform d-dimensional lattices can be reduced to a set of independent one-dimensional chains. This reduction leads to the expression for ballistic energy fluxes in uniform fermionic and bosonic lattices. By the use of the Jordan–Wigner transformation we can extend our analysis to spin lattices, proving the coexistence of both ballistic and non-ballistic subspaces in any dimension and for any system size. Lastly, we then relate the nature of transport to the number of excitations in the homogeneous spin lattice, indicating that a single excitation always propagates ballistically and that the non-ballistic behaviour ofmore » uniform spin lattices is a consequence of the interaction between different excitations.« less

Two-dimensional limit of crystalline order in perovskite membrane films

PubMed Central

Hong, Seung Sae; Yu, Jung Ho; Lu, Di; Marshall, Ann F.; Hikita, Yasuyuki; Cui, Yi; Hwang, Harold Y.

2017-01-01

Long-range order and phase transitions in two-dimensional (2D) systems—such as magnetism, superconductivity, and crystallinity—have been important research topics for decades. The issue of 2D crystalline order has reemerged recently, with the development of exfoliated atomic crystals. Understanding the dimensional limit of crystalline phases, with different types of bonding and synthetic techniques, is at the foundation of low-dimensional materials design. We study ultrathin membranes of SrTiO3, an archetypal perovskite oxide with isotropic (3D) bonding. Atomically controlled membranes are released after synthesis by dissolving an underlying epitaxial layer. Although all unreleased films are initially single-crystalline, the SrTiO3 membrane lattice collapses below a critical thickness (5 unit cells). This crossover from algebraic to exponential decay of the crystalline coherence length is analogous to the 2D topological Berezinskii-Kosterlitz-Thouless (BKT) transition. The transition is likely driven by chemical bond breaking at the 2D layer-3D bulk interface, defining an effective dimensional phase boundary for coherent crystalline lattices. PMID:29167822

Two-dimensional limit of crystalline order in perovskite membrane films

DOE PAGES

Hong, Seung Sae; Yu, Jung Ho; Lu, Di; ...

2017-11-17

Long-range order and phase transitions in two-dimensional (2D) systems—such as magnetism, superconductivity, and crystallinity—have been important research topics for decades. The issue of 2D crystalline order has reemerged recently, with the development of exfoliated atomic crystals. Understanding the dimensional limit of crystalline phases, with different types of bonding and synthetic techniques, is at the foundation of low-dimensional materials design. We study ultrathin membranes of SrTiO 3, an archetypal perovskite oxide with isotropic (3D) bonding. Atomically controlled membranes are released after synthesis by dissolving an underlying epitaxial layer. Although all unreleased films are initially single-crystalline, the SrTiO 3 membrane lattice collapsesmore » below a critical thickness (5 unit cells). This crossover from algebraic to exponential decay of the crystalline coherence length is analogous to the 2D topological Berezinskii-Kosterlitz-Thouless (BKT) transition. Finally, the transition is likely driven by chemical bond breaking at the 2D layer-3D bulk interface, defining an effective dimensional phase boundary for coherent crystalline lattices.« less

Hierarchical Freezing in a Lattice Model

NASA Astrophysics Data System (ADS)

Byington, Travis W.; Socolar, Joshua E. S.

2012-01-01

A certain two-dimensional lattice model with nearest and next-nearest neighbor interactions is known to have a limit-periodic ground state. We show that during a slow quench from the high temperature, disordered phase, the ground state emerges through an infinite sequence of phase transitions. We define appropriate order parameters and show that the transitions are related by renormalizations of the temperature scale. As the temperature is decreased, sublattices with increasingly large lattice constants become ordered. A rapid quench results in a glasslike state due to kinetic barriers created by simultaneous freezing on sublattices with different lattice constants.

A lattice Boltzmann model for the Burgers-Fisher equation.

PubMed

Zhang, Jianying; Yan, Guangwu

2010-06-01

A lattice Boltzmann model is developed for the one- and two-dimensional Burgers-Fisher equation based on the method of the higher-order moment of equilibrium distribution functions and a series of partial differential equations in different time scales. In order to obtain the two-dimensional Burgers-Fisher equation, vector sigma(j) has been used. And in order to overcome the drawbacks of "error rebound," a new assumption of additional distribution is presented, where two additional terms, in first order and second order separately, are used. Comparisons with the results obtained by other methods reveal that the numerical solutions obtained by the proposed method converge to exact solutions. The model under new assumption gives better results than that with second order assumption. (c) 2010 American Institute of Physics.

On the Wiener Polarity Index of Lattice Networks

PubMed Central

Chen, Lin; Li, Tao; Liu, Jinfeng; Shi, Yongtang; Wang, Hua

2016-01-01

Network structures are everywhere, including but not limited to applications in biological, physical and social sciences, information technology, and optimization. Network robustness is of crucial importance in all such applications. Research on this topic relies on finding a suitable measure and use this measure to quantify network robustness. A number of distance-based graph invariants, also known as topological indices, have recently been incorporated as descriptors of complex networks. Among them the Wiener type indices are the most well known and commonly used such descriptors. As one of the fundamental variants of the original Wiener index, the Wiener polarity index has been introduced for a long time and known to be related to the cluster coefficient of networks. In this paper, we consider the value of the Wiener polarity index of lattice networks, a common network structure known for its simplicity and symmetric structure. We first present a simple general formula for computing the Wiener polarity index of any graph. Using this formula, together with the symmetric and recursive topology of lattice networks, we provide explicit formulas of the Wiener polarity index of the square lattices, the hexagonal lattices, the triangular lattices, and the 33 ⋅ 42 lattices. We also comment on potential future research topics. PMID:27930705

The Harper–Hofstadter Hamiltonian and conical diffraction in photonic lattices with grating assisted tunneling

DOE PAGES

Dubček, Tena; Lelas, Karlo; Jukić, Dario; ...

2015-12-07

Here we propose the realization of a grating assisted tunneling scheme for tunable synthetic magnetic fields in optically induced one- and two-dimensional dielectric photonic lattices. As a signature of the synthetic magnetic fields, we demonstrate conical diffraction patterns in particular realization of these lattices, which possess Dirac points in k-space. Lastly, we compare the light propagation in these realistic (continuous) systems with the evolution in discrete models representing the Harper-Hofstadter Hamiltonian, and obtain excellent agreement.

Phonons, Diffusons, and the Boson Peak in Two-Dimensional Lattices with Random Bonds

NASA Astrophysics Data System (ADS)

Konyukh, D. A.; Bel'tyukov, Ya. M.; Parshin, D. A.

2018-02-01

Within the model of stable random matrices possessing translational invariance, a two-dimensional (on a square lattice) disordered oscillatory system with random strongly fluctuating bonds is considered. By a numerical analysis of the dynamic structure factor S( q, ω), it is shown that vibrations with frequencies below the Ioffe-Regel frequency ωIR are ordinary phonons with a linear dispersion law ω( q) ∝ q and a reciprocal lifetime б q 3. Vibrations with frequencies above ωIR, although being delocalized, cannot be described by plane waves with a definite dispersion law ω( q). They are characterized by a diffusion structure factor with a reciprocal lifetime б q 2, which is typical of a diffusion process. In the literature, they are often referred to as diffusons. It is shown that, as in the three-dimensional model, the boson peak at the frequency ωb in the reduced density of vibrational states g(ω)/ω is on the order of the frequency ωIR. It is located in the transition region between phonons and diffusons and is proportional to the Young's modulus of the lattice, ω b ≃ E.

High-resolution neutron diffraction study of CuNCN: New evidence of structure anomalies at low temperature

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jacobs, Philipp; Houben, Andreas; Dronskowski, Richard, E-mail: drons@HAL9000.ac.rwth-aachen.de

Copper carbodiimide (CuNCN) is the nitrogen-containing analogue of cupric oxide. Based on high-resolution neutron-diffraction data, CuNCN's lattice parameters are derived as a function of the temperature. In accordance with a recent synchrotron study, a clear trend in the cell parameter a is observed accompanying the changing magnetic behavior. With decreasing temperature, a slowly decreases to a minimum at ∼100 K after which it rises again. The same trend—albeit more pronounced—is observed for the c lattice parameter at ∼35 K. The herein presented neutron powder-diffraction data also support the conjectured sequence of transitions from the high-temperature one-dimensional resonating valence-bond (RVB) statemore » to a transient two-dimensional RVB state and eventually, at lowest temperatures, into another two-dimensional RVB state, presumably the ground state.« less

Resonant scattering from a two-dimensional honeycomb PT dipole structure

NASA Astrophysics Data System (ADS)

Markoš, P.; Kuzmiak, V.

2018-05-01

We studied numerically the electromagnetic response of the finite periodic structure consisting of the PT dipoles represented by two infinitely long, parallel cylinders with the opposite sign of the imaginary part of a refractive index, which are centered at the positions of a two-dimensional honeycomb lattice. We observed that the total scattered energy reveals a series of sharp resonances at which the energy increases by two orders of magnitude and an incident wave is scattered only in a few directions given by spatial symmetry of the periodic structure. We explain this behavior by analysis of the complex frequency spectra associated with an infinite honeycomb array of the PT dipoles and identify the lowest resonance with the broken PT -symmetry mode formed by a doubly degenerate pair with complex conjugate eigenfrequencies corresponding to the K point of the reciprocal lattice.

Laterally structured ripple and square phases with one and two dimensional thickness modulations in a model bilayer system.

PubMed

Debnath, Ananya; Thakkar, Foram M; Maiti, Prabal K; Kumaran, V; Ayappa, K G

2014-10-14

Molecular dynamics simulations of bilayers in a surfactant/co-surfactant/water system with explicit solvent molecules show formation of topologically distinct gel phases depending upon the bilayer composition. At low temperatures, the bilayers transform from the tilted gel phase, Lβ', to the one dimensional (1D) rippled, Pβ' phase as the surfactant concentration is increased. More interestingly, we observe a two dimensional (2D) square phase at higher surfactant concentration which, upon heating, transforms to the gel Lβ' phase. The thickness modulations in the 1D rippled and square phases are asymmetric in two surfactant leaflets and the bilayer thickness varies by a factor of ∼2 between maximum and minimum. The 1D ripple consists of a thinner interdigitated region of smaller extent alternating with a thicker non-interdigitated region. The 2D ripple phase is made up of two superimposed square lattices of maximum and minimum thicknesses with molecules of high tilt forming a square lattice translated from the lattice formed with the thickness minima. Using Voronoi diagrams we analyze the intricate interplay between the area-per-head-group, height modulations and chain tilt for the different ripple symmetries. Our simulations indicate that composition plays an important role in controlling the formation of low temperature gel phase symmetries and rippling accommodates the increased area-per-head-group of the surfactant molecules.

Extra-dimensional models on the lattice

DOE PAGES

Knechtli, Francesco; Rinaldi, Enrico

2016-08-05

In this paper we summarize the ongoing effort to study extra-dimensional gauge theories with lattice simulations. In these models the Higgs field is identified with extra-dimensional components of the gauge field. The Higgs potential is generated by quantum corrections and is protected from divergences by the higher dimensional gauge symmetry. Dimensional reduction to four dimensions can occur through compactification or localization. Gauge-Higgs unification models are often studied using perturbation theory. Numerical lattice simulations are used to go beyond these perturbative expectations and to include nonperturbative effects. We describe the known perturbative predictions and their fate in the strongly-coupled regime formore » various extra-dimensional models.« less

Enhanced light absorption of solar cells and photodetectors by diffraction

DOEpatents

Zaidi, Saleem H.; Gee, James M.

2005-02-22

Enhanced light absorption of solar cells and photodetectors by diffraction is described. Triangular, rectangular, and blazed subwavelength periodic structures are shown to improve performance of solar cells. Surface reflection can be tailored for either broadband, or narrow-band spectral absorption. Enhanced absorption is achieved by efficient optical coupling into obliquely propagating transmitted diffraction orders. Subwavelength one-dimensional structures are designed for polarization-dependent, wavelength-selective absorption in solar cells and photodetectors, while two-dimensional structures are designed for polarization-independent, wavelength-selective absorption therein. Suitable one and two-dimensional subwavelength periodic structures can also be designed for broadband spectral absorption in solar cells and photodetectors. If reactive ion etching (RIE) processes are used to form the grating, RIE-induced surface damage in subwavelength structures can be repaired by forming junctions using ion implantation methods. RIE-induced surface damage can also be removed by post RIE wet-chemical etching treatments.

Lattice spin models for non-Abelian chiral spin liquids

DOE PAGES

Lecheminant, P.; Tsvelik, A. M.

2017-04-26

Here, we suggest a class of two-dimensional lattice spin Hamiltonians describing non-Abelian SU(2) chiral spin liquids—spin analogs of fractional non-Abelian quantum Hall states—with gapped bulk and gapless chiral edge excitations described by the SU(2) n Wess-Zumino-Novikov-Witten conformal field theory. The models are constructed from an array of generalized spin-n/2 ladders with multi-spin-exchange interactions which are coupled by isolated spins. Such models allow a controllable analytic treatment starting from the one-dimensional limit and are characterized by a bulk gap and non-Abelian SU(2) n gapless edge excitations.

Monte carlo simulations of enzyme reactions in two dimensions: fractal kinetics and spatial segregation.

PubMed

Berry, Hugues

2002-10-01

Conventional equations for enzyme kinetics are based on mass-action laws, that may fail in low-dimensional and disordered media such as biological membranes. We present Monte Carlo simulations of an isolated Michaelis-Menten enzyme reaction on two-dimensional lattices with varying obstacle densities, as models of biological membranes. The model predicts that, as a result of anomalous diffusion on these low-dimensional media, the kinetics are of the fractal type. Consequently, the conventional equations for enzyme kinetics fail to describe the reaction. In particular, we show that the quasi-stationary-state assumption can hardly be retained in these conditions. Moreover, the fractal characteristics of the kinetics are increasingly pronounced as obstacle density and initial substrate concentration increase. The simulations indicate that these two influences are mainly additive. Finally, the simulations show pronounced S-P segregation over the lattice at obstacle densities compatible with in vivo conditions. This phenomenon could be a source of spatial self organization in biological membranes.

Monte carlo simulations of enzyme reactions in two dimensions: fractal kinetics and spatial segregation.

PubMed Central

Berry, Hugues

2002-01-01

Conventional equations for enzyme kinetics are based on mass-action laws, that may fail in low-dimensional and disordered media such as biological membranes. We present Monte Carlo simulations of an isolated Michaelis-Menten enzyme reaction on two-dimensional lattices with varying obstacle densities, as models of biological membranes. The model predicts that, as a result of anomalous diffusion on these low-dimensional media, the kinetics are of the fractal type. Consequently, the conventional equations for enzyme kinetics fail to describe the reaction. In particular, we show that the quasi-stationary-state assumption can hardly be retained in these conditions. Moreover, the fractal characteristics of the kinetics are increasingly pronounced as obstacle density and initial substrate concentration increase. The simulations indicate that these two influences are mainly additive. Finally, the simulations show pronounced S-P segregation over the lattice at obstacle densities compatible with in vivo conditions. This phenomenon could be a source of spatial self organization in biological membranes. PMID:12324410

Thermoelectric and phonon transport properties of two-dimensional IV-VI compounds.

PubMed

Shafique, Aamir; Shin, Young-Han

2017-03-30

We explore the thermoelectric and phonon transport properties of two-dimensional monochalcogenides (SnSe, SnS, GeSe, and GeS) using density functional theory combined with Boltzmann transport theory. We studied the electronic structures, Seebeck coefficients, electrical conductivities, lattice thermal conductivities, and figures of merit of these two-dimensional materials, which showed that the thermoelectric performance of monolayer of these compounds is improved in comparison compared to their bulk phases. High figures of merit (ZT) are predicted for SnSe (ZT = 2.63, 2.46), SnS (ZT = 1.75, 1.88), GeSe (ZT = 1.99, 1.73), and GeS (ZT = 1.85, 1.29) at 700 K along armchair and zigzag directions, respectively. Phonon dispersion calculations confirm the dynamical stability of these compounds. The calculated lattice thermal conductivities are low while the electrical conductivities and Seebeck coefficients are high. Thus, the properties of the monolayers show high potential toward thermoelectric applications.

Stabilizers as a design tool for new forms of the Lechner-Hauke-Zoller annealer

PubMed Central

Rocchetto, Andrea; Benjamin, Simon C.; Li, Ying

2016-01-01

In a recent paper, Lechner, Hauke, and Zoller (LHZ) described a means to translate a Hamiltonian of N spin-1/2 particles with “all-to-all” interactions into a larger physical lattice with only on-site energies and local parity constraints. LHZ used this mapping to propose a novel form of quantum annealing. We provide a stabilizer-based formulation within which we can describe both this prior approach and a wide variety of variants. Examples include a triangular array supporting all-to-all connectivity as well as arrangements requiring only 2N or N log N spins but providing interesting bespoke connectivities. Further examples show that arbitrarily high-order logical terms can be efficiently realized, even in a strictly two-dimensional layout. Our stabilizers can correspond to either even-parity constraints, as in the LHZ proposal, or odd-parity constraints. Considering the latter option applied to the original LHZ layout, we note that it may simplify the physical realization because the required ancillas are only spin-1/2 systems (that is, qubits rather than qutrits); moreover, the interactions are very simple. We make a preliminary assessment of the impact of these design choices by simulating small (few-qubit) systems; we find some indications that the new variant may maintain a larger minimum energy gap during the annealing process. PMID:27819050

The one-dimensional minesweeper game: What are your chances of winning?

NASA Astrophysics Data System (ADS)

Rodríguez-Achach, M.; Coronel-Brizio, H. F.; Hernández-Montoya, A. R.; Huerta-Quintanilla, R.; Canto-Lugo, E.

2016-04-01

Minesweeper is a famous computer game consisting usually in a two-dimensional lattice, where cells can be empty or mined and gamers are required to locate the mines without dying. Even if minesweeper seems to be a very simple system, it has some complex and interesting properties as NP-completeness. In this paper and for the one-dimensional case, given a lattice of n cells and m mines, we calculate the winning probability. By numerical simulations this probability is also estimated. We also find out by mean of these simulations that there exists a critical density of mines that minimize the probability of winning the game. Analytical results and simulations are compared showing a very good agreement.

Relativistic energy-dispersion relations of 2D rectangular lattices

NASA Astrophysics Data System (ADS)

Ata, Engin; Demirhan, Doğan; Büyükkılıç, Fevzi

2017-04-01

An exactly solvable relativistic approach based on inseparable periodic well potentials is developed to obtain energy-dispersion relations of spin states of a single-electron in two-dimensional (2D) rectangular lattices. Commutation of axes transfer matrices is exploited to find energy dependencies of the wave vector components. From the trace of the lattice transfer matrix, energy-dispersion relations of conductance and valence states are obtained in transcendental form. Graphical solutions of relativistic and nonrelativistic transcendental energy-dispersion relations are plotted to compare how lattice parameters V0, core and interstitial size of the rectangular lattice affects to the energy-band structures in a situation core and interstitial diagonals are of equal slope.

A quest for 2D lattice materials for actuation

NASA Astrophysics Data System (ADS)

Pronk, T. N.; Ayas, C.; Tekõglu, C.

2017-08-01

In the last two decades, most of the studies in shape morphing technology have focused on the Kagome lattice materials, which have superior properties such as in-plane isotropy, high specific stiffness and strength, and low energy requirement for actuation of its members. The Kagome lattice is a member of the family of semi-regular tessellations of the plane. Two fundamental questions naturally arise: i-) What makes a lattice material suitable for actuation? ii-) Are there other tessellations more effective than the Kagome lattice for actuation? The present paper tackles both questions, and provides a clear answer to the first one by comparing an alternative lattice material, the hexagonal cupola, with the Kagome lattice in terms of mechanical/actuation properties. The second question remains open, but, hopefully easier to challenge owing to a newly-discovered criterion: for an n-dimensional (n = 2 , 3) in-plane isotropic lattice material to be suitable for actuation, its pin-jointed equivalent must obey the generalised Maxwell's rule, and must possess M = 3(n - 1) non strain-producing finite kinematic mechanisms.

Bond and flux-disorder effects on the superconductor-insulator transition of a honeycomb array of Josephson junctions

NASA Astrophysics Data System (ADS)

Granato, Enzo

2018-05-01

We study the effects of disorder on the zero-temperature quantum phase transition of a honeycomb array of Josephson junctions in a magnetic field with an average of fo flux quantum per plaquette. Bond disorder due to spatial variations in the Josephson couplings and magnetic flux disorder due to variations in the plaquette areas are considered. The model can describe the superconductor-insulator transition in ultra-thin films with a triangular pattern of nanoholes. Path integral Monte Carlo simulations of the equivalent (2 + 1)-dimensional classical model are used to study the critical behavior and estimate the universal resistivity at the transition. The results show that bond disorder leads to a rounding of the first-order phase transition for fo = 1 / 3 to a continuous transition. For integer fo, the decrease of the critical coupling parameter with flux disorder is significantly different from that of the same model defined on a square lattice. The results are compared with recent experimental observations on nanohole thin films with geometrical disorder and external magnetic field.

The Fundamental Structure and the Reproduction of Spiral Wave in a Two-Dimensional Excitable Lattice.

PubMed

Qian, Yu; Zhang, Zhaoyang

2016-01-01

In this paper we have systematically investigated the fundamental structure and the reproduction of spiral wave in a two-dimensional excitable lattice. A periodically rotating spiral wave is introduced as the model to reproduce spiral wave artificially. Interestingly, by using the dominant phase-advanced driving analysis method, the fundamental structure containing the loop structure and the wave propagation paths has been revealed, which can expose the periodically rotating orbit of spiral tip and the charity of spiral wave clearly. Furthermore, the fundamental structure is utilized as the core for artificial spiral wave. Additionally, the appropriate parameter region, in which the artificial spiral wave can be reproduced, is studied. Finally, we discuss the robustness of artificial spiral wave to defects.

The Self-Assembly of DNA Nanostructures for use as Organizing Templates

NASA Astrophysics Data System (ADS)

Samec, Timothy; Cholewinski, Mitchell; Reamer, Nickalas; Reardon, Michael; Ford, Arlene

There is growing interest in the self-assembling capabilities of DNA to create functional nanodevices for use in cancer detection and treatment. One important reason for this interest is that DNA nanostructures are highly programmable molecules. This means that these structures allow for increased stability and control when designing biomacromolecules via adhesion of plasmonic nanoparticles and other similar materials. Our current work reports on the procedure and construction of hexagonal two-dimensional DNA lattice structures using three specific DNA single strands. We also reflect on several barriers that were presented during fabrication as well as the adaptations made to overcome the aforementioned barriers by improving the quality, reproducibility, and yield of the hexagonal two-dimensional DNA lattice as organizing templates.

Nonlinearity-dependent asymmetric transmission in a sawtooth photonic lattice with defects

NASA Astrophysics Data System (ADS)

Ji, Kaiwen; Qi, Xinyuan; Li, Shasha; Han, Kun; Wen, Zengrun; Zhang, Guoquan; Bai, Jintao

2018-04-01

We study both theoretically and numerically the asymetric transmission of a Gaussian beam in a two-dimensional nonlinear sawtooth lattice with two defects. The results show that quasi-total reflection, asymmetric propagation and asymmetric reflection can all be achieved in such a system by adjusting the input intensity, the magnitude of defects and the number of nonlinear waveguides. This study may provide a new way to realize an optical switch and optical diode.

Superalgebraically convergent smoothly windowed lattice sums for doubly periodic Green functions in three-dimensional space

PubMed Central

Bruno, Oscar P.; Turc, Catalin; Venakides, Stephanos

2016-01-01

This work, part I in a two-part series, presents: (i) a simple and highly efficient algorithm for evaluation of quasi-periodic Green functions, as well as (ii) an associated boundary-integral equation method for the numerical solution of problems of scattering of waves by doubly periodic arrays of scatterers in three-dimensional space. Except for certain ‘Wood frequencies’ at which the quasi-periodic Green function ceases to exist, the proposed approach, which is based on smooth windowing functions, gives rise to tapered lattice sums which converge superalgebraically fast to the Green function—that is, faster than any power of the number of terms used. This is in sharp contrast to the extremely slow convergence exhibited by the lattice sums in the absence of smooth windowing. (The Wood-frequency problem is treated in part II.) This paper establishes rigorously the superalgebraic convergence of the windowed lattice sums. A variety of numerical results demonstrate the practical efficiency of the proposed approach. PMID:27493573