Charged topological entanglement entropy
NASA Astrophysics Data System (ADS)
Matsuura, Shunji; Wen, Xueda; Hung, Ling-Yan; Ryu, Shinsei
2016-05-01
A charged entanglement entropy is a new measure which probes quantum entanglement between different charge sectors. We study symmetry-protected topological (SPT) phases in (2+1)-dimensional space-time by using this charged entanglement entropy. SPT phases are short-range entangled states without topological order and hence cannot be detected by the topological entanglement entropy. We demonstrate that the universal part of the charged entanglement entropy is nonzero for nontrivial SPT phases and therefore it is a useful measure to detect short-range entangled topological phases. We also discuss that the classification of SPT phases based on the charged topological entanglement entropy is related to that of the braiding statistics of quasiparticles.
Topological charge conservation in stochastic optical fields
NASA Astrophysics Data System (ADS)
Roux, Filippus S.
2016-05-01
The fact that phase singularities in scalar stochastic optical fields are topologically conserved implies the existence of an associated conserved current, which can be expressed in terms of local correlation functions of the optical field and its transverse derivatives. Here, we derive the topological charge current for scalar stochastic optical fields and show that it obeys a conservation equation. We use the expression for the topological charge current to investigate the topological charge flow in inhomogeneous stochastic optical fields with a one-dimensional topological charge density.
Topological Charge Pumping with Cold Atoms
NASA Astrophysics Data System (ADS)
Takahashi, Yoshiro
More than 30 years ago, Thouless considered an interesting phenomenon of quantum transport of an electron gas in an infinite one-dimensional periodic potential, driven in a periodic cycle. The charge pumped by this Thouless pump is a topological quantum number and does not depend on a smooth change of parameters. Importantly, this charge pumping shares the same topological origin as the integer quantum Hall effect. In spite of the importance in a topological quantum physics, this Thouless pump has never been realized in any system. In this study, we successfully realize the Thouless topological pump by exploiting the controllability of ultracold atoms in an optical superlattice. The charge pumping is detected as a shift of the center of mass of an atomic cloud measured with in situ absorption imaging. We extract the Chern number of the system from the average shift of the center of mass per pumping cycle. The topological nature of the pump is revealed by the clear dependence on the topology of the pumping trajectories in parameter space of our superlattice. We will describe the detail of our experiments using fermionic ytterbium atoms and also discuss the prospects of our research.
Cumulants of the QCD topological charge distribution
NASA Astrophysics Data System (ADS)
Guo, Feng-Kun; Meißner, Ulf-G.
2015-10-01
The distribution of the QCD topological charge can be described by cumulants, with the lowest one being the topological susceptibility. The vacuum energy density in a θ-vacuum is the generating function for these cumulants. In this paper, we derive the vacuum energy density in SU(2) chiral perturbation theory up to next-to-leading order keeping different up and down quark masses, which can be used to calculate any cumulant of the topological charge distribution. We also give the expression for the case of SU(N) with degenerate quark masses. In this case, all cumulants depend on the same linear combination of low-energy constants and chiral logarithm, and thus there are sum rules between the N-flavor quark condensate and the cumulants free of next-to-leading order corrections.
Topological charge selection rule for phase singularities
Zacares, M.; Vijande, J.; Ferrando, A.; Merino, E.
2009-10-15
We present a study of the dynamics and decay pattern of phase singularities due to the action of a system with a discrete rotational symmetry of finite order. A topological charge conservation rule is identified. The role played by the underlying symmetry is emphasized. An effective model describing the short range dynamics of the vortex clusters has been designed. A method to engineer any desired configuration of clusters of phase singularities is proposed. Its flexibility to create and control clusters of vortices is discussed.
Topology-based Feature Definition and Analysis
Weber, Gunther H.; Bremer, Peer-Timo; Gyulassy, Attila; Pascucci, Valerio
2010-12-10
Defining high-level features, detecting them, tracking them and deriving quantities based on them is an integral aspect of modern data analysis and visualization. In combustion simulations, for example, burning regions, which are characterized by high fuel-consumption, are a possible feature of interest. Detecting these regions makes it possible to derive statistics about their size and track them over time. However, features of interest in scientific simulations are extremely varied, making it challenging to develop cross-domain feature definitions. Topology-based techniques offer an extremely flexible means for general feature definitions and have proven useful in a variety of scientific domains. This paper will provide a brief introduction into topological structures like the contour tree and Morse-Smale complex and show how to apply them to define features in different science domains such as combustion. The overall goal is to provide an overview of these powerful techniques and start a discussion how these techniques can aid in the analysis of astrophysical simulations.
Light-controlled topological charge in a nematic liquid crystal
NASA Astrophysics Data System (ADS)
Nikkhou, Maryam; Škarabot, Miha; Čopar, Simon; Ravnik, Miha; Žumer, Slobodan; Muševič, Igor
2015-02-01
Creating, imaging, and transforming the topological charge in a superconductor, a superfluid, a system of cold atoms, or a soft ferromagnet is a difficult--if not impossible--task because of the shortness of the length scales and lack of control. The length scale and softness of defects in liquid crystals allow the easy observation of charges, but it is difficult to control charge creation. Here we demonstrate full control over the creation, manipulation and analysis of topological charges that are pinned to a microfibre in a nematic liquid crystal. Oppositely charged pairs are created through the Kibble-Zurek mechanism by applying a laser-induced local temperature quench in the presence of symmetry-breaking boundaries. The pairs are long-lived, oppositely charged rings or points that either attract and annihilate, or form a long-lived, charge-neutral loop made of two segments with a fractional topological charge.
Topological Charge Screening in Disordered Aharonov-Bohm Wavefunctions
NASA Astrophysics Data System (ADS)
Houston, Alexander; Hannay, John; Taylor, Alexander; Dennis, Mark
Free electrical charges are typically subject to screening relations. For example, in ionic fluids and Coulomb gases there is screening (both global and local) of the electrical charges, described by the first and second Stillinger-Lovett sum rules. A topological analogy governs the statistical behaviour of the nodal points in Gaussian random superpositions of plane waves. These nodal points are integer topological charges, i.e. vortices and antivortices of the complex wavefunction, whose sign is that of the phase circulation. Such superpositions are known to model high energy eigenfunctions in the presence of wave chaos, and display topological charge screening in the bulk. We investigate how these screening relations are affected by the introduction of a magnetic flux line, which may be fractional in strength. We find that the global screening relation is broken, with the average total topological charge of the vortices given by the flux strength, and that the local screening of the flux itself shows unexpected features.
Topological Charge Evolution in the Markov-Chain of QCD
Derek Leinweber; Anthony Williams; Jian-bo Zhang; Frank Lee
2004-04-01
The topological charge is studied on lattices of large physical volume and fine lattice spacing. We illustrate how a parity transformation on the SU(3) link-variables of lattice gauge configurations reverses the sign of the topological charge and leaves the action invariant. Random applications of the parity transformation are proposed to traverse from one topological charge sign to the other. The transformation provides an improved unbiased estimator of the ensemble average and is essential in improving the ergodicity of the Markov chain process.
Non-Gaussianities in the topological charge distribution of the SU(3) Yang-Mills theory
NASA Astrophysics Data System (ADS)
Cè, Marco; Consonni, Cristian; Engel, Georg P.; Giusti, Leonardo
2015-10-01
We study the topological charge distribution of the SU(3) Yang-Mills theory with high precision in order to be able to detect deviations from Gaussianity. The computation is carried out on the lattice with high statistics Monte Carlo simulations by implementing a naive discretization of the topological charge evolved with the Yang-Mills gradient flow. This definition is far less demanding than the one suggested from Neuberger's fermions and, as shown in this paper, in the continuum limit its cumulants coincide with those of the universal definition appearing in the chiral Ward identities. Thanks to the range of lattice volumes and spacings considered, we can extrapolate the results for the second and fourth cumulant of the topological charge distribution to the continuum limit with confidence by keeping finite volume effects negligible with respect to the statistical errors. Our best results for the topological susceptibility is t02χ =6.67 (7 )×1 0-4 , where t0 is a standard reference scale, while for the ratio of the fourth cumulant over the second, we obtain R =0.233 (45 ). The latter is compatible with the expectations from the large Nc expansion, while it rules out the θ behavior of the vacuum energy predicted by the dilute instanton model. Its large distance from 1 implies that, in the ensemble of gauge configurations that dominate the path integral, the fluctuations of the topological charge are of quantum nonperturbative nature.
Effect of topology on the critical charge in graphene
Chakraborty, Baishali; Gupta, Kumar S.
2011-03-15
We show that the critical charge for the Dirac excitations in gapless graphene depends on the spatial topology of the sample. In particular, for graphene cones, the effective value of the critical charge can tend toward zero for a suitable angle of the conical sample. We discuss the nature of the scattering phase shifts, quasibound state energies, and local density of states for a gapless graphene cone and determine the dependence of these physical quantities on the sample topology.
Topological charges in 2D N =(2 ,2 ) theories and massive BPS states
NASA Astrophysics Data System (ADS)
Park, Daniel S.
2015-07-01
We study how charges of global symmetries that are manifest in the ultraviolet definition of a theory are realized as topological charges in its infrared effective theory for two-dimensional theories with N =(2 ,2 ) supersymmetry. We focus on the charges that the states living on S1 carry. The central charge—or Bogomol'nyi-Prasad-Sommerfield (BPS) masses—of the supersymmetry algebra play a crucial role in making this correspondence precise. We study two examples: U (1 ) gauge theories with chiral matter and world-volume theories of "dynamical surface operators" of four-dimensional N =2 gauge theories. In the former example, we show that the flavor charges of the theory are realized as topological winding numbers in the effective theory on the Coulomb branch. In the latter, we show that there is a one-to-one correspondence between topological charges of the effective theory of the dynamical surface operator and the electric, magnetic, and flavor charges of the four-dimensional gauge theory. We also examine the topologically charged massive BPS states on S1 and discover that the massive BPS spectrum is sensitive to the radius of the circle in the simplest theory—the free theory of a periodic twisted chiral field. We clarify this behavior by showing that the massive BPS spectrum on S1, unlike the BPS ground states, cannot be identified as elements of a cohomology.
Topological charge algebra of optical vortices in nonlinear interactions.
Zhdanova, Alexandra A; Shutova, Mariia; Bahari, Aysan; Zhi, Miaochan; Sokolov, Alexei V
2015-12-28
We investigate the transfer of orbital angular momentum among multiple beams involved in a coherent Raman interaction. We use a liquid crystal light modulator to shape pump and Stokes beams into optical vortices with various integer values of topological charge, and cross them in a Raman-active crystal to produce multiple Stokes and anti-Stokes sidebands. We measure the resultant vortex charges using a tilted-lens technique. We verify that in every case the generated beams' topological charges obey a simple relationship, resulting from angular momentum conservation for created and annihilated photons, or equivalently, from phase-matching considerations for multiple interacting beams. PMID:26832066
Stable structures with high topological charge in nonlinear photonic quasicrystals
Law, K. J. H.; Saxena, Avadh; Bishop, A. R.; Kevrekidis, P. G.
2010-09-15
Stable vortices with topological charges of 3 and 4 are examined numerically and analytically in photonic quasicrystals created by interference of five as well as eight beams, for cubic as well as saturable nonlinearities. Direct numerical simulations corroborate the analytical and numerical linear stability analysis predictions for such experimentally realizable structures.
Topological charge correlators, spectral bounds, and contact terms
F.X. Lee; S.J. Dong; T. Draper; I. Horvath; K.F. Liu; H. Thacker; J.B. Zhang
2003-05-01
The structure of topological charge fluctuations in the QCD vacuum is strongly restricted by the spectral negativity of the Euclidean correlator for x = 0 and the presence of a positive contact term. Some examples are considered which illustrate the physical origin of these properties.
Charge d-wave topological insulator
Kopaev, Yu. V.; Kapaev, V. V.; Belyavskii, V. I.
2013-10-15
Formation of a condensate of singlet electron-hole pairs in a two-dimensional metal lattice with the nesting of the Fermi contour is investigated. A numerical solution is obtained for the self-consistency equation for the insulating order parameter depending on the ratio of the coupling constants in the s- and d-wave channels of electron-hole pairing. Solutions with the pure orbital symmetry of s- and d-type are found, as well as solutions with the mixed s + d-symmetry. It is shown that in a wide range of values of the s- and d-wave coupling constants, the two-dimensional insulating order with the orbital symmetry d{sub x{sup 2}-y{sup 2}} can compete with pure ordered s- and d{sub xy}-states and mixed s + d-states. Time reversal symmetry breaking under an established real order with d{sub x{sup 2}-y{sup 2}} -wave symmetry may generate the imaginary component of the order parameter with symmetry d{sub xy} and cause a rise in topologically nontrivial d + id-wave ordering similar to the quantum Hall state in the absence of external magnetic field.
Topological charge analysis of ultrafast single skyrmion creation
NASA Astrophysics Data System (ADS)
Yin, Gen; Li, Yufan; Kong, Lingyao; Lake, Roger K.; Chien, C. L.; Zang, Jiadong
2016-05-01
Magnetic skyrmions are topologically nontrivial spin textures of potential interest for future information storage applications, and for such purposes, the control and understanding of single skyrmion creation is required. A scheme is analyzed to create single Néel-type and Bloch-type skyrmions in helimagnetic thin films utilizing the dynamical excitations induced by the Oersted field and the spin transfer torque given by a vertically injected spin-polarized current. A topological charge analysis using a lattice version of the topological charge provides insight into the locally triggered transition from a trivial to a nontrivial topological spin texture of the Néel or Bloch type skyrmion. The topological protection of the magnetic skyrmion is determined by the symmetric Heisenberg exchange energy. The critical switching current density is ˜107A/cm 2 , which decreases with the easy-plane type uniaxial anisotropy and thermal fluctuations. The in-plane spin polarization of the injected current performs better than out-of-plane polarization, and it provides ultrafast switching times (within 100 ps) and reliable switching outcomes.
Incoherent control of topological charges in nonequilibrium polariton condensates
NASA Astrophysics Data System (ADS)
Ma, Xuekai; Peschel, Ulf; Egorov, Oleg A.
2016-01-01
We study stability and switching dynamics of topological dislocations forming in a nonequilibrium polariton condensate sustained by an incoherent ring-shaped optical pump. In particular, we report on an elegant method for creation of vortices with predefined angular momenta by means of a purely incoherent (off-resonant) elliptically-shaped control beam. The control beam breaks the radiale symmetry of the system and induces chirality required for a topological charge transfer with a predefined sign. Numerical analysis encloses the optimal parameters for an effective switching between states with opposite orbital angular momenta.
Few-cycle vortex wavepackets with tunable topological charge
NASA Astrophysics Data System (ADS)
Grunwald, R.; Bock, M.; Brunne, J.; Wallrabe, U.
2014-02-01
The control of the orbital angular momentum (OAM) of ultrashort laser pulses with highly compact, low-dispersion and flexible devices opens new prospects for momentum-sensitive applications in plasmonics, materials processing, biochemistry, microscopy or optical data transfer. We report on the generation of few-cycle vortex pulses of variable topological charge from a Ti:sapphire laser oscillator with novel types of thermally tunable reflective, spiral-phase micro-electro-mechanical systems (MEMS). The spatial and temporal properties of the pulses were characterized by a reconfigurable, nondiffracting Shack-Hartmann wavefront autocorrelator. The intensity propagation can be described by a Laguerre-Gaussian beam with slight distortions caused by the line of maximum phase step. The different topological charges were indicated by quantitatively comparing the lengths of measured transversal Poynting-vector components to corresponding numerical simulations.
Stability of topological charge of magnetic skyrmion configurations
NASA Astrophysics Data System (ADS)
Jalil, M. B. A.; Tan, S. G.; Siu, Z. B.; Gan, W.; Purnama, I.; Lew, W. S.
2016-02-01
We analyze the topological charge of a skyrmion qs, and the corresponding Hall conductivity σxy, which can serve as an electrical read-out for skyrmion-based memory. We derived the general form of the Dzyaloshinskii-Moriya (DM) interaction for any arbitrary orientation of the DM vector D. Based on the DM interaction energy, we obtained the dependence the skyrmion helicity angle γ on the orientation of D. We showed via general mathematical arguments, the topological nature of the skyrmionic charge qs, and its independence of γ and specific details of the interior of the skyrmion (e.g., its core size). Finally, we showed via numerical micromagnetics the stability of qs under varying applied B-fields till the annihilation field, despite the drastic reduction in the skyrmion core size.
Topological charge using cooling and the gradient flow
NASA Astrophysics Data System (ADS)
Alexandrou, C.; Athenodorou, A.; Jansen, K.
2015-12-01
The equivalence of cooling to the gradient flow when the cooling step nc and the continuous flow step of gradient flow τ are matched is generalized to gauge actions that include rectangular terms. By expanding the link variables up to subleading terms in perturbation theory, we relate nc and τ and show that the results for the topological charge become equivalent when rescaling τ ≃nc/(3 -15 c1 ) , where c1 is the Symanzik coefficient multiplying the rectangular term. We, subsequently, apply cooling and the gradient flow using the Wilson, the Symanzik tree-level improved, and the Iwasaki gauge actions to configurations produced with Nf=2 +1 +1 twisted mass fermions. We compute the topological charge, its distribution, and the correlators between cooling and gradient flow at three values of the lattice spacing demonstrating that the perturbative rescaling τ ≃nc/(3 -15 c1 ) leads to equivalent results.
Fractional charge and spin states in topological insulator constrictions
NASA Astrophysics Data System (ADS)
Klinovaja, Jelena; Loss, Daniel
2015-09-01
We theoretically investigate the properties of two-dimensional topological insulator constrictions both in the integer and fractional regimes. In the presence of a perpendicular magnetic field, the constriction functions as a spin filter with near-perfect efficiency and can be switched by electric fields only. Domain walls between different topological phases can be created in the constriction as an interface between tunneling, magnetic fields, charge density wave, or electron-electron interaction dominated regions. These domain walls host non-Abelian bound states with fractional charge and spin and result in degenerate ground states with parafermions. If a proximity gap is induced bound states give rise to an exotic Josephson current with 8 π periodicity.
Scattering from multicomponent charged ramified polymeric networks of arbitrary topology
NASA Astrophysics Data System (ADS)
Ghaouar, N.; Benhamou, M.; Gharbi, A.
2006-01-01
The scattering and critical properties of weakly charged ramified polymeric systems for any arbitrary topology are investigated by using the random phase approximation. The interaction matrix is modeled as the sum of the short-range excluded volume matrix and the long-range Debye-Hûckel matrix. We consider three kinds of systems, namely weakly charged ramified polymers in solution when the scattering behavior is controlled by the presence of the peak that is related to the wave-vector and the system density. For weakly charged ramified polymer blends the same behavior is seen. For the ternary mixture made of two weakly charged ramified polymers immersed in a good solvent, several cases are considered and the scattering behavior depends strongly on the thermodynamic parameter. The critical properties of the systems are also investigated using the stability condition.
Simultaneous Magnetic and Charge Doping of Topological Insulators with Carbon
NASA Astrophysics Data System (ADS)
Shen, Lei; Zeng, Minggang; Lu, Yunhao; Yang, Ming; Feng, Yuan Ping
2013-12-01
A two-step doping process, magnetic followed by charge or vice versa, is required to produce massive topological surface states (TSS) in topological insulators for many physics and device applications. Here, we demonstrate simultaneous magnetic and hole doping achieved with a single dopant, carbon, in Bi2Se3 by first-principles calculations. Carbon substitution for Se (CSe) results in an opening of a sizable surface Dirac gap (up to 82 meV), while the Fermi level remains inside the bulk gap and close to the Dirac point at moderate doping concentrations. The strong localization of 2p states of CSe favors spontaneous spin polarization via a p-p interaction and formation of ordered magnetic moments mediated by surface states. Meanwhile, holes are introduced into the system by CSe. This dual function of carbon doping suggests a simple way to realize insulating massive TSS.
Characterization of topological charge and orbital angular momentum of shaped optical vortices.
Amaral, Anderson M; Falcão-Filho, Edilson L; de Araújo, Cid B
2014-12-01
Optical vortices (OV) are usually associated to cylindrically symmetric light beams. However, they can have more general geometries that extends their applicability. Since the typical experimental characterization methods are not appropriate for OV with arbitrary shapes, we discuss in this work how the definitions of the classical orbital angular momentum and the topological charge can be used to retrieve these informations in the general case. The concepts discussed are experimentally demonstrated and may be specially useful in areas such as optical tweezers and plasmonics. PMID:25606960
Optical phased array radiating optical vortex with manipulated topological charges.
Ma, Xiaoliang; Pu, Mingbo; Li, Xiong; Huang, Cheng; Pan, Wenbo; Zhao, Bo; Cui, Jianhua; Luo, Xiangang
2015-02-23
Optical antennas are key elements in quantum optics emitting and sensing, and behave wide range applications in optical domain. However, integration of optical antenna radiating orbital angular momentum is still a challenge in nano-scale. We theoretically demonstrate a sub-wavelength phased optical antenna array, which manipulates the distribution of the orbital angular momentum in the near field. Orbital angular momentum with topological charge of 4 can be obtained by controlling the phase distribution of the fundamental mode orbital angular momentum in each antenna element. Our results indicate this phased array may be utilized in high integrated optical communication systems. PMID:25836522
Propagation of optical vortices with fractional topological charge in free space
NASA Astrophysics Data System (ADS)
Ali, Tamelia; Kreminska, Liubov; Golovin, Andrii B.; Crouse, David T.
2014-10-01
The behavior of the optical vortices with fractional topological charges in the far-field is assessed through numerical modeling and confirmed by experimental results. The generation of fractional topological charge variations of the phase within a Gaussian beam was achieved by using a liquid crystal spatial light modulator (LCoS SLM). It is shown that a laser beam carrying an optical vortex with a fractional topological charge evolves into a beam with a topological charge of integer value, specifically an integer value closer to the fractional number in the far field. A potential application of this work is for data transmission within optical telecommunication systems.
Direct instantons, topological charge screening, and QCD glueball sum rules
Forkel, Hilmar
2005-03-01
Nonperturbative Wilson coefficients of the operator product expansion (OPE) for the spin-0 glueball correlators are derived and analyzed. A systematic treatment of the direct instanton contributions is given, based on a realistic instanton size distribution and renormalization at the operator scale. In the pseudoscalar channel, topological charge screening is identified as an additional source of (semi-) hard nonperturbative physics. The screening contributions are shown to be vital for consistency with the anomalous axial Ward identity, and previously encountered pathologies (positivity violations and the disappearance of the 0{sup -+} glueball signal) are traced to their neglect. On the basis of the extended OPE, a comprehensive quantitative analysis of eight Borel-moment sum rules in both spin-0 glueball channels is then performed. The nonperturbative OPE coefficients turn out to be indispensable for consistent sum rules and for their reconciliation with the underlying low-energy theorems. The topological short-distance physics strongly affects the sum rule results and reveals a rather diverse pattern of glueball properties. New predictions for the spin-0 glueball masses and decay constants and an estimate of the scalar glueball width are given, and several implications for glueball structure and experimental glueball searches are discussed.
Thermodynamics of topological nonlinear charged Lifshitz black holes
NASA Astrophysics Data System (ADS)
Zangeneh, M. Kord; Sheykhi, A.; Dehghani, M. H.
2015-07-01
In this paper, we construct a new class of analytic topological Lifshitz black holes with constant curvature horizon in the presence of a power-law Maxwell field in four or more dimensions. We find that in order to obtain these exact Lifshitz solutions, we need a dilaton and at least three electromagnetic fields. Interestingly enough, we find that the reality of the charge of the electromagnetic field which is needed for having solutions with a curved horizon rules out black holes with a hyperbolic horizon. Next, we study the thermodynamics of these nonlinear charged Lifshitz black holes with spherical and flat horizons by calculating all of the conserved and thermodynamic quantities of the solutions. Furthermore, we obtain a generalized Smarr formula and show that the first law of thermodynamics is satisfied. We also perform a stability analysis in both canonical and grand-canonical ensembles. We find that the solutions are thermally stable in proper ranges of the metric parameters. Finally, we comment on the dynamical stability of the obtained solutions under perturbations in four dimensions.
Quantum information transfer between topological and conventional charge qubits
NASA Astrophysics Data System (ADS)
Jun, Li; Yan, Zou
2016-02-01
We propose a scheme to realize coherent quantum information transfer between topological and conventional charge qubits. We first consider a hybrid system where a quantum dot (QD) is tunnel-coupled to a semiconductor Majorana-hosted nanowire (MNW) via using gated control as a switch, the information encoded in the superposition state of electron empty and occupied state can be transferred to each other through choosing the proper interaction time to make measurements. Then we consider another system including a double QDs and a pair of parallel MNWs, it is shown that the entanglement information transfer can be realized between the two kinds of systems. We also realize long distance quantum information transfer between two quantum dots separated by an MNW, by making use of the nonlocal fermionic level formed with the pared Majorana feimions (MFs) emerging at the two ends of the MNW. Furthermore, we analyze the teleportationlike electron transfer phenomenon predicted by Tewari et al. [Phys. Rev. Lett. 100, 027001 (2008)] in our considered system. Interestingly, we find that this phenomenon exactly corresponds to the case that the information encoded in one QD just returns back to its original place during the dynamical evolution of the combined system from the perspective of quantum state transfer. Project supported by the National Natural Science Foundation of China (Grant No. 11304031).
Charge topology of the coherent dissociation of relativistic 11C and 12N nuclei
NASA Astrophysics Data System (ADS)
Artemenkov, D. A.; Bradnova, V.; Zaitsev, A. A.; Zarubin, P. I.; Zarubina, I. G.; Kattabekov, R. R.; Kornegrutsa, N. K.; Mamatkulov, K. Z.; Rukoyatkin, P. A.; Rusakova, V. V.; Stanoeva, R.
2015-09-01
The charge topology of coherent-dissociation events is presented for 11С and 12N nuclei of energy 1.2 GeV per nucleon bombarding nuclear track emulsions. This topology is compared with respective data for 7Be, 8,10B, 9,10C, and 14N nuclei.
Charge topology of the coherent dissociation of relativistic {sup 11}C and {sup 12}N nuclei
Artemenkov, D. A.; Bradnova, V.; Zaitsev, A. A.; Zarubin, P. I. Zarubina, I. G.; Kattabekov, R. R.; Kornegrutsa, N. K.; Mamatkulov, K. Z.; Rukoyatkin, P. A.; Rusakova, V. V.; Stanoeva, R.
2015-09-15
The charge topology of coherent-dissociation events is presented for {sup 11}C and {sup 12}N nuclei of energy 1.2 GeV per nucleon bombarding nuclear track emulsions. This topology is compared with respective data for {sup 7}Be, {sup 8,10}B, {sup 9,10}C, and {sup 14}N nuclei.
NASA Astrophysics Data System (ADS)
Hui, Xiaonnan; Zheng, Shilie; Zhang, Weite; Jin, Xiaofeng; Chi, Hao; Zhang, Xianmin
2016-03-01
The topological charge of an electromagnetic vortex beam depends on its wavefront helicity. For mixed vortex beams composed of several different coaxial vortices, the topological charge spectrum can be obtained by Fourier transform. However, the vortex beam is generally divergent and imperfect. It makes it significant to investigate the local topological charges, especially in radio frequency regime. Fourier transform based methods are restrained by the uncertainty principle and cannot achieve high angular resolution and mode resolution simultaneously. In this letter, an analysis method for local topological charges of vortex beams is presented based on the empirical mode decomposition (EMD). From EMD, the intrinsic mode functions (IMFs) can be obtained to construct the bases of the electromagnetic wave, and each local topological charge can be respectively defined. With this method the local value achieves both high resolution of azimuth angle and topological charge, meanwhile the amplitudes of each OAM modes are presented as well. The simulation and experimental results confirm the validity of the EMD based method.
Asymmetric topological interfaces and charge transfer in epitaxial Bi2 Se3 /II-VI superlattices
NASA Astrophysics Data System (ADS)
Chen, Zhiyi; Zhao, Lukasf; Korzhovska, Inna; Garcia, Thor; Tamargo, Maria; Krusin-Elbaum, Lia; Park, Kyungwha
Access to charge transport through Dirac surface states in topological insulators (TIs) can be challenging due to their intermixing with the bulk or with non-topological subsurface two-dimensional electron gas (2DEG) quantum well states. Formed by bending of bulk electronic bands near the surface, 2DEG states arise via charge transfer to the topological surfaces, so the choice of layers abutting these surfaces is critical. Here we report molecular beam epitaxial growth of Bi2Se3/ZnxCd1-xSe superlattices that support only one topological surface channel per TI layer. The topological nature of conducting channels is evidenced by π-Berry phase and by the two-dimensional weak antilocalization. Both density functional theory calculations and transport measurements suggest that a single topological Dirac cone per TI layer arises from the asymmetry between the Se-terminated and Zn-terminated interfaces of ZnxCd1-xSe with Bi2Se3. Our findings suggest that topological transport could be controlled by adjusting charge transfer from non-topological spacers in hybrid structures. Supported by NSF-DMR-1420634, NSF-DMR-1312483, DOD-W911NF-13-1-0159, NSF DMR-1206354 and computer resources from SDSC under DMR060009N and VT ARC.
Kogan, Ya.I. ); Polyubin, I.V. . Inst. Teoreticheskoj i Ehksperimental'noj Fiziki)
1990-06-01
The particles interaction in the 2 + 1 topologically massive gauge theories is given. It turns out, that contrary to the usual case, two equally charged particles (fermions or the non-Abelian topologically massive vector bosons) attract each other, not repulse. This attraction can lead in principle to vacuum instability, in which we will use some trial wave function techniques. Possible applications are briefly discussed. 12 refs., 9 figs.
Determination of the topological charge of a twisted beam with a Fresnel bi-prism
NASA Astrophysics Data System (ADS)
Emile, Olivier; Emile, Janine; Brousseau, Christian
2014-12-01
The self-interference pattern of a Laguerre Gaussian beam using a Fresnel bi-prism is shown to be very different from what could be expected from a usual laser beam. It resembles the interference pattern that could be obtained using a double slit experiment. The interferences are shifted and the topological charge and its sign can be readily determined considering the shift order of the pattern only. However, since there is no diffraction nor absorption losses unlike in a double slit interference, such a set up could be used even for low power twisted beams or beams with high topological charge. Even fractional topological charges could be determined with an absolute precision of 0.05.
Low-Lying Dirac Eigenmodes, Topological Charge Fluctuations and the Instanton Liquid Model
I. Horvath; S.J. Dong; T. Draper; F.X. Lee; H.B. Thacker; J.B. Zhang
2002-05-01
The local structure of low-lying eigenmodes of the overlap Dirac operator is studied. It is found that these modes cannot be described as linear combinations of 't Hooft ''would-be'' zeromodes associated with instanton excitations that underly the Instanton Liquid Model. This implies that the instanton liquid scenario for spontaneous chiral symmetry breaking in QCD is not accurate. More generally, our data suggests that the vacuum fluctuations of topological charge are not effectively dominated by localized lumps of unit charge with which the topological ''would-be'' zeromodes could be associated.
Charge quantisation without magnetic poles: A topological approach to electromagnetism
NASA Astrophysics Data System (ADS)
Solha, Romero
2016-01-01
The present work provides a theoretical explanation for the quantisation of electric charges, an open problem since Millikan's oil drop experiment in 1909. This explanation is based solely on Maxwell's theory, it recasts Electromagnetic theory under the language of complex line bundles; therefore, neither magnetic poles nor quantum mechanics are invoked.
Topology preservation in self-organizing feature maps: exact definition and measurement.
Villmann, T; Der, R; Herrmann, M; Martinetz, T M
1997-01-01
The neighborhood preservation of self-organizing feature maps like the Kohonen map is an important property which is exploited in many applications. However, if a dimensional conflict arises this property is lost. Various qualitative and quantitative approaches are known for measuring the degree of topology preservation. They are based on using the locations of the synaptic weight vectors. These approaches, however, may fail in case of nonlinear data manifolds. To overcome this problem, in this paper we present an approach which uses what we call the induced receptive fields for determining the degree of topology preservation. We first introduce a precise definition of topology preservation and then propose a tool for measuring it, the topographic function. The topographic function vanishes if and only if the map is topology preserving. We demonstrate the power of this tool for various examples of data manifolds. PMID:18255630
Antipolar ordering of topological charges in active liquid crystals
NASA Astrophysics Data System (ADS)
Dunkel, Jorn; Oza, Anand
Recent experiments demonstrated that ATP-driven microtubule-kinesin bundles can self-assemble into two-dimensional active liquid crystals that exhibit a rich creation and annihilation dynamics of topological defects, reminiscent of particle-pair production processes in quantum systems. This remarkable discovery has sparked considerable theoretical and experimental interest. Here, we present and validate a minimal continuum theory for this new class of active matter systems by merging universality ideas with the classical Landau-de Gennes theory. The resulting model agrees quantitatively with recently published data and, in particular, predicts a previously unexplained regime of antipolar order. Our analysis implies that active liquid crystals are governed by the same generic ordering principles that determine the non-equilibrium dynamics of dense bacterial suspensions and elastic bilayer materials. Moreover, the theory manifests a profound energetic analogy with strongly interacting quantum gases. Generally, our results suggest that complex nonequilibrium pattern-formation phenomena might be predictable from a few fundamental symmetric-breaking and scale-selection principles.
Integral expression for a topological charge in the Faddeev-Niemi nonlinear sigma model
NASA Astrophysics Data System (ADS)
Kisielowski, Marcin
2016-04-01
We have introduced Faddeev-Niemi type variables for static SU(3) Yang-Mills theory. The variables suggest that a nonlinear sigma model whose sigma fields take values in SU(3)/(U(1) × U(1)) and SU(3)/(SU(2) × U(1)) may be relevant to infrared limit of the theory. Shabanov showed that the energy functional of the nonlinear sigma model is bounded from below by certain functional. However, Shabanov’s functional is not homotopy invariant, and its value can be an arbitrary real number—therefore it is not a topological charge. Since the third homotopy group of SU(3)/(U(1) × U(1)) is isomorphic to the group of integer numbers, there is a non-trivial topological charge (given by the isomorphism). We apply Novikov’s procedure to obtain integral expression for this charge. The resulting formula is analogous to the Whitehead’s realization of the Hopf invariant.
Direct Observation of Chiral Topological Solitons in 1D Charge-Density Waves
NASA Astrophysics Data System (ADS)
Kim, Tae-Hwan; Cheon, Sangmo; Lee, Sung-Hoon; Yeom, Han Woong
2015-03-01
Macroscopic and classical solitons are easily and ubiquitously found, from tsunami to blood pressure pulses, but those in microscopic scale are hard to observe. While the existence of such topological solitons were predicted theoretically and evidenced indirectly by the transport and infrared spectroscopy measurements, the direct observation has been hampered by their high mobility and small dimension. In this talk, we show direct observation of topological solitons in the quasi-1D charge-density wave (CDW) ground state of indium atomic wires, which are consisting of interacting double Peierls chains. Such solitons exhibit a characteristic spatial variation of the CDW amplitudes as expected from the electronic structure. Furthermore, these solitons have an exotic hidden topology originated by topologically different 4-fold degenerate CDW ground states. Their exotic topology leads to the chirality of 1D topological solitons through interaction between two solitons in the double Peierls chains. Detailed scanning tunneling microscopy and spectroscopy reveal their chiral nature at the atomic scale. This work paves the avenue toward the microscopic exploitation of the peculiar properties of nanoscale chiral solitons.
Zalazar, M Fernanda; Peruchena, Nélida M
2007-08-16
In the present work, the distribution of the electronic charge density in the ethene protonation reaction by a zeolite acid site is studied within the framework of the density functional theory and the atoms in molecules (AIM) theory. The key electronic effects such as topological distribution of the charge density involved in the reaction are presented and discussed. The results are obtained at B3LYP/6-31G(**) level theory. Attention is focused on topological parameters such as electron density, its Laplacian, kinetic energy density, potential energy density, and electronic energy density at the bond critical points (BCP) in all bonds involved in the interaction zone, in the reactants, pi-complex, transition state, and alkoxy product. In addition, the topological atomic properties are determined on the selected atoms in the course of the reaction (average electron population, N(Omega), atomic net charge, q(Omega), atomic energy, E(Omega), atomic volume, v(Omega), and first moment of the atomic charge distribution, M(Omega)) and their changes are analyzed exhaustively. The topological study clearly shows that the ethene interaction with the acid site of the zeolite cluster, T5-OH, in the ethene adsorbed, is dominated by a strong O-H...pi interaction with some degree of covalence. AIM analysis based on DFT calculation for the transition state (TS) shows that the hydrogen atom from the acid site in the zeolitic fragment is connected to the carbon atom by a covalent bond with some contribution of electrostatic interaction and to the oxygen atom by closed shell interaction with some contribution of covalent character. The C-O bond formed in the alkoxy product can be defined as a weaker shared interaction. Our results show that in the transition state, the dominant interactions are partially electrostatic and partially covalent in nature, in which the covalent contribution increases as the concentration and accumulation of the charge density along the bond path between the nuclei linked increases. PMID:17658733
Disorder Effects in Charge Transport and Spin Response of Topological Insulators
NASA Astrophysics Data System (ADS)
Zhao, Lukas Zhonghua
Topological insulators are a class of solids in which the non-trivial inverted bulk band structure gives rise to metallic surface states that are robust against impurity backscattering. First principle calculations predicted Bi2Te3, Sb2Te3 and Bi2Se3 to be three-dimensional (3D) topological insulators with a single Dirac cone on the surface. The topological surface states were subsequently observed by angle-resolved photoemission (ARPES) and scanning tunneling microscopy (STM). The investigations of charge transport through topological surfaces of 3D topological insulators, however, have faced a major challenge due to large charge carrier densities in the bulk donated by randomly distributed defects such as vacancies and antisites. This bulk disorder intermixes surface and bulk conduction channels, thereby complicating access to the low-energy (Dirac point) charge transport or magnetic response and resulting in the relatively low measured carrier mobilities. Moreover, charge inhomogeneity arising from bulk disorder can result in pronounced nanoscale spatial fluctuations of energy on the surface, leading to the formation of surface `puddles' of different carrier types. Great efforts have been made to combat the undesirable effects of disorder in 3D topological insulators and to reduce bulk carriers through chemical doping, nanostructure fabrication, and electric gating. In this work we have developed a new way to reduce bulk carrier densities using high-energy electron irradiation, thereby allowing us access to the topological surface quantum channels. We also found that disorder in 3D topological insulators can be beneficial. It can play an important part in enabling detection of unusual magnetic response from Dirac fermions and in uncovering new excitations, namely surface superconductivity in Dirac `puddles'. In Chapter 3 we show how by using differential magnetometry we could probe spin rotation in the 3D topological material family (Bi2Se 3, Bi2Te3 and Sb2Te3), and describe our detection of paramagnetic singularity in the magnetic susceptibility at low magnetic fields that persists up to room temperature, and which we have demonstrated to arise from the surfaces of the samples. The singularity is universal to the entire family, largely independent of the bulk carrier density, and consistent with the existence of electronic states near the spin-degenerate Dirac point of the 2D helical metal. The exceptional thermal stability of the signal points to an intrinsic surface cooling process, probably of thermoelectric organ, and establishes a sustainable platform for the singular field-tunable Dirac spin response. In Chapter 4 we describe our discovery of surface superconductivity in a hole-conducting topological insulator Sb2Te3 with transition to zero resistance induced through a minor tuning of growth chemistry that depletes bulk conduction channels. The depletion shifts Fermi energy towards the Dirac point as witnessed by over two orders of magnitude reduced bulk hole density and by the largest carrier mobility (~ 25,000 cm 2 V-1 s-1) found in any topological material. Direct evidence from transport, the unprecedentedly large diamagnetic screening, and the presence of up to ~ 25 meV gaps in differential conductance detected by scanning tunneling spectroscopy (STM) reveal the superconducting condensate to emerge first in surface puddles at unexpectedly high temperature, near 50 K. Percolative Josephson paths mediated by diffusing quasiparticles establish global phase coherence around 9 K. Rich structure of this state lends itself to manipulation and tuning via growth conditions and the topological material's parameters such as Fermi velocity and mean free path. In Chapter 5 we describe a new approach we have developed to reaching stable charge neutrality in 3D topological materials. The technique uses swift (~ 2.5 MeV energy) electron beams to compensate charged bulk defects and bring the Fermi level back into the bulk gap. By controlling the beam fluence we could tune bulk conductivity from p- (hole-like) to n-type (electron-like), crossing the Dirac point and back, while preserving the robust topological signatures of surface channels. We establish that at charge neutrality conductance has a two-dimensional (2D) character with a minimum value on the order of ten conductance quanta G=e 2 /h. From quantum interference contribution to 2D conductance we demonstrate in two systems, Bi2Te3 and Bi2Se 3, that at charge neutrality only two quantum channels corresponding to two topological surfaces are present. The charge neutrality point achieved using electron irradiation with long penetration range shows a route to intrinsic quantum transport of the topological states unconstrained by the bulk size.
NASA Astrophysics Data System (ADS)
Durganandini, P.
2015-03-01
We consider thin planar charged quantum rings on the surface of a three dimensional topological insulator coated with a thin ferromagnetic layer. We show theoretically, that when the ring is threaded by a magnetic field, then, due to the Aharanov-Bohm effect, there are not only the well known circulating persistent currents in the ring but also oscillating persistent Hall voltages across the thin ring. Such oscillating persistent Hall voltages arise due to the topological magneto-electric effect associated with the axion electrodynamics exhibited by the surface electronic states of the three dimensional topological insulator when time reversal symmetry is broken. We further generalize to the case of dipole currents and show that analogous Hall dipole voltages arise. We also discuss the robustness of the effect and suggest possible experimental realizations in quantum rings made of semiconductor heterostructures. Such experiments could also provide new ways of observing the predicted topological magneto-electric effect in three dimensional topological insulators with time reversal symmetry breaking. I thank BCUD, Pune University, Pune for financial support through research grant.
Controlling the flow of spin and charge in nanoscopic topological insulators
NASA Astrophysics Data System (ADS)
Van Dyke, John S.; Morr, Dirk K.
2016-02-01
Controlling the flow of spin and charge currents in topological insulators (TIs) is a crucial requirement for applications in quantum computation and spin electronics. We demonstrate that such control can be established in nanoscopic two-dimensional TIs by breaking their time-reversal symmetry via magnetic defects. This allows for the creation of nearly fully spin-polarized charge currents, and the design of highly tunable spin diodes. Similar effects can also be realized in mesoscale hybrid structures in which TIs interface with ferro- or antiferromagnets.
Comparison of converter topologies for charging capacitors used in pulsed load applications
NASA Technical Reports Server (NTRS)
Nelms, R. M.; Schatz, J. E.; Pollard, Barry
1991-01-01
The authors present a qualitative comparison of different power converter topologies which may be utilized for charging capacitors in pulsed power applications requiring voltages greater than 1 kV. The operation of the converters in capacitor charging applications is described, and relevant advantages are presented. All of the converters except one may be classified in the high-frequency switching category. One of the benefits from high-frequency operation is a reduction in size and weight. The other converter discussed is a member of the command resonant changing category. The authors first describe a boost circuit which functions as a command resonant charging circuit and utilizes a single pulse of current to charge the capacitor. The discussion of high-frequency converters begins with the flyback and Ward converters. Then, the series, parallel, and series/parallel resonant converters are examined.
Miyamoto, K.; Suizu, K.; Akiba, T.; Omatsu, T.
2014-06-30
A terahertz (THz) spiral phase plate with high transmission (>90% after Fresnel correction) and low dispersion has been developed based on the Tsurupica olefin polymer. Direct observations of the topological charge (both magnitude and sign) of a THz vortex beam are performed by using a THz camera with tilted lens focusing and radial defect introduction. The vortex outputs with a topological charge of ±1 (or ±2) are obtained at a frequency of 2 (or 4) THz.
Topologically protected charge transfer along the edge of a chiral p -wave superconductor
NASA Astrophysics Data System (ADS)
Gnezdilov, N. V.; van Heck, B.; Diez, M.; Hutasoit, Jimmy A.; Beenakker, C. W. J.
2015-09-01
The Majorana fermions propagating along the edge of a topological superconductor with px+i py pairing deliver a shot noise power of 1/2 ×e2/h per eV of voltage bias. We calculate the full counting statistics of the transferred charge and find that it becomes trinomial in the low-temperature limit, distinct from the binomial statistics of charge-e transfer in a single-mode nanowire or charge-2 e transfer through a normal-superconductor interface. All even-order correlators of current fluctuations have a universal quantized value, insensitive to disorder and decoherence. These electrical signatures are experimentally accessible, because they persist for temperatures and voltages large compared to the Thouless energy.
An acoustic charge transport imager for high definition television applications
NASA Technical Reports Server (NTRS)
Hunt, W. D.; Brennan, Kevin F.
1994-01-01
The primary goal of this research is to develop a solid-state high definition television (HDTV) imager chip operating at a frame rate of about 170 frames/sec at 2 Megapixels per frame. This imager offers an order of magnitude improvement in speed over CCD designs and will allow for monolithic imagers operating from the IR to the UV. The technical approach of the project focuses on the development of the three basic components of the imager and their integration. The imager chip can be divided into three distinct components: (1) image capture via an array of avalanche photodiodes (APD's), (2) charge collection, storage and overflow control via a charge transfer transistor device (CTD), and (3) charge readout via an array of acoustic charge transport (ACT) channels. The use of APD's allows for front end gain at low noise and low operating voltages while the ACT readout enables concomitant high speed and high charge transfer efficiency. Currently work is progressing towards the development of manufacturable designs for each of these component devices. In addition to the development of each of the three distinct components, work towards their integration is also progressing. The component designs are considered not only to meet individual specifications but to provide overall system level performance suitable for HDTV operation upon integration. The ultimate manufacturability and reliability of the chip constrains the design as well. The progress made during this period is described in detail in Sections 2-4.
Quasinormal modes of four-dimensional topological nonlinear charged Lifshitz black holes
NASA Astrophysics Data System (ADS)
Bécar, Ramón; González, P. A.; Vásquez, Yerko
2016-02-01
We study scalar perturbations of four- dimensional topological nonlinear charged Lifshitz black holes with spherical and plane transverse sections, and we find numerically the quasinormal modes for scalar fields. Then we study the stability of these black holes under massive and massless scalar field perturbations. We focus our study on the dependence of the dynamical exponent, the nonlinear exponent, the angular momentum, and the mass of the scalar field in the modes. It is found that the modes are overdamped, depending strongly on the dynamical exponent and the angular momentum of the scalar field for a spherical transverse section. In contrast, for plane transverse sections the modes are always overdamped.
Chen, Zhiyi; Zhao, Lukas; Park, Kyungwha; Garcia, Thor Axtmann; Tamargo, Maria C.; Krusin-Elbaum, Lia
2015-01-01
Access to charge transport through Dirac surface states in topological insulators (TIs) can be challenging due to their intermixing with bulk states or nontopological two-dimensional electron gas (2DEG) quantum well states caused by bending of electronic bands near the surface. The band bending arises via charge transfer from surface adatoms or interfaces and, therefore, the choice of layers abutting topological surfaces is critical. Here we report molecular beam epitaxial growth of Bi2Se3/ZnxCd1–xSe superlattices that hold only one topological surface channel per TI layer. The topological nature of conducting channels is supported by π-Berry phase evident from observed Shubnikov de Haas quantum oscillations and by the associated two-dimensional (2D) weak antilocalization quantum interference correction to magnetoresistance. Both density functional theory (DFT) calculations and transport measurements suggest that a single topological Dirac cone per TI layer can be realized by asymmetric interfaces: Se-terminated ZnxCd1–xSe interface with the TI remains “electronically intact”, while charge transfer occurs at the Zn-terminated interface. Our findings indicate that topological transport could be controlled by adjusting charge transfer from nontopological spacers in hybrid structures. PMID:26348593
Topological charges in SL(2,R) covariant massive 11-dimensional and type IIB supergravity
NASA Astrophysics Data System (ADS)
Callister, Andrew K.; Smith, Douglas J.
2009-12-01
In this paper we construct closed expressions that correspond to the topological charges of the various 1/2-BPS states of the maximal 10- and 11-dimensional supergravity theories. These expressions are related to the structure of the supersymmetry algebras in curved spacetimes. We mainly focus on IIB supergravity and 11-dimensional supergravity in a double M9-brane background, with an emphasis on the SL(2,R) multiplet structure of the charges and how these map between theories. This includes the charges corresponding to the multiplets of 7- and 9-branes in IIB. We find that examining the possible multiplet structures of the charges provides another tool for exploring the spectrum of BPS states that appear in these theories. As a prerequisite to constructing the charges we determine the field equations and multiplet structure of the 11-dimensional gauge potentials, extending previous results on the subject. The massive gauge transformations of the fields are also discussed. We also demonstrate how these massive gauge transformations are compatible with the construction of an SL(2,R) covariant kinetic term in the 11-dimensional Kaluza-Klein monopole worldvolume action.
NASA Astrophysics Data System (ADS)
Guo, Jianjun; Guo, Banghong; Fan, Ronghua; Zhang, Wenjie; Wang, Yu; Zhang, Litao; Zhang, Panpan
2016-03-01
We demonstrate, theoretically and experimentally, a new method to measure high-order topological charges (TCs) of Laguerre-Gaussian vortex beams, including the magnitude and the sign, by analyzing the interference intensity patterns. The magnitude is determined by analyzing the interference intensity patterns between the vortex beam and its conjugate beam, and using an improved Mach-Zehnder interferometer with a dove prism. Counting the number of interference bright petals attests to the magnitude of high-order TCs through half of the bright petal number. After the TC is modulated by a spiral phase plate, the sign is acquired by comparing the counting results of two charge-coupled devices. Just by this method, we have been able to measure both the magnitude and the sign of the TCs up to l=±90. Our experimental results are in good agreement with the numerical simulations.
Development of a subwavelength grating vortex coronagraph of topological charge 4 (SGVC4)
NASA Astrophysics Data System (ADS)
Delacroix, Christian; Absil, Olivier; Carlomagno, Brunella; Piron, Pierre; Forsberg, Pontus; Karlsson, Mikael; Mawet, Dimitri; Habraken, Serge; Surdej, Jean
2014-08-01
One possible solution to achieve high contrast direct imaging at a small inner working angle (IWA) is to use a vector vortex coronagraph (VVC), which provides a continuous helical phase ramp in the focal plane of the telescope with a phase singularity in its center. Such an optical vortex is characterized by its topological charge, i.e., the number of times the phase accumulates 2π radians along a closed path surrounding the singularity. Over the past few years, we have been developing a charge-2 VVC induced by rotationally symmetric subwavelength gratings (SGVC2), also known as the Annular Groove Phase Mask (AGPM). Since 2013, several SGVC2s (or AGPMs) were manufactured using synthetic diamond substrate, then validated on dedicated optical benches, and installed on 10-m class telescopes. Increasing the topological charge seems however mandatory for cancelling the light of bright stars which will be partially resolved by future Extremely Large Telescopes in the near-infrared. In this paper, we first detail our motivations for developing an SGVC4 (charge 4) dedicated to the near-infrared domain. The challenge lies in the design of the pattern which is unrealistic in the theoretically perfect case, due to state-of-the-art manufacturing limitations. Hence, we propose a new realistic design of SGVC4 with minimized discontinuities and optimized phase ramp, showing conclusive improvements over previous works in this field. A preliminary validation of our concept is given based on RCWA simulations, while full 3D finite-difference time-domain simulations (and eventually laboratory tests) will be required for a final validation.
Charged Particle Environment Definition for NGST: Model Development
NASA Technical Reports Server (NTRS)
Blackwell, William C.; Minow, Joseph I.; Evans, Steven W.; Hardage, Donna M.; Suggs, Robert M.
2000-01-01
NGST will operate in a halo orbit about the L2 point, 1.5 million km from the Earth, where the spacecraft will periodically travel through the magnetotail region. There are a number of tools available to calculate the high energy, ionizing radiation particle environment from galactic cosmic rays and from solar disturbances. However, space environment tools are not generally available to provide assessments of charged particle environment and its variations in the solar wind, magnetosheath, and magnetotail at L2 distances. An engineering-level phenomenology code (LRAD) was therefore developed to facilitate the definition of charged particle environments in the vicinity of the L2 point in support of the NGST program. LRAD contains models tied to satellite measurement data of the solar wind and magnetotail regions. The model provides particle flux and fluence calculations necessary to predict spacecraft charging conditions and the degradation of materials used in the construction of NGST. This paper describes the LRAD environment models for the deep magnetotail (XGSE < -100 Re) and solar wind, and presents predictions of the charged particle environment for NGST.
Phase fluctuations and the absence of topological defects in photo-excited charge ordered nickelate
Lee, W.S.; Chuang, Y.D.; Moore, R.G.; Zhu, Y.; Patthey, L.; Trigo, M.; Lu, D.H.; Kirchmann, P.S.; Krupin, O.; Yi, M.; Langner, M.; Huse, N.; Robinson, J.S.; Chen, Y.; Zhou, S.Y.; Coslovich, G.; Huber, B.; Reis, D.A.; Kaindl, R.A.; Schoenlein, R.W.; Doering, D.; Denes, P.; Schlotter, W.F.; Turner, J.J.; Johnson, S.L.; Fö rst, M.; Sasagawa, T.; Kung, Y.F.; Sorini, A.P.; Kemper, A.F.; Moritz, B.; Devereaux, T.P.; Lee, D.-H.; Shen, Z.X.; Hussain, Z.
2012-01-01
The dynamics of an order parameter's amplitude and phase determines the collective behaviour of novel states emerging in complex materials. Time- and momentum-resolved pump-probe spectroscopy, by virtue of measuring material properties at atomic and electronic time scales out of equilibrium, can decouple entangled degrees of freedom by visualizing their corresponding dynamics in the time domain. Here we combine time-resolved femotosecond optical and resonant X-ray diffraction measurements on charge ordered La1.75Sr0.25NiO4 to reveal unforeseen photoinduced phase fluctuations of the charge order parameter. Such fluctuations preserve long-range order without creating topological defects, distinct from thermal phase fluctuations near the critical temperature in equilibrium. Importantly, relaxation of the phase fluctuations is found to be an order of magnitude slower than that of the order parameter's amplitude fluctuations, and thus limits charge order recovery. This new aspect of phase fluctuations provides a more holistic view of the phase's importance in ordering phenomena of quantum matter.
Electrical Detection of Spin-to-Charge Conversion in a Topological Insulator Bi2Te3
NASA Astrophysics Data System (ADS)
Li, Connie H.; van't Erve, Olaf M. J.; Li, Yaoyi; Li, Lian; Jonker, Berry T.
Spin-momentum locking in topological insulators (TIs) dictates that an unpolarized charge current creates a net spin polarization. We recently demonstrated the first electrical detection of this spontaneous polarization in a transport geometry, using a ferromagnetic (FM) / tunnel barrier contact, where the projection of the TI surface state spin on the magnetization of detector is measured as a voltage [1]. Alternatively, if spins are injected into the TI surface state system, it is distinctively associated with a unique carrier momentum, and hence should generated a charge accumulation, similar to that of inverse spin Hall effect. Here we experimentally demonstrate both effects in the same device fabricated in Bi2Te3: the electrical detection of the spin accumulation generated by an unpolarized current flowing through the surface states, and that of the charge accumulation generated by spins injected into the surface states system. This reverse measurement is an independent confirmation of spin-momentum locking in the TI surface states, and offers additional avenue for spin manipulation. It further demonstrates the robustness and versatility of electrical access to the TI surface state spin system, an important step towards its utilization in TI-based spintronics devices. C.H. Li et al., Nat. Nanotech. 9, 218 (2014). Supported by NRL core funds and Nanoscience Institute.
Phase Fluctuations and the Absence of Topological Defects in Photo-excited Charge Ordered Nickelate
Lee, W.S.; Chuang, Y.D.; Moore, R.G.; Zhu, Y.; Patthey, L.; Trigo, M.; Lu, D.H.; Kirchmann, P.S.; Krupin, O.; Yi, M.; Langner, M.; Huse, N.; Robinson, J.S.; Chen, Y.; Zhou, S.Y.; Coslovich, G.; Huber, B.; Reis, D.A.; Kaindl, R.A.; Schoenlein, R.W.; Doering, D.
2012-05-15
The dynamics of an order parameter's amplitude and phase determines the collective behaviour of novel states emerging in complex materials. Time- and momentum-resolved pump-probe spectroscopy, by virtue of measuring material properties at atomic and electronic time scales out of equilibrium, can decouple entangled degrees of freedom by visualizing their corresponding dynamics in the time domain. Here we combine time-resolved femotosecond optical and resonant X-ray diffraction measurements on charge ordered La{sub 1.75}Sr{sub 0.25}NiO{sub 4} to reveal unforeseen photoinduced phase fluctuations of the charge order parameter. Such fluctuations preserve long-range order without creating topological defects, distinct from thermal phase fluctuations near the critical temperature in equilibrium. Importantly, relaxation of the phase fluctuations is found to be an order of magnitude slower than that of the order parameter's amplitude fluctuations, and thus limits charge order recovery. This new aspect of phase fluctuations provides a more holistic view of the phase's importance in ordering phenomena of quantum matter.
Duarte, Darío J R; de las Vallejos, Margarita M; Peruchena, Nélida M
2010-04-01
In this work, the intermolecular distribution of the electronic charge density in the aromatic hydrogen/halogen bonds is studied within the framework of the atoms in molecules (AIM) theory and the molecular electrostatic potentials (MEP) analysis. The study is carried out in nine complexes formed between benzene and simple lineal molecules, where hydrogen, fluorine and chlorine atoms act as bridge atoms. All the results are obtained at MP2 level theory using cc-pVTZ basis set. Attention is focused on topological features observed at the intermolecular region such as bond, ring and cage critical points of the electron density, as well as the bond path, the gradient of the density maps, molecular graphs and interatomic surfaces. The strength of the interaction increases in the following order: F[Symbol: see text]pi < Cl[Symbol: see text]pi < H[Symbol: see text]pi. Our results show that the fluorine atom has the capability to interact with the pi-cloud to form an aromatic halogen bond, as long as the donor group is highly electron withdrawing. The Laplacian topology allows us to state that the halogen atoms can act as nucleophiles as well as electrophiles, showing clearly their dual character. PMID:19820973
Arithmetic with optical topological charges in stepwise-excited Rb vapor
NASA Astrophysics Data System (ADS)
Akulshin, Alexander M.; Novikova, Irina; Mikhailov, Eugeniy E.; Suslov, Sergey A.; McLean, Russell J.
2016-03-01
We report on experimentally observed addition, subtraction and cancellation of orbital angular momentum (OAM) in the process of parametric four-wave mixing that results in frequency up- and down-converted emission in Rb vapour. Specific features of OAM transfer from resonant laser fields with different optical topological charges to the spatially and temporally coherent blue light have been considered. We have observed the conservation of OAM in nonlinear wave mixing in a wide range of experimental conditions including a non-collinear geometry of the applied laser beams and furthermore that the coherent blue light accumulates the total orbital angular momentum of the applied laser light. Spectral and power dependences of vortex and plane wave front blue light beams have been compared.
Arithmetic with optical topological charges in stepwise-excited Rb vapor.
Akulshin, Alexander M; Novikova, Irina; Mikhailov, Eugeniy E; Suslov, Sergey A; McLean, Russell J
2016-03-15
We report on experimentally observed addition, subtraction, and cancellation of orbital angular momentum (OAM) in the process of parametric four-wave mixing that results in frequency up- and down-converted emission in Rb vapor. Specific features of OAM transfer from resonant laser fields with different optical topological charges to the spatially and temporally coherent blue light (CBL) have been considered. We have observed the conservation of OAM in nonlinear wave mixing in a wide range of experimental conditions, including a noncollinear geometry of the applied laser beams, and furthermore, that the CBL accumulates the total OAM of the applied laser light. Spectral and power dependences of vortex and plane wavefront blue light beams have been compared. PMID:26977655
NASA Astrophysics Data System (ADS)
Durganandini, P.
2016-03-01
We study theoretically, the electromagnetic response due to localized charge current distributions above a topological insulator (coated with a thin ferromagnetic layer) using the electromagnetic SL(2,Z) duality symmetry. We show that the localized current induces an electric field which depends on the current —this is a manifestation of the topological magnetoelectric (TME) effect. We also show that if the charge carriers have spin, then they acquire Aharanov-Casher phases which depend on the current. As an application, we consider thin planar charged quantum rings with persistent currents on the surface of a TI and show that the TME manifests itself as persistent Hall voltages across the charged ring. If the spin is also taken into account, then persistent spin Hall voltages develop across the ring.
Chen, Yue; Fang, Zhao-Xiang; Ren, Yu-Xuan; Gong, Lei; Lu, Rong-De
2015-09-20
Optical vortices are associated with a spatial phase singularity. Such a beam with a vortex is valuable in optical microscopy, hyper-entanglement, and optical levitation. In these applications, vortex beams with a perfect circle shape and a large topological charge are highly desirable. But the generation of perfect vortices with high topological charges is challenging. We present a novel method to create perfect vortex beams with large topological charges using a digital micromirror device (DMD) through binary amplitude modulation and a narrow Gaussian approximation. The DMD with binary holograms encoding both the spatial amplitude and the phase could generate fast switchable, reconfigurable optical vortex beams with significantly high quality and fidelity. With either the binary Lee hologram or the superpixel binary encoding technique, we were able to generate the corresponding hologram with high fidelity and create a perfect vortex with topological charge as large as 90. The physical properties of the perfect vortex beam produced were characterized through measurements of propagation dynamics and the focusing fields. The measurements show good consistency with the theoretical simulation. The perfect vortex beam produced satisfies high-demand utilization in optical manipulation and control, momentum transfer, quantum computing, and biophotonics. PMID:26406501
Formation of optical vortices with topological charge |l|=1 and |l|=1/2 by use of the S-waveplate
NASA Astrophysics Data System (ADS)
Matijosˇius, Aidas; Stanislovaitis, Paulius; Gertus, Titas; Smilgevicˇius, Valerijus
We theoretically and experimentally demonstrate the generation of optical vortices using an S-waveplate, fabricated by femtosecond laser writing in silica glass. It is shown that this method allows to form orthogonally polarized vortices with fractional topological charge. At the double wavelength of the S-waveplate, the superposition of orthogonally polarized optical vortices with topological charge l=1/2 was generated. After separating the resulting beam with polarizer, optical vortices of topological charge l=1/2 were obtained. Vortices of fractional topological charge were detected by interfering the vortex beam with a Gaussian beam. A slightly laterally misadjusted Michelson interferometer was used for detection of vortices with integer topological charge.
Andersson, H; von Heijne, G
1994-01-01
The membrane electrochemical potential is critical for the export of most periplasmic proteins in Escherichia coli. Its exact role during insertion of integral inner membrane proteins, however, remains obscure. Using derivatives of the inner membrane protein leader peptidase (Lep), we now show that the membrane potential appears to stimulate the membrane translocation of chain segments containing negatively charged residues, that positively charged regions appear to be more easily translocated in the absence of a potential, and that certain Lep constructs insert with different topologies in the presence and absence of a membrane potential, suggesting that the electrochemical potential introduces an asymmetry between the topological effects of positively and negatively charged amino acids during the process of membrane protein insertion in E. coli. Images PMID:8194517
NASA Astrophysics Data System (ADS)
Ozfidan, Isil; Vladisavljevic, Milos; Korkusinski, Marek; Hawrylak, Pawel
2015-12-01
We present a theory of the electronic and optical properties of a charged artificial benzene ring (ABR). The ABR is described by the extended Hubbard model solved using exact diagonalization methods in both real and Fourier space as a function of the tunneling matrix element t , Hubbard on-site repulsion U , and interdot interaction V . In the strongly interacting case, we discuss exact analytical results for the spectrum of the hole in a half-filled ABR dressed by the spin excitations of the remaining electrons. The spectrum is interpreted in terms of the appearance of a topological phase associated with an effective gauge field piercing through the ring. We show that the maximally spin-polarized (S =5 /2 ) and maximally spin-depolarized (S =1 /2 ) states are the lowest energy, orbitally nondegenerate, states. We discuss the evolution of the phase diagram and level crossings as interactions are switched off and the ground state becomes spin nondegenerate but orbitally degenerate S =1 /2 . We present a theory of optical absorption spectra and show that the evolution of the ground and excited states, level crossings, and presence of artificial gauge can be detected optically.
Topology of charge density and elastic properties of Ti3SiC2 polymorphs
Yu, Rong; Zhang, Xiao Feng; He, Lian Long; Ye, Heng Qiang
2004-06-24
Using an all-electron, full potential first-principles method, we have investigated the topology of charge density and elastic properties of the two polymorphs, alpha and beta, of Ti3SiC2. The bonding effect was analyzed based on Bader's quantum theory of ''atoms in molecules'' (AIM). It was found that the Ti-Si bonding effect is significantly weaker in beta than in alpha, giving less stabilizing effect for beta. The Si-C bonds, which are absent in alpha, are formed in beta and provide additional stabilizing effect for beta. In contrast to conventional thinking, there is no direction interaction between Ti atoms in both alpha and beta. The calculated elastic properties are in good agreement with the experimental results, giving the bulk modulus of about 180 GPa and the Poisson's ratio of 0.2. The beta phase is generally softer than the alpha phase. As revealed by the direction dependent Young's modulus, there is only slight elastic anisotropy in Ti3SiC2. For alpha, Young's modulus is minimum in the c direction and maximum in the directions 42o from c. For beta, the maximum lies in the c direction, in part due to the formation of Si-C bonds in this direction.
An Acoustic Charge Transport Imager for High Definition Television
NASA Technical Reports Server (NTRS)
Hunt, William D.; Brennan, Kevin; May, Gary; Glenn, William E.; Richardson, Mike; Solomon, Richard
1999-01-01
This project, over its term, included funding to a variety of companies and organizations. In addition to Georgia Tech these included Florida Atlantic University with Dr. William E. Glenn as the P.I., Kodak with Mr. Mike Richardson as the P.I. and M.I.T./Polaroid with Dr. Richard Solomon as the P.I. The focus of the work conducted by these organizations was the development of camera hardware for High Definition Television (HDTV). The focus of the research at Georgia Tech was the development of new semiconductor technology to achieve a next generation solid state imager chip that would operate at a high frame rate (I 70 frames per second), operate at low light levels (via the use of avalanche photodiodes as the detector element) and contain 2 million pixels. The actual cost required to create this new semiconductor technology was probably at least 5 or 6 times the investment made under this program and hence we fell short of achieving this rather grand goal. We did, however, produce a number of spin-off technologies as a result of our efforts. These include, among others, improved avalanche photodiode structures, significant advancement of the state of understanding of ZnO/GaAs structures and significant contributions to the analysis of general GaAs semiconductor devices and the design of Surface Acoustic Wave resonator filters for wireless communication. More of these will be described in the report. The work conducted at the partner sites resulted in the development of 4 prototype HDTV cameras. The HDTV camera developed by Kodak uses the Kodak KAI-2091M high- definition monochrome image sensor. This progressively-scanned charge-coupled device (CCD) can operate at video frame rates and has 9 gm square pixels. The photosensitive area has a 16:9 aspect ratio and is consistent with the "Common Image Format" (CIF). It features an active image area of 1928 horizontal by 1084 vertical pixels and has a 55% fill factor. The camera is designed to operate in continuous mode with an output data rate of 5MHz, which gives a maximum frame rate of 4 frames per second. The MIT/Polaroid group developed two cameras under this program. The cameras have effectively four times the current video spatial resolution and at 60 frames per second are double the normal video frame rate.
NASA Astrophysics Data System (ADS)
Malzard, Simon; Poli, Charles; Schomerus, Henning
2015-11-01
We show that topologically protected defect states can exist in open (leaky or lossy) systems even when these systems are topologically trivial in the closed limit. The states appear from within the continuum, thus in the absence of a band gap, and are generated via exceptional points (a spectral transition that occurs in open wave and quantum systems with a generalized time-reversal symmetry), or via a degeneracy induced by charge-conjugation symmetry (which is related to the pole transition of Majorana zero modes). We demonstrate these findings for a leaking passive coupled-resonator optical waveguide with asymmmetric internal scattering, where the required symmetries (non-Hermitian versions of time-reversal symmetry, chirality, and charge conjugation) emerge dynamically.
Malzard, Simon; Poli, Charles; Schomerus, Henning
2015-11-13
We show that topologically protected defect states can exist in open (leaky or lossy) systems even when these systems are topologically trivial in the closed limit. The states appear from within the continuum, thus in the absence of a band gap, and are generated via exceptional points (a spectral transition that occurs in open wave and quantum systems with a generalized time-reversal symmetry), or via a degeneracy induced by charge-conjugation symmetry (which is related to the pole transition of Majorana zero modes). We demonstrate these findings for a leaking passive coupled-resonator optical waveguide with asymmmetric internal scattering, where the required symmetries (non-Hermitian versions of time-reversal symmetry, chirality, and charge conjugation) emerge dynamically. PMID:26613422
NASA Astrophysics Data System (ADS)
Beck, Horst P.
2015-10-01
The notion of a "size" of the ions plays an important role in crystal chemistry. In this paper we demonstrate how "size" varies with the combination of elements and also with varying stoichiometric composition of a compound taking the A-Ti-O series (A = Li, Na, K, Mg, Ca, Sr, Ba) as an example. We analyse the correlation between the topology of a structure, i.e. the coordination geometry and the distances observed, and the charges of the atoms as derived from a Bader analysis of the electron distribution which has been calculated in DFT relaxations of the structures. We demonstrate how charge relations of the atoms in specific stoichiometric relations are strictly fixed within small ranges which are constraint by electronegativity differences of the constituting atoms and how atomic charges are "delicately" balanced by minute movements of the atoms and changes in coordination. The balance of charges proves to be a decisive structure determining parameter.
NASA Astrophysics Data System (ADS)
Gu, Zheng-Cheng; Wang, Juven C.; Wen, Xiao-Gang
2016-03-01
Quantum disordering a discrete-symmetry-breaking state by condensing domain walls can lead to a trivial symmetric insulator state. In this work, we show that if we bind a one-dimensional representation of the symmetry (such as a charge) to the intersection point of several domain walls, condensing such modified domain walls can lead to a nontrivial symmetry-protected topological (SPT) state. This result is obtained by showing that the modified domain-wall condensed state has a nontrivial SPT invariant, the symmetry-twist-dependent partition function. We propose two different kinds of field theories that can describe the above-mentioned SPT states. The first one is a Ginzburg-Landau-type nonlinear sigma model theory, but with an additional multikink domain-wall topological term. Such theory has an anomalous Uk(1 ) symmetry but an anomaly-free ZNk symmetry. The second one is a gauge theory, which is beyond Abelian Chern-Simons/BF gauge theories. We argue that the two field theories are equivalent at low energies. After coupling to the symmetry twists, both theories produce the desired SPT invariant.
Construction of a topological charge on fuzzy S{sup 2}xS{sup 2} via a Ginsparg-Wilson relation
Aoki, Hajime; Hirayama, Yoshiko; Iso, Satoshi
2009-12-15
We construct a topological charge of gauge field configurations on a fuzzy S{sup 2}xS{sup 2} by using a Dirac operator satisfying the Ginsparg-Wilson relation. The topological charge defined on the fuzzy S{sup 2}xS{sup 2} can be interpreted as a noncommutative (or matrix) generalization of the 2nd Chern character on S{sup 2}xS{sup 2}. We further calculate the number of chiral zero modes of the Dirac operator in topologically nontrivial gauge configurations. Generalizations of our formulation to fuzzy (S{sup 2}){sup k} are also discussed.
An acoustic charge transport imager for high definition television applications
NASA Technical Reports Server (NTRS)
Hunt, William D.; Brennan, Kevin F.; Summers, Chris J.
1992-01-01
In this report we present the progress during the second six month period of the project. This includes both experimental and theoretical work on the acoustic charge transport (ACT) portion of the chip, the theoretical program modelling of both the avalanche photodiode (APD) and the charge transfer and overflow transistor and the materials growth and fabrication part of the program.
Spin and charge transport induced by a twisted light beam on the surface of a topological insulator
NASA Astrophysics Data System (ADS)
Shintani, Kunitaka; Taguchi, Katsuhisa; Tanaka, Yukio; Kawaguchi, Yuki
2016-05-01
We theoretically study spin and charge transport induced by a twisted light beam irradiated on a disordered surface of a doped three-dimensional topological insulator (TI). We find that various types of spin vortices are imprinted on the surface of the TI depending on the spin and orbital angular momentum of the incident light. The key mechanism for the appearance of the unconventional spin structure is the spin-momentum locking in the surface state of the TI. Besides, the diffusive transport of electrons under an inhomogeneous electric field causes a gradient of the charge density, which then induces nonlocal charge current and spin density as well as the spin current. We discuss the relation between these quantities within the linear response to the applied electric field using the Keldysh-Green's function method.
NASA Astrophysics Data System (ADS)
Jäykkä, Juha; Hietarinta, Jarmo; Salo, Petri
2008-03-01
We study the stability of Hopfions embedded in the Ginzburg-Landau (GL) model of two oppositely charged components. It has been shown by Babaev [Phys. Rev. B 65, 100512 (2002)] that this model contains the Faddeev-Skyrme (FS) model, which is known to have topologically stable configurations with a given Hopf charge, the so-called Hopfions. Hopfions are typically formed from a unit-vector field that points to a fixed direction at spatial infinity and locally forms a knot with a soft core. The GL model, however, contains extra fields beyond the unit-vector field of the FS model and this can, in principle, change the fate of topologically nontrivial configurations. We investigate the stability of Hopfions in the two-component GL model both analytically (scaling) and numerically (first order dissipative dynamics). A number of initial states with different Hopf charges are studied; we also consider various different scalar potentials, including a singular one. In all the cases studied, we find that the Hopfions tend to shrink into a thin loop that is too close to a singular configuration for our numerical methods to investigate.
Spataru, Catalin D.; Léonard, François
2014-08-13
Topological insulators are of interest for many applications in electronics and optoelectronics, but harnessing their unique properties requires detailed understanding and control of charge injection at electrical contacts. Here we present large-scale ab initio calculations of the electronic properties of Au, Ni, Pt, Pd, and graphene contacts to Bi_{2}Se_{3}. We show that regardless of the metal, the Fermi level is located in the conduction band, leading to n-type Ohmic contact to the first quintuplet. Furthermore, we find strong charge transfer and band-bending in the first few quintuplets, with no Schottky barrier for charge injection even when the topoplogical insulator is undoped. Our calculations indicate that Au and graphene leave the spin-momentum locking mostly unaltered, but on the other hand, Ni, Pd, and Pt strongly hybridize with Bi_{2}Se_{3} and relax spin-momentum locking. In conclusion, our results indicate that judicious choice of the contact metal is essential to reveal the unique surface features of topological insulators.
Spataru, Catalin D.; Léonard, François
2014-08-13
Topological insulators are of interest for many applications in electronics and optoelectronics, but harnessing their unique properties requires detailed understanding and control of charge injection at electrical contacts. Here we present large-scale ab initio calculations of the electronic properties of Au, Ni, Pt, Pd, and graphene contacts to Bi2Se3. We show that regardless of the metal, the Fermi level is located in the conduction band, leading to n-type Ohmic contact to the first quintuplet. Furthermore, we find strong charge transfer and band-bending in the first few quintuplets, with no Schottky barrier for charge injection even when the topoplogical insulator ismore » undoped. Our calculations indicate that Au and graphene leave the spin-momentum locking mostly unaltered, but on the other hand, Ni, Pd, and Pt strongly hybridize with Bi2Se3 and relax spin-momentum locking. In conclusion, our results indicate that judicious choice of the contact metal is essential to reveal the unique surface features of topological insulators.« less
Definition of the topological structure of the automatic control system of spacecrafts
NASA Astrophysics Data System (ADS)
Zelenkov, P. V.; Karaseva, M. V.; Tsareva, E. A.; Tsarev, R. Y.
2015-01-01
The paper considers the problem of selection the topological structure of the automated control system of spacecrafts. The integer linear model of mathematical programming designed to define the optimal topological structure for spacecraft control is proposed. To solve the determination problem of topological structure of the control system of spacecrafts developed the procedure of the directed search of some structure variants according to the scheme "Branch and bound". The example of the automated control system of spacecraft development included the combination of ground control stations, managing the spacecraft of three classes with a geosynchronous orbit with constant orbital periods is presented.
NASA Astrophysics Data System (ADS)
Mendoza, J. H.; Díaz, C. F.; Acevedo, C. H.; Torres, Y.
2016-02-01
The orbital angular momentum of light has a big contribution in many engineering applications like optical communications, because this physical property allows eigenstates characteristic of the wavefront rotation when the beam is propagated. The nature of these eigenstates allows that information can be encoded and gives immunity to electromagnetic interference, allowing an increase of bandwidth, cadence and capacity of the communication channel. This work shown the methodology using nanometric thin films like Titanium based (TiO2) grown over strontium titanate (SrTiO3) support, to distinguish and discriminate a well- defined integer value of the topological charge of an OAM beam.
An acoustic charge transport imager for high definition television applications
NASA Technical Reports Server (NTRS)
Hunt, W. D.; Brennan, K. F.; Summers, C. J.
1994-01-01
The primary goal of this research is to develop a solid-state television (HDTV) imager chip operating at a frame rate of about 170 frames/sec at 2 Megapixels/frame. This imager will offer an order of magnitude improvements in speed over CCD designs and will allow for monolithic imagers operating from the IR to UV. The technical approach of the project focuses on the development of the three basic components of the imager and their subsequent integration. The camera chip can be divided into three distinct functions: (1) image capture via an array of avalanche photodiodes (APD's); (2) charge collection, storage, and overflow control via a charge transfer transistor device (CTD); and (3) charge readout via an array of acoustic charge transport (ACT) channels. The use of APD's allows for front end gain at low noise and low operating voltages while the ACT readout enables concomitant high speed and high charge transfer efficiency. Currently work is progressing towards the optimization of each of these component devices. In addition to the development of each of the three distinct components, work towards their integration and manufacturability is also progressing. The component designs are considered not only to meet individual specifications but to provide overall system level performance suitable for HDTV operation upon integration. The ultimate manufacturability and reliability of the chip constrains the design as well. The progress made during this period is described in detail.
Symmetry, winding number, and topological charge of vortex solitons in discrete-symmetry media
Garcia-March, Miguel-Angel; Zacares, Mario; Sahu, Sarira; Ceballos-Herrera, Daniel E.
2009-05-15
We determine the functional behavior near the discrete rotational symmetry axis of discrete vortices of the nonlinear Schroedinger equation. We show that these solutions present a central phase singularity whose charge is restricted by symmetry arguments. Consequently, we demonstrate that the existence of high-charged discrete vortices is related to the presence of other off-axis phase singularities, whose positions and charges are also restricted by symmetry arguments. To illustrate our theoretical results, we offer two numerical examples of high-charged discrete vortices in photonic crystal fibers showing hexagonal discrete rotational invariance.
NASA Astrophysics Data System (ADS)
Rojas-Sánchez, J.-C.; Oyarzún, S.; Fu, Y.; Marty, A.; Vergnaud, C.; Gambarelli, S.; Vila, L.; Jamet, M.; Ohtsubo, Y.; Taleb-Ibrahimi, A.; Le Fèvre, P.; Bertran, F.; Reyren, N.; George, J.-M.; Fert, A.
2016-03-01
We present results on spin to charge current conversion in experiments of resonant spin pumping into the Dirac cone with helical spin polarization of the elemental topological insulator (TI) α -Sn. By angle-resolved photoelectron spectroscopy (ARPES), we first check that the Dirac cone (DC) at the α -Sn (0 0 1) surface subsists after covering Sn with Ag. Then we show that resonant spin pumping at room temperature from Fe through Ag into α -Sn layers induces a lateral charge current that can be ascribed to the inverse Edelstein effect by the DC states. Our observation of an inverse Edelstein effect length much longer than those generally found for Rashba interfaces demonstrates the potential of TIs for the conversion between spin and charge in spintronic devices. By comparing our results with data on the relaxation time of TI free surface states from time-resolved ARPES, we can anticipate the ultimate potential of the TI for spin to charge conversion and the conditions to reach it.
An acoustic charge transport imager for high definition television applications
NASA Technical Reports Server (NTRS)
Hunt, William D.; Brennan, Kevin F.; Summers, Christopher J.
1993-01-01
This report covers: (1) invention of a new, ultra-low noise, low operating voltage APD which is expected to offer far better performance than the existing volume doped APD device; (2) performance of a comprehensive series of experiments on the acoustic and piezoelectric properties of ZnO films sputtered on GaAs which can possibly lead to a decrease in the required rf drive power for ACT devices by 15dB; (3) development of an advanced, hydrodynamic, macroscopic simulator used for evaluating the performance of ACT and CTD devices and aiding in the development of the next generation of devices; (4) experimental development of CTD devices which utilize a p-doped top barrier demonstrating charge storage capacity and low leakage currents; (5) refinements in materials growth techniques and in situ controls to lower surface defect densities to record levels as well as increase material uniformity and quality.
[ital S][sup 1][times][ital S][sup 2] wormholes and topological charge
Ridgway, S.A. )
1994-07-15
I investigate solutions to the Euclidean Einstein-matter field equations with the topology [ital S][sup 1][times][ital S][sup 2][times][ital R] in a theory with a massless periodic scalar field and electromagnetism. These solutions carry the winding number of the periodic scalar as well as magnetic flux. They induce violations of a quasitopological conservation law which conserves the product of the magnetic flux and winding number on the background spacetime. I extend these solutions to a model with stable loops of superconducting cosmic string and interpret them as contributing to the decay of such loops.
Lee, W S; Chuang, Y D; Moore, R G; Zhu, Y; Patthey, L; Trigo, M; Lu, D H; Kirchmann, P S; Krupin, O; Yi, M; Langner, M; Huse, N; Robinson, J S; Chen, Y; Zhou, S Y; Coslovich, G; Huber, B; Reis, D A; Kaindl, R A; Schoenlein, R W; Doering, D; Denes, P; Schlotter, W F; Turner, J J; Johnson, S L; Frst, M; Sasagawa, T; Kung, Y F; Sorini, A P; Kemper, A F; Moritz, B; Devereaux, T P; Lee, D-H; Shen, Z X; Hussain, Z
2012-01-01
The dynamics of an order parameter's amplitude and phase determines the collective behaviour of novel states emerging in complex materials. Time- and momentum-resolved pump-probe spectroscopy, by virtue of measuring material properties at atomic and electronic time scales out of equilibrium, can decouple entangled degrees of freedom by visualizing their corresponding dynamics in the time domain. Here we combine time-resolved femotosecond optical and resonant X-ray diffraction measurements on charge ordered La(1.75)Sr(0.25)NiO(4) to reveal unforeseen photoinduced phase fluctuations of the charge order parameter. Such fluctuations preserve long-range order without creating topological defects, distinct from thermal phase fluctuations near the critical temperature in equilibrium. Importantly, relaxation of the phase fluctuations is found to be an order of magnitude slower than that of the order parameter's amplitude fluctuations, and thus limits charge order recovery. This new aspect of phase fluctuations provides a more holistic view of the phase's importance in ordering phenomena of quantum matter. PMID:22588300
Etienne, Thibaud; Assfeld, Xavier; Monari, Antonio
2014-09-01
In parallel with the derivation of a novel descriptor (ϕS) related to chromophores' electronic excited states topology, the present article emphasizes some congruence of significance between our ϕS index and formerly developed centroid-related indices. We especially point out the possibility to formally adapt a barycenter (centroid) approach to the use of detachment/attachment densities. While the reciprocity of the two approaches can be mathematically evidenced, we will show that some difficulties brought by the use of ground and excited states electron densities in direct space can be overcome by undertaking some operations on the Hilbert space-related detachment/attachment matrices. We further wish to point out the crucial case of some chromophores holding two electron-withdrawing groups symmetrically disposed in a rod-like structure. Finally, we will qualitatively highlight the quadratic-like relationship between the amount of displaced charge induced by light absorption and the ϕS index. PMID:26588534
NASA Astrophysics Data System (ADS)
Sigalov, Michael; Kamenetskii, E. O.; Shavit, Reuven
2008-01-01
In microwaves, a TE-polarized rectangular-waveguide resonator with an inserted thin ferrite disk gives an example of a nonintegrable system. The interplay of reflection and transmission at the disk interfaces together with the material gyrotropy effect gives rise to whirlpool-like electromagnetic vortices in the proximity of the ferromagnetic resonance. Based on numerical simulation, we show that a character of microwave vortices in a cavity can be analyzed by means of consideration of equivalent magnetic currents. Maxwell equations allows introduction of a magnetic current as a source of the electromagnetic field. Specifically, we found that in such nonintegrable structures, magnetic gyrotropy and geometrical factors leads to the effect of symmetry breaking resulting in effective chiral magnetic currents and topological magnetic charges. As an intriguing fact, one can observe precessing behavior of the electric-dipole polarization inside a ferrite disk.
NASA Astrophysics Data System (ADS)
Morimoto, Takahiro; Furusaki, Akira; Nagaosa, Naoto
2015-04-01
Three-dimensional topological insulators of finite thickness can show the quantum Hall effect (QHE) at the filling factor ν =0 under an external magnetic field if there is a finite potential difference between the top and bottom surfaces. We calculate energy spectra of surface Weyl fermions in the ν =0 QHE and find that gapped edge states with helical spin structure are formed from Weyl fermions on the side surfaces under certain conditions. These edge channels account for the nonlocal charge transport in the ν =0 QHE which is observed in a recent experiment on (Bi1 -xSbx)2Te3 films. The edge channels also support spin transport due to the spin-momentum locking. We propose an experimental setup to observe various spintronics functions such as spin transport and spin conversion.
NASA Astrophysics Data System (ADS)
de Vries, E. K.; Kamerbeek, A. M.; Koirala, N.; Brahlek, M.; Salehi, M.; Oh, S.; van Wees, B. J.; Banerjee, T.
2015-11-01
Topological insulators provide a new platform for spintronics due to the spin texture of the surface states that are topologically robust against elastic backscattering. Here we report on an investigation of the measured voltage obtained from efforts to electrically probe spin-momentum locking in the topological insulator Bi2Se3 using ferromagnetic contacts. Upon inverting the magnetization of the ferromagnetic contacts, we find a reversal of the measured voltage. Extensive analysis of the bias and temperature dependence of this voltage was done, considering the orientation of the magnetization relative to the current. Our findings indicate that the measured voltage can arise due to fringe-field-induced Hall voltages, different from current-induced spin polarization of the surface state charge carriers, as reported recently. Understanding the nontrivial origin of the measured voltage is important for realizing spintronic devices with topological insulators.
Orbital Topology Controlling Charge Injection in Quantum-Dot-Sensitized Solar Cells.
Hansen, Thorsten; Žídek, Karel; Zheng, Kaibo; Abdellah, Mohamed; Chábera, Pavel; Persson, Petter; Pullerits, Tõnu
2014-04-01
Quantum-dot-sensitized solar cells are emerging as a promising development of dye-sensitized solar cells, where photostable semiconductor quantum dots replace molecular dyes. Upon photoexcitation of a quantum dot, an electron is transferred to a high-band-gap metal oxide. Swift electron transfer is crucial to ensure a high overall efficiency of the solar cell. Using femtosecond time-resolved spectroscopy, we find the rate of electron transfer to be surprisingly sensitive to the chemical structure of the linker molecules that attach the quantum dots to the metal oxide. A rectangular barrier model is unable to capture the observed variation. Applying bridge-mediated electron-transfer theory, we find that the electron-transfer rates depend on the topology of the frontier orbital of the molecular linker. This promises the capability of fine tuning the electron-transfer rates by rational design of the linker molecules. PMID:26274464
Senyuk, Bohdan; Liu, Qingkun; He, Sailing; Kamien, Randall D; Kusner, Robert B; Lubensky, Tom C; Smalyukh, Ivan I
2013-01-10
Smoke, fog, jelly, paints, milk and shaving cream are common everyday examples of colloids, a type of soft matter consisting of tiny particles dispersed in chemically distinct host media. Being abundant in nature, colloids also find increasingly important applications in science and technology, ranging from direct probing of kinetics in crystals and glasses to fabrication of third-generation quantum-dot solar cells. Because naturally occurring colloids have a shape that is typically determined by minimization of interfacial tension (for example, during phase separation) or faceted crystal growth, their surfaces tend to have minimum-area spherical or topologically equivalent shapes such as prisms and irregular grains (all continuously deformable--homeomorphic--to spheres). Although toroidal DNA condensates and vesicles with different numbers of handles can exist and soft matter defects can be shaped as rings and knots, the role of particle topology in colloidal systems remains unexplored. Here we fabricate and study colloidal particles with different numbers of handles and genus g ranging from 1 to 5. When introduced into a nematic liquid crystal--a fluid made of rod-like molecules that spontaneously align along the so-called 'director'--these particles induce three-dimensional director fields and topological defects dictated by colloidal topology. Whereas electric fields, photothermal melting and laser tweezing cause transformations between configurations of particle-induced structures, three-dimensional nonlinear optical imaging reveals that topological charge is conserved and that the total charge of particle-induced defects always obeys predictions of the Gauss-Bonnet and Poincaré-Hopf index theorems. This allows us to establish and experimentally test the procedure for assignment and summation of topological charges in three-dimensional director fields. Our findings lay the groundwork for new applications of colloids and liquid crystals that range from topological memory devices, through new types of self-assembly, to the experimental study of low-dimensional topology. PMID:23263182
Netzel, Jeanette; van Smaalen, Sander
2009-01-01
Charge densities have been determined by the Maximum Entropy Method (MEM) from the high-resolution, low-temperature (T ≃ 20 K) X-ray diffraction data of six different crystals of amino acids and peptides. A comparison of dynamic deformation densities of the MEM with static and dynamic deformation densities of multipole models shows that the MEM may lead to a better description of the electron density in hydrogen bonds in cases where the multipole model has been restricted to isotropic displacement parameters and low-order multipoles (l max = 1) for the H atoms. Topological properties at bond critical points (BCPs) are found to depend systematically on the bond length, but with different functions for covalent C—C, C—N and C—O bonds, and for hydrogen bonds together with covalent C—H and N—H bonds. Similar dependencies are known for AIM properties derived from static multipole densities. The ratio of potential and kinetic energy densities |V(BCP)|/G(BCP) is successfully used for a classification of hydrogen bonds according to their distance d(H⋯O) between the H atom and the acceptor atom. The classification based on MEM densities coincides with the usual classification of hydrogen bonds as strong, intermediate and weak [Jeffrey (1997) ▶. An Introduction to Hydrogen Bonding. Oxford University Press]. MEM and procrystal densities lead to similar values of the densities at the BCPs of hydrogen bonds, but differences are shown to prevail, such that it is found that only the true charge density, represented by MEM densities, the multipole model or some other method can lead to the correct characterization of chemical bonding. Our results do not confirm suggestions in the literature that the promolecule density might be sufficient for a characterization of hydrogen bonds. PMID:19767685
Bouchard, Frédéric; De Leon, Israel; Schulz, Sebastian A.; Upham, Jeremy; Karimi, Ebrahim; Boyd, Robert W.
2014-09-08
Orbital angular momentum associated with the helical phase-front of optical beams provides an unbounded “space” for both classical and quantum communications. Among the different approaches to generate and manipulate orbital angular momentum states of light, coupling between spin and orbital angular momentum allows a faster manipulation of orbital angular momentum states because it depends on manipulating the polarisation state of light, which is simpler and generally faster than manipulating conventional orbital angular momentum generators. In this work, we design and fabricate an ultra-thin spin-to-orbital angular momentum converter, based on plasmonic nano-antennas and operating in the visible wavelength range that is capable of converting spin to an arbitrary value of orbital angular momentum ℓ. The nano-antennas are arranged in an array with a well-defined geometry in the transverse plane of the beam, possessing a specific integer or half-integer topological charge q. When a circularly polarised light beam traverses this metasurface, the output beam polarisation switches handedness and the orbital angular momentum changes in value by ℓ=±2qℏ per photon. We experimentally demonstrate ℓ values ranging from ±1 to ±25 with conversion efficiencies of 8.6% ± 0.4%. Our ultra-thin devices are integratable and thus suitable for applications in quantum communications, quantum computations, and nano-scale sensing.
NASA Astrophysics Data System (ADS)
Ovchinnikov, Igor V.; Schwartz, Robert N.; Wang, Kang L.
2016-03-01
The concept of deterministic dynamical chaos has a long history and is well established by now. Nevertheless, its field theoretic essence and its stochastic generalization have been revealed only very recently. Within the newly found supersymmetric theory of stochastics (STS), all stochastic differential equations (SDEs) possess topological or de Rahm supersymmetry and stochastic chaos is the phenomenon of its spontaneous breakdown. Even though the STS is free of approximations and thus is technically solid, it is still missing a firm interpretational basis in order to be physically sound. Here, we make a few important steps toward the construction of the interpretational foundation for the STS. In particular, we discuss that one way to understand why the ground states of chaotic SDEs are conditional (not total) probability distributions, is that some of the variables have infinite memory of initial conditions and thus are not “thermalized”, i.e., cannot be described by the initial-conditions-independent probability distributions. As a result, the definitive assumption of physical statistics that the ground state is a steady-state total probability distribution is not valid for chaotic SDEs.
Charged Particle Environment Definition for NGST: L2 Plasma Environment Statistics
NASA Technical Reports Server (NTRS)
Minow, Joseph I.; Blackwell, William C.; Neergaard, Linda F.; Evans, Steven W.; Hardage, Donna M.; Owens, Jerry K.
2000-01-01
The plasma environment encountered by the Next Generation Space Telescope satellite in a halo orbit about L2 can include the Earth's magnetotail and magnetosheath in addition to the solar wind depending on the orbital radius chosen for the mission. Analysis of plasma environment impacts on the satellite requires knowledge of the average and extreme plasma characteristics to assess the magnitude of spacecraft charging and materials degradation expected for the mission lifetime. This report describes the analysis of plasma data from instruments onboard the IMP 8 and Geotail spacecraft used to produce the plasma database for the LRAD engineering-level phenomenology code developed to provide the NGST L2 environment definition.
Topological and differential geometrical gauge field theory
NASA Astrophysics Data System (ADS)
Saaty, Joseph
Recent Quantum Field Theory books have defined the topological charge (Q) in terms of the winding number (N). Contrary to this definition, my proof defines Q in terms of the quantum number (n). Defining Q in terms of n, instead of in terms of N, enables me to determine a precise value for Q. The solutions of all kinds of homotopy classification are referred to as instanton solutions, hence the terms homotopy classification and instanton solution will be used interchangeably. My proof replaces the use of these techniques with the use of the Dirac quantization condition, the covariant Dirac's equation, and the covariant Maxwell's equation. Unlike the earlier approaches, my proof accounts for the concept of the spin quantum number and the concept of time. Using the three methods noted above, my proof yields results not obtained by earlier methods. I have dealt similarly with the Pontryagin Index. I have used the Covariant Electrodynamics, in place of homotopy classification techniques, to create for the Pontryagin Index a proof that is alternative to the one cited in recent literature. The homotopy classification techniques gives an expression that excludes the fact that particles have spin quantum number. Therefore, the homotopy classification techniques does not really describe what the topological charge is in reality. I did derive an expression which does include the spin quantum numbers for particles and this has not been done before. Therefore, this will give a better idea for theoretical physicists about the nature of the topological charge. Contribution to knowledge includes creativity. I created an alternative method to the instanton solution for deriving an expression for the topological charge and this method led to new discoveries as a contribution to knowledge in which I found that topological charge for fermions cannot be quantized (to be quantized means to take discrete values only in integer steps), whereas the instanton solution cannot distinguish between bosons (quantized) and fermions (not quantized). Thus I produced results that were previously unobtainable. Furthermore, since topological charge takes place in Flat Spacetime, I investigated the quantization of the Curved Spacetime version of topological charge (Differential Geometrical Charge) by developing the differential geometrical Gauge Field Theory. It should be noted that the homotopy classification method is not at all applicable to Curved Spacetime. I also modified the Dirac equation in Curved Spacetime by using Einstein's field equation in order to account for the presence of matter. As a result, my method has allowed me to address four cases of topological charge (both spinless and spin one- half, in both Flat and in Curved Spacetime) whereas earlier methods had been blind to all but one of these cases (spinless in Flat Spacetime). (Abstract shortened by UMI.)
Topological Solitons in Physics.
ERIC Educational Resources Information Center
Parsa, Zohreh
1979-01-01
A broad definition of solitons and a discussion of their role in physics is given. Vortices and magnetic monopoles which are examples of topological solitons in two and three spatial dimensions are described in some detail. (BB)
Rojas-Sánchez, J-C; Oyarzún, S; Fu, Y; Marty, A; Vergnaud, C; Gambarelli, S; Vila, L; Jamet, M; Ohtsubo, Y; Taleb-Ibrahimi, A; Le Fèvre, P; Bertran, F; Reyren, N; George, J-M; Fert, A
2016-03-01
We present results on spin to charge current conversion in experiments of resonant spin pumping into the Dirac cone with helical spin polarization of the elemental topological insulator (TI) α-Sn. By angle-resolved photoelectron spectroscopy (ARPES), we first check that the Dirac cone (DC) at the α-Sn (0 0 1) surface subsists after covering Sn with Ag. Then we show that resonant spin pumping at room temperature from Fe through Ag into α-Sn layers induces a lateral charge current that can be ascribed to the inverse Edelstein effect by the DC states. Our observation of an inverse Edelstein effect length much longer than those generally found for Rashba interfaces demonstrates the potential of TIs for the conversion between spin and charge in spintronic devices. By comparing our results with data on the relaxation time of TI free surface states from time-resolved ARPES, we can anticipate the ultimate potential of the TI for spin to charge conversion and the conditions to reach it. PMID:26991190
Espinosa, Enrique; Alkorta, Ibon; Mata, Ignasi; Molins, Elies
2005-07-28
Within the framework of the molecular orbital (MO) theory, the addition of one electron to the 4sigma antibonding orbital of the neutral (F...H) system or the removal of one electron from its pi nonbonding orbitals, leading to (F...H)- and to (F...H)+, has permitted the investigation of these charge perturbations on the bond properties of the hydrogen fluoride molecule by using the topological analysis of rho(r). For (F...H), (F...H)-, and (F...H)+, the topological and energetic properties calculated at the F...H bond critical point (BCP) have been related to the 3sigma bonding molecular orbital (BMO) distribution, as this orbital is the main contributor to rho(r) at the interatomic surface. The analysis has been carried out at several F...H internuclear distances, ranging from 0.8 to 3.0 A. As far as the BMO distribution results from its interaction with the average Coulomb and exchange potential generated by the charge filling the other MOs, and in particular by the pi and 4sigma electrons, the comparison between the BCP properties calculated for the charged systems and those corresponding to the neutral one permits the interpretation of the differences in terms of the charge perturbation on BMO. Along with the BCP properties of (F...H), (F...H)-, and (F...H)+, the interaction energy magnitudes of these systems have been also calculated within the same range of internuclear distances, indicating that the applied perturbations do not break the F-H bond but soften it, giving rise to the stable species (F-H)- and (F-H)+. Comparing the three systems at their equilibrium geometries, the most stable configuration, which corresponds to the unperturbed (F...H) system, shows the highest quantity and the most locally concentrated charge density distribution, along with the largest total electron energy density magnitude, at the interatomic surface as a consequence of the BMO contraction toward the fluorine nucleus in (F...H)+ and of the BMO expansion toward both nuclei in (F...H)-. On the other hand, if the comparison is carried out at the equilibrium distance of (F...H) (d(eq)0), this one exhibits both the smallest total energy density magnitude and the largest quantity of bonding charge at the interatomic surface. Hence, being the signature of the most stable configuration, the characteristic magnitudes of the neutral system rho(d(eq)0), inverted triangle2 rho(d(eq)0), and H(d(eq)0) appear as boundary conditions at the interatomic surface of its unperturbed and relaxed electron distribution. PMID:16833999
Spanning set of silica cluster isomer topologies from QTAIM.
Jenkins, Samantha; Rong, Chunying; Kirk, Steven R; Yin, Dulin; Liu, Shubin
2011-11-17
Structural and chemical properties of the building block of silica nanowires, (SiO(2))(6), are investigated with the theory of atoms and molecules (QTAIM). Twenty-five conformers have been analyzed, ten of which have not been reported before. We extend the silica (SiO(2))(6) topology phase space using QTAIM; the Poincaré-Hopf topological sum rules are applied and used to identify the spanning set of topologies, and this includes finding eight new distinct topologies that satisfy the Poincaré-Hopf relation. A simple phase diagram of the solutions of the Poincaré-Hopf relation is created with the aid of a new classification scheme to determine the boundary between topological stability and instability. Sum rules are then found to be applicable to any set of isomers. We determine that O-O bonding interactions exist for the silica (SiO(2))(6) conformers in regions where the energy surface is flattest. In addition, we identify unstable local minima in the topology of the charge density in order to further compare conformer instabilities. We quantify the dimensionality of a molecule using the Poincaré-Hopf relation instead of Euclidean geometry. This quantum topological definition of geometry shows that the four most energetically stable (SiO(2))(6) conformers are quantified as two-dimensional within the new quantum topology. PMID:21557588
NASA Astrophysics Data System (ADS)
Beck, Horst P.
2016-02-01
Referring to the experimental results of high pressure experiments of Léger et al. (1998) we have calculated the energies of all phases observed for CaCl2 within the DFT formalism using the VASP package, and we have retrieved enthalpies and transition pressures. All phases can be considerably compressed or dilated without much change in energy. This energetic "softness" could even be quantified. We classify the high temperature TiO2-type structure and the PbCl2-type one at highest pressures as the energetically "softest" ones and the SrI2-type one as the "hardest". We furthermore discuss the energy density (E/V) of the different phases and redefine it as a fictive cohesive pressure within these structures. Pursuing our earlier approaches we have analysed the charges of the atoms in the different CaCl2 phases and their change on compression or dilation. On comparing the gradients of the charge curves we define a sort of "charge hardness" which will generally depend on the type of cation-anion pair but also on their topological connection in the respective structures. We speculate that exhausting the "charge softness or hardness" of individual ions in such arrangements may initiate the structural reorganization at the transition pressures.
Duarte, Darío J R; Sosa, Gladis L; Peruchena, Nélida M
2013-05-01
In this work we investigate the nature of the Cl···N interactions in complexes formed between substituted ammonium [NHn(X3-n) (with n = 0, 1, 2, 3 and X = -CH3, -F] as Lewis bases and F-Cl molecule as Lewis acid. They have been chosen as a study case due to the wide range of variation of their binding energies, BEs. Møller-Plesset [MP2/6-311++G(2d,2p)] calculations show that the BEs for this set of complexes lie in the range from 1.27 kcal/mol (in F-Cl···NF3) to 27.62 kcal/mol [in F-Cl···N(CH3)3]. The intermolecular distribution of the electronic charge density and their L(r) = -¼∇(2)ρ(r) function have been investigated within the framework of the atoms in molecules (AIM) theory. The intermolecular interaction energy decomposition has also been analyzed using the reduced variational space (RVS) method. The topological analysis of the L(r) function reveals that the local topological properties measured at the (3,+1) critical point [in L(r) topology] are good descriptors of the strength of the halogen bonding interactions. The results obtained from energy decomposition analysis indicate that electrostatic interactions play a key role in these halogen bonding interactions. These results allow us to establish that, when the halogen atom is bonded to a group with high electron-withdrawing capacity, the electrostatic interaction between the electron cloud of the Lewis base and the halogen atom unprotected nucleus of the Lewis acid produces the formation and determines the geometry of the halogen bonded complexes. In addition, a good linear relationship has been established between: the natural logarithm of the BEs and the electrostatic interaction energy between electron charge distribution of N atom and nucleus of Cl atom, denoted as V e-n(N,Cl) within the AIM theory. PMID:23076553
Ando, Yuichiro; Hamasaki, Takahiro; Kurokawa, Takayuki; Ichiba, Kouki; Yang, Fan; Novak, Mario; Sasaki, Satoshi; Segawa, Kouji; Ando, Yoichi; Shiraishi, Masashi
2014-11-12
We detected the spin polarization due to charge flow in the spin nondegenerate surface state of a three-dimensional topological insulator by means of an all-electrical method. The charge current in the bulk-insulating topological insulator Bi1.5Sb0.5Te1.7Se1.3 (BSTS) was injected/extracted through a ferromagnetic electrode made of Ni80Fe20, and an unusual current-direction-dependent magnetoresistance gave evidence for the appearance of spin polarization, which leads to a spin-dependent resistance at the BSTS/Ni80Fe20 interface. In contrast, our control experiment on Bi2Se3 gave null result. These observations demonstrate the importance of the Fermi-level control for the electrical detection of the spin polarization in topological insulators. PMID:25330016
NASA Astrophysics Data System (ADS)
Tanda, Satoshi; Matsuyama, Toyoki; Oda, Migaku; Asano, Yasuhiro; Yakubo, Kousuke
2006-08-01
I. Topology as universal concept. Optical vorticulture / M. V. Berry. On universality of mathematical structure in nature: topology / T. Matsuyama. Topology in physics / R. Jackiw. Isoholonomic problem and holonomic quantum computation / S. Tanimura -- II. Topological crystals. Topological crystals of NbSe[symbol] / S. Tanda ... [et al.]. Superconducting states on a Möbius strip / M. Hayashi ... [et al.]. Structure analyses of topological crystals using synchrotron radiation / Y. Nogami ... [et al.]. Transport measurement for topological charge density waves / T. Matsuura ... [et al.]. Theoretical study on Little-Parks oscillation in nanoscale superconducting ring / T. Suzuki, M. Hayashi and H. Ebisawa. Frustrated CDW states in topological crystals / K. Kuboki ... [et al.]. Law of growth in topological crystal / M. Tsubota ... [et al.]. Synthesis and electric properties of NbS[symbol]: possibility of room temperature charge density wave devices / H. Nobukane ... [et al.]. How does a single crystal become a Möbius strip? / T. Matsuura ... [et al.]. Development of X-ray analysis method for topological crystals / K. Yamamoto ... [et al.] -- III. Topological materials. Femtosecond-timescale structure dynamics in complex materials: the case of (NbSe[symbol])[symbol]I / D. Dvorsek and D. Mihailovic. Ultrafast dynamics of charge-density-wave in topological crystals / K. Shimatake ... [et al.]. Topology in morphologies of a folded single-chain polymer / Y. Takenaka, D. Baigl and K. Yoshikawa. One to two-dimensional conversion in topological crystals / T. Toshima, K. Inagaki and S. Tanda. Topological change of Fermi surface in Bismuth under high pressure / M. Kasami ... [et al.]. Topological change of 4, 4'-bis[9-dicarbazolyl]-2, 2'-biphenyl (CBP) by international rearrangement / K. S. Son ... [et al.]. Spin dynamics in Heisenberg triangular system VI5 cluster studied by [symbol]H-NMR / Y. Furukawa ... [et al.]. STM/STS on NbSe[symbol] nanotubes / K. Ichimura ...[et al.]. Nanofibers of hydrogen storage alloy / I. Saita ... [et al.]. Synthesis of stable icosahedral quasicrystals in Zn-Sc based alloys and their magnetic properties / S. Kashimoto and T. Ishimasa. One-armed spiral wave excited by eam pressure in accretion disks in Be/X-Ray binaries / K. Hayasaki and A. T. Okazaki -- IV. Topological defects and excitations. Topological excitations in the ground state of charge density wave systems / P. Monceau. Soliton transport in nanoscale charge-density-wave systems / K. Inagaki, T. Toshima and S. Tanda. Topological defects in triplet superconductors UPt3, Sr[symbol]RuO[symbol], etc. / K. Maki ... [et al.]. Microscopic structure of vortices in type II superconductors / K. Machida ... [et al.]. Microscopic neutron investigation of the Abrikosov state of high-temperature superconductors / J. Mesot. Energy dissipation at nano-scale topological defects of high-Tc superconductors: microwave study / A. Maeda. Pressure induced topological phase transition in the heavy Fermion compound CeAl[symbol] / H. Miyagawa ... [et al.]. Explanation for the unusual orientation of LSCO square vortex lattice in terms of nodal superconductivity / M. Oda. Local electronic states in Bi[symbol]Sr[symbol]CaCu[symbol]O[symbol] / A. Hashimoto ... [et al.] -- V. Topology in quantum phenomena. Topological vortex formation in a Bose-Einstein condensate of alkali-metal atoms / M. Nakahara. Quantum phase transition of [symbol]He confined in nano-porous media / K. Shirahama, K. Yamamoto and Y. Shibayama. A new mean-field theory for Bose-Einstein condensates / T. Kita. Spin current in topological cristals / Y. Asano. Antiferromagnetic defects in non-magnetic hidden order of the heavy-electron system URu[symbol]Si[symbol] / H. Amitsuka, K. Tenya and M. Yokoyama. Magnetic-field dependences of thermodynamic quantities in the vortex state of Type-II superconductors / K. Watanabe, T. Kita and M. Arai. Three-magnon-mediated nuclear spin relaxation in quantum ferrimagnets of topological origin / H. Hori and S, Yamamoto. Topological aspects of wave function statistics at the Anderson transition / H. Obuse and K. Yakubo. Metal-insulator transition in 1D correlated disorder / H. Shima and T. Nakayama. Superconductivity in URu[symbol]Si[symbol] under high pressure / K. Tenya ...[et al.] -- VI. Topology in optics. Optical vorticulture / M. V. Berry. The topology of vortex lines in light beams / M. J. Padgett ... [et al.]. Optical spin vortex: topological objects in nonlinear polarization optics / H. Kuratsuji and S. Kakigi. Coherent dynamics of collective motion in the NbSe[symbol] charge density wave state / Y. Toda ... [et al.]. Coherent collective excitation of charge-density wave in the commensurate phase of the TaS[symbol] compound / T. Minami ... [et al.]. Real time imaging of surface acoustic waves on topological structures / H. Yamazaki, O. B. Wright and O. Matsuda. Optical vortex generation for characterization of topological materials / Y. Tokizane ... [et al.]. Real time imaging techniques for surface waves on topological structures / T. Tachizaki ... [et al.]. Nonlinear oscillations of the Stokes parameters in birefringent media / R. Seto, H. Kuratsuji and R. Botet. Phonon vortex localized in a quantum wire / N. Nishiguchi -- VII. Topology in quantum device. Quantum device applications of mesoscopic superconductivity / P. J. Hakonen. Theory of current-driven domain wall dynamics / G. Tatara ... [et al.]. Squid of a Ruthenate superconductor / Y. Asano, Y. Tanaka and S. Kashiwaya. Path integral formalism for quantum tunneling of relativistic fluxon / K. Konno, T. Fujii and N. Hatakenaka. Experimental study of two and three-dimensional superconducting networks / S. Tsuchiya ... [et al.].
NASA Astrophysics Data System (ADS)
Barnes, G.; Leka, K. D.; Longcope, D. W.
2003-05-01
The complexity of the coronal magnetic field extrapolated from a Magnetic Charge Topology (MCT) model, is examined for pre-event signatures unique to solar energetic phenomena. Although extensive use has been made of quantities measured at the photosphere, it is important to consider the magnetic field in the corona, where (for example) the hard X-ray signatures of energy release in solar flares are observed. By quantifying the inferred coronal magnetic topology we are no longer limited to considering solely the magnetic state of the photosphere. MCT is applied to temporally sampled photospheric magnetic data from the U. Hawai`i Imaging Vector Magnetograph, for 24 flare-event and flare-quiet epochs from seven active regions. We outline the methodology employed for automating the application of MCT to large data sets of complex active regions: partitioning the observed Bz at the photosphere, assigning a charge to each partition, and using this charge distribution to extrapolate the field in the corona. From the resulting field we compute the connectivity matrix ψ ij, the location of null points and the intersection of separatrix surfaces, i.e. separator field lines. Parameters are constructed to describe, for example, the magnetic connectivities, the magnetic flux in those connections, and the number of separators. Examining particular events results in no obvious trends in the magnitude and temporal evolution of the parameters just prior to flare events. Thus, we employ the same quantitative statistical approach outlined in Leka and Barnes [this session], i.e. applying discriminant analysis and Hotelling's T2-test, and ranking all four-variable discriminant functions as a proxy for a single all-variable discriminant function. We present those parameters which consistently appear in the best combinations, indicating that they may play an important role in defining a pre-event coronal state. This work was performed under Air Force Office of Scientific Research contracts F49620-00-C-0004, F49620-03-C-0019 and F49620-02-C-0191.
Topological susceptibility from slabs
NASA Astrophysics Data System (ADS)
Bietenholz, Wolfgang; de Forcrand, Philippe; Gerber, Urs
2015-12-01
In quantum field theories with topological sectors, a non-perturbative quantity of interest is the topological susceptibility χ t. In principle it seems straightforward to measure χ t by means of Monte Carlo simulations. However, for local update algorithms and fine lattice spacings, this tends to be difficult, since the Monte Carlo history rarely changes the topological sector. Here we test a method to measure χ t even if data from only one sector are available. It is based on the topological charges in sub-volumes, which we denote as slabs. Assuming a Gaussian distribution of these charges, this method enables the evaluation of χ t, as we demonstrate with numerical results for non-linear σ-models.
ERIC Educational Resources Information Center
Lynch, Mark
2012-01-01
We continue our study of topological X-rays begun in Lynch ["Topological X-rays and MRI's," iJMEST 33(3) (2002), pp. 389-392]. We modify our definition of a topological magnetic resonance imaging and give an affirmative answer to the question posed there: Can we identify a closed set in a box by defining X-rays to probe the interior and without
ERIC Educational Resources Information Center
Lynch, Mark
2012-01-01
We continue our study of topological X-rays begun in Lynch ["Topological X-rays and MRI's," iJMEST 33(3) (2002), pp. 389-392]. We modify our definition of a topological magnetic resonance imaging and give an affirmative answer to the question posed there: Can we identify a closed set in a box by defining X-rays to probe the interior and without…
Thermodynamic and topological phase diagrams of correlated topological insulators
NASA Astrophysics Data System (ADS)
Zdulski, Damian; Byczuk, Krzysztof
2015-09-01
A definition of topological phases of density matrices is presented. The topological invariants in case of both noninteracting and interacting systems are extended to nonzero temperatures. The influence of electron interactions on topological insulators at finite temperatures is investigated. A correlated topological insulator is described by the Kane-Mele model, which is extended by the interaction term of the Falicov-Kimball type. Within the Hartree-Fock and the Hubbard I approximations, thermodynamic and topological phase diagrams are determined where the long-range order is included. The results show that correlation effects lead to a strong suppression of the existence of the nontrivial topological phase. In the homogeneous phase, we find a purely correlation driven phase transition into the topologically trivial Mott insulator.
Pabit, Suzette A.; Qiu, Xiangyun; Lamb, Jessica S.; Li, Li; Meisburger, Steve P.; Pollack, Lois
2009-01-01
The recent discovery of the RNA interference mechanism emphasizes the biological importance of short, isolated, double-stranded (ds) RNA helices and calls for a complete understanding of the biophysical properties of dsRNA. However, most previous studies of the electrostatics of nucleic acid duplexes have focused on DNA. Here, we present a comparative investigation of electrostatic effects in RNA and DNA. Using resonant (anomalous) and non-resonant small-angle X-ray scattering, we characterized the charge screening efficiency and counterion distribution around short (25 bp) dsDNA and RNA molecules of comparable sequence. Consistent with theoretical predictions, we find counterion mediated screening to be more efficient for dsRNA than dsDNA. Furthermore, the topology of the RNA A-form helix alters the spatial distribution of counterions relative to B-form DNA. The experimental results reported here agree well with ion-size-corrected non-linear PoissonBoltzmann calculations. We propose that differences in electrostatic properties aid in selective recognition of different types of short nucleic acid helices by target binding partners. PMID:19395592
Topological superconductivity, topological confinement, and the vortex quantum Hall effect
Diamantini, M. Cristina; Trugenberger, Carlo A.
2011-09-01
Topological matter is characterized by the presence of a topological BF term in its long-distance effective action. Topological defects due to the compactness of the U(1) gauge fields induce quantum phase transitions between topological insulators, topological superconductors, and topological confinement. In conventional superconductivity, because of spontaneous symmetry breaking, the photon acquires a mass due to the Anderson-Higgs mechanism. In this paper we derive the corresponding effective actions for the electromagnetic field in topological superconductors and topological confinement phases. In topological superconductors magnetic flux is confined and the photon acquires a topological mass through the BF mechanism: no symmetry breaking is involved, the ground state has topological order, and the transition is induced by quantum fluctuations. In topological confinement, instead, electric charge is linearly confined and the photon becomes a massive antisymmetric tensor via the Stueckelberg mechanism. Oblique confinement phases arise when the string condensate carries both magnetic and electric flux (dyonic strings). Such phases are characterized by a vortex quantum Hall effect potentially relevant for the dissipationless transport of information stored on vortices.
QCD Vacuum Topology and Glueballs
Forkel, Hilmar
2004-12-02
We outline a comprehensive study of spin-0 glueball properties which, in particular, keeps track of the topological gluon structure. Specifically, we implement (semi-hard) topological instanton physics as well as topological charge screening in the QCD vacuum into the operator product expansion (OPE) of the glueball correlators. A realistic instanton size distribution and the (gauge-invariant) renormalization of the instanton contributions are also implemented. Predictions for 0++ and 0-+ glueball properties are presented.
NASA Astrophysics Data System (ADS)
Zelenyuk, E. G.; Protasov, I. V.
1991-04-01
A filter phi on an abelian group G is called a T-filter if there exists a Hausdorff group topology under which phi converges to zero. G{phi} will denote the group G with the largest topology among those making phi converge to zero. This method of defining a group topology is completely equivalent to the definition of an abstract group by defining relations. We shall obtain characterizations of T-filters and of T-sequences; among these, we shall pay particular attention to T-sequences on the integers. The method of T-sequences will be used to construct a series of counterexamples for several open problems in topological algebra. For instance there exists, on every infinite abelian group, a topology distinguishing between sequentiality and the Fréchet-Urysohn property (this solves a problem posed by V.I. Malykhin) we also find a topology on the group of integers admitting no nontrivial continuous character, thus solving a problem of Nienhuys. We show also that on every infinite abelian group there exists a free ultrafilter which is not a T-ultrafilter.
NASA Astrophysics Data System (ADS)
Schleich, K.; Witt, D. M.
Classically, all topologies are allowed as solutions to the Einstein equations. However, one does not observe any topological structures on medium range distance scales, that is scales that are smaller than the size of the observed universe but larger than the microscopic scales for which quantum gravity becomes important. Recently, Friedman, Schleich and Witt (1993) have proven that there is topological censorship on these medium range distance scales: the Einstein equations, locally positive energy, and local predictability of physics imply that any medium distance scale topological structures cannot be seen. More precisely we show that the topology of physically reasonable isolated systems is shrouded from distant observers, or in other words there is a topological censorship principle.
NASA Astrophysics Data System (ADS)
Mahfouzi, Farzad
Current and future technological needs increasingly motivate the intensive scientific research of the properties of materials at the nano-scale. One of the most important domains in this respect at present concerns nano-electronics and its diverse applications. The great interest in this domain arises from the potential reduction of the size of the circuit components, maintaining their quality and functionality, and aiming at greater efficiency, economy, and storage characteristics for the corresponding physical devices. The aim of this thesis is to present a contribution to the analysis of the electronic charge and spin transport phenomena that occur at the quantum level in nano-structures. This thesis spans the areas of quantum transport theory through time-dependent systems, electron-boson interacting systems and systems of interest to spintronics. A common thread in the thesis is to develop the theoretical foundations and computational algorithms to numerically simulate such systems. In order to optimize the numerical calculations I resort to different techniques (such as graph theory in finding inverse of a sparse matrix, adaptive grids for integrations and programming languages (e.g., MATLAB and C++) and distributed computing tools (MPI, CUDA). Outline of the Thesis: After giving an introduction to the topics covered in this thesis in Chapter 1, I present the theoretical foundations to the field of non-equilibrium quantum statistics in Chapter 2. The applications of this formalism and the results are covered in the subsequent chapters as follows: Spin and charge quantum pumping in time-dependent systems: Covered in Chapters 3, 4 and 5, this topics was initially motivated by experiments on measuring voltage signal from a magnetic tunnel junction (MTJ) exposed to a microwave radiation in ferromagnetic resonance (FMR) condition. In Chapter 3 we found a possible explanation for the finite voltage signal measured from a tunnel junction consisting of only a single ferromagnet (FM). I show that this could be due to the existence of Rashba spin-orbit coupling (SOC) at the interface of the FM and insulator. Assuming that the measured signals are quantum mechanical effect where a solution to the time dependent Schrodinger equation is required, I use Keldysh Green function formalism to introduce a "multi-photon" approach which takes into account the effects of time-dependent term exactly up to scatterings from a finite number of photons. We then proceed to find the corresponding Green function numerically using a recursive method which allows us to increase the size of the system significantly. We also implement other approximations such as adiabatic and rotating frame approaches and compared them with our approach. In Chapter 4, I investigate the spin and charge pumping from a precessing magnetization attached to the edge of a 2-dimensional topological insulator (2DTI). We show that, in this system a huge spin current (or voltage signal if the FM covers only one edge) can be pumped for very small cone angles of the precessing FM (proportional to the intensity of the applied microwave). In Chapter 5 I present the third project in this field of research, where, I investigated the pumping from FM attached to a 3-dimensional TI. Spin-transfer torque: Presented in Chapter 6, in this work I investigate the torque induced by a flow of spin-polarized current into a FM and check the condition in which it can cause the magnetization to flip. Motivated by recent experimental developments in the field, here I consider systems with strong SOC such as TIs within a magnetic tunnel junction (MTJ) heterostructure. In the theoretical part I show the correct way (as opposed to the conventional approach used in some theoretical works which suffers from violation of the gauge invariance) to calculate linear-response torque to the external applied voltage and for the numerical calculation I adopted a parallelized adaptive integration algorithm in order to take care of very sharp changes that appear in momentum and energy dependence of the spin-transfer torques. Transport through many-body interacting system: As demonstrated in Chapter 7, in this research I use Keldysh Green function formalism resummation of the corresponding Feynman diagrams, including the self-consistent second Born approximation with and without bubble diagrams ( GW-like), to find the effect of coupling on I-V characteristics and STT in MTJs. Particularly, I investigated if the electron-magnon coupling can explain the zero-bias anomaly observed experimentally in MTJs which is considered to be a signature of inelastic tunneling spectrum.
NASA Astrophysics Data System (ADS)
Hsieh, Chang-Tse; Cho, Gil Young; Ryu, Shinsei
2016-02-01
Quantum anomalies, breakdown of classical symmetries by quantum effects, provide a sharp definition of symmetry protected topological phases. In particular, they can diagnose interaction effects on the noninteracting classification of fermionic symmetry protected topological phases. In this paper, we identify quantum anomalies in two kinds of (3+1)d fermionic symmetry protected topological phases: (i) topological insulators protected by CP (charge conjugation × reflection) and electromagnetic U (1 ) symmetries, and (ii) topological superconductors protected by reflection symmetry. For the first example, which is related to, by CPT-theorem, time-reversal symmetric topological insulators, we show that the CP-projected partition function of the surface theory is not invariant under large U (1 ) gauge transformations, but picks up an anomalous sign, signaling a Z2 topological classification. Similarly, for the second example, which is related to, by CPT-theorem, class DIII topological superconductors, we discuss the invariance/noninvariance of the partition function of the surface theory, defined on the three-torus and its descendants generated by the orientifold projection, under large diffeomorphisms (coordinate transformations). The connection to the collapse of the noninteracting classification by an integer (Z ) to Z16, in the presence of interactions, is discussed.
Topology Explains Why Automobile Sunshades Fold Oddly
ERIC Educational Resources Information Center
Feist, Curtis; Naimi, Ramin
2009-01-01
Automobile sunshades always fold into an "odd" number of loops. The explanation why involves elementary topology (braid theory and linking number, both explained in detail here with definitions and examples), and an elementary fact from algebra about symmetric group.
Topological structures in the Husimi flow
NASA Astrophysics Data System (ADS)
Veronez, M.; de Aguiar, M. A. M.
2016-02-01
We study the topological properties of the quantum phase space current in the Husimi representation, focusing on the dynamical differences, induced by these properties, between the quantum and the classical flows. We show that the zeros of the Husimi function are stagnation points of the current and have a nonzero topological charge. Due to overall charge conservation, new stagnation points with opposite charge appear in pairs in the Husimi current and they have important roles in dynamical processes. As an example we show the topological effect of the zeros in the transmission rate of a particle through a potential barrier.
NASA Astrophysics Data System (ADS)
Luminet, Jean-Pierre
2015-08-01
Cosmic Topology is the name given to the study of the overall shape of the universe, which involves both global topological features and more local geometrical properties such as curvature. Whether space is finite or infinite, simply-connected or multi-connected like a torus, smaller or greater than the portion of the universe that we can directly observe, are questions that refer to topology rather than curvature. A striking feature of some relativistic, multi-connected "small" universe models is to create multiples images of faraway cosmic sources. While the most recent cosmological data fit the simplest model of a zero-curvature, infinite space model, they are also consistent with compact topologies of the three homogeneous and isotropic geometries of constant curvature, such as, for instance, the spherical Poincaré Dodecahedral Space, the flat hypertorus or the hyperbolic Picard horn. After a "dark age" period, the field of Cosmic Topology has recently become one of the major concerns in cosmology, not only for theorists but also for observational astronomers, leaving open a number of unsolved issues.
Topological Thouless pumping of ultracold fermions
NASA Astrophysics Data System (ADS)
Nakajima, Shuta; Tomita, Takafumi; Taie, Shintaro; Ichinose, Tomohiro; Ozawa, Hideki; Wang, Lei; Troyer, Matthias; Takahashi, Yoshiro
2016-04-01
An electron gas in a one-dimensional periodic potential can be transported even in the absence of a voltage bias if the potential is slowly and periodically modulated in time. Remarkably, the transferred charge per cycle is sensitive only to the topology of the path in parameter space. Although this so-called Thouless charge pump was first proposed more than thirty years ago, it has not yet been realized. Here we report the demonstration of topological Thouless pumping using ultracold fermionic atoms in a dynamically controlled optical superlattice. We observe a shift of the atomic cloud as a result of pumping, and extract the topological invariance of the pumping process from this shift. We demonstrate the topological nature of the Thouless pump by varying the topology of the pumping path and verify that the topological pump indeed works in the quantum regime by varying the speed and temperature.
The nucleon as a topological chiral soliton
Rho, M.
1984-02-20
Through topology, baryon charge ''leaks'' from a confinement region into a meson-cloud region. This suggests that there is a sort of topological equivalence principle which renders the Skyrmion description with a zero bag radius physically equivalent to the chiral bag description with a non-zero bag radius. The issue as to whether future nuclear physics experiments will reveal a ''smoking-gun'' evidence for a quark presence in nuclei is discussed in light of this recently discovered topological structure.
Topological insulators: A romance with many dimensions
NASA Astrophysics Data System (ADS)
Manoharan, Hari C.
2010-07-01
Electric charges on the boundaries of certain insulators are programmed by topology to keep moving forward when they encounter an obstacle, rather than scattering backwards and increasing the resistance of the system. This is just one reason why topological insulators are one of the hottest topics in physics right now.
Topological forms of information
Baudot, Pierre; Bennequin, Daniel
2015-01-13
We propose that entropy is a universal co-homological class in a theory associated to a family of observable quantities and a family of probability distributions. Three cases are presented: 1) classical probabilities and random variables; 2) quantum probabilities and observable operators; 3) dynamic probabilities and observation trees. This gives rise to a new kind of topology for information processes. We discuss briefly its application to complex data, in particular to the structures of information flows in biological systems. This short note summarizes results obtained during the last years by the authors. The proofs are not included, but the definitions and theorems are stated with precision.
Measurement-only topological quantum computation via anyonic interferometry
Bonderson, Parsa Freedman, Michael Nayak, Chetan
2009-04-15
We describe measurement-only topological quantum computation using both projective and interferometrical measurement of topological charge. We demonstrate how anyonic teleportation can be achieved using 'forced measurement' protocols for both types of measurement. Using this, it is shown how topological charge measurements can be used to generate the braiding transformations used in topological quantum computation, and hence that the physical transportation of computational anyons is unnecessary. We give a detailed discussion of the anyonics for implementation of topological quantum computation (particularly, using the measurement-only approach) in fractional quantum Hall systems.
Novel Z2 Topological Metals and Semimetals
NASA Astrophysics Data System (ADS)
Zhao, Y. X.; Wang, Z. D.
2016-01-01
We report two theoretical discoveries for Z2 topological metals and semimetals. It is shown first that any dimensional Z2 Fermi surface is topologically equivalent to a Fermi point. Then the famous conventional no-go theorem, which was merely proven before for Z Fermi points in a periodic system without any discrete symmetry, is generalized so that the total topological charge is zero for all cases. Most remarkably, we find and prove an unconventional strong no-go theorem: all Z2 Fermi points have the same topological charge νZ 2=1 or 0 for periodic systems. Moreover, we also establish all six topological types of Z2 models for realistic physical dimensions.
Dynamics of topological defects in continuous and discrete systems
NASA Astrophysics Data System (ADS)
Gecse, Zoltan
Topological defects are part of various physical systems, from superfluids and superconductors to gauge theories of elementary particles. Investigations of their rich dynamics are part of current research. Experiments show that topological defects in form of vortices in clean two-dimensional superconductors move along with the supercurrent while in discrete superconducting Josephson-junction arrays they move perpendicular to it. Our numerical solutions of the Gross-Pitaevsky equation on fine and coarse grids, corresponding to the continuous and discrete systems respectively, correctly reproduce the qualitative behavior. This suggests that the discreteness itself is responsible for the phenomenon. In brane-world scenarios, the theta-angle of the QCD vacuum can be interpreted as a constant current of topologically non-trivial instantons through the brane. If the topology of the bulk precludes such a current, it leads to a vanishing theta-angle and thereby to a solution of the Strong CP problem. We present a low-dimensional example exhibiting these properties. A 1+1 dimensional Ising model with spatially dependent coupling plays the role of the gauge field in the bulk. A spontaneous symmetry breaking in the bulk allows transitions between states corresponding to different theta-angles on the pointlike brane, which gives the possibility for the theta-angle to vanish. In a five-dimensional bulk the particle like instantons of QCD are gravitationally unstable and they collapse to a topologically charged black hole. Our numerical simulations of the collapse allow the study of the thermodynamic properties of the time-dependent black hole, in particular, they suggest a classical definition of free energy. The obtained results agree with the standard thermodynamics of static black holes.
Topological Aspects of Information Retrieval.
ERIC Educational Resources Information Center
Egghe, Leo; Rousseau, Ronald
1998-01-01
Discusses topological aspects of theoretical information retrieval, including retrieval topology; similarity topology; pseudo-metric topology; document spaces as topological spaces; Boolean information retrieval as a subsystem of any topological system; and proofs of theorems. (LRW)
NASA Astrophysics Data System (ADS)
Zhao, Y. X.; Wang, Z. D.
2015-08-01
We develop a general response theory of gapless Fermi points with nontrivial topological charges for gauge and nonlinear sigma fields, which asserts that the topological character of the Fermi points is embodied as the terms with discrete coefficients proportional to the corresponding topological charges. Applying the theory to the effective nonlinear sigma models for topological Fermi points with disorders in the framework of replica approach, we derive rigorously the Wess-Zumino terms with the topological charges being their levels in the two complex symmetry classes of A and AIII. Intriguingly, two nontrivial examples of quadratic Fermi points with the topological charge 2 are respectively illustrated for the classes A and AIII. We also address a qualitative connection of topological charges of Fermi points in the real symmetry classes to the topological terms in the nonlinear sigma models, based on the one-to-one classification correspondence.
NASA Astrophysics Data System (ADS)
Afriat, Alexander
2013-03-01
The Aharonov-Bohm effect is often called "topological." But it seems no more topological than magnetostatics, electrostatics or Newton-Poisson gravity (or just about any radiation, propagation from a source). I distinguish between two senses of "topological."
NASA Astrophysics Data System (ADS)
Teper, M.
2000-03-01
I review recent (and some not so recent) results on the topological susceptibility (with and without fermions), the eta-prime mass, topology and chiral symmetry breaking, vacuum topological structure, and the possible role of instantons in confinement.
Topological BF field theory description of topological insulators
Cho, Gil Young; Moore, Joel E.
2011-06-15
Research Highlights: > We show that a BF theory is the effective theory of 2D and 3D topological insulators. > The non-gauge-invariance of the bulk theory yields surface terms for a bosonized Dirac fermion. > The 'axion' term in electromagnetism is correctly obtained from gapped surfaces. > Generalizations to possible fractional phases are discussed in closing. - Abstract: Topological phases of matter are described universally by topological field theories in the same way that symmetry-breaking phases of matter are described by Landau-Ginzburg field theories. We propose that topological insulators in two and three dimensions are described by a version of abelian BF theory. For the two-dimensional topological insulator or quantum spin Hall state, this description is essentially equivalent to a pair of Chern-Simons theories, consistent with the realization of this phase as paired integer quantum Hall effect states. The BF description can be motivated from the local excitations produced when a {pi} flux is threaded through this state. For the three-dimensional topological insulator, the BF description is less obvious but quite versatile: it contains a gapless surface Dirac fermion when time-reversal-symmetry is preserved and yields 'axion electrodynamics', i.e., an electromagnetic E . B term, when time-reversal symmetry is broken and the surfaces are gapped. Just as changing the coefficients and charges of 2D Chern-Simons theory allows one to obtain fractional quantum Hall states starting from integer states, BF theory could also describe (at a macroscopic level) fractional 3D topological insulators with fractional statistics of point-like and line-like objects.
Induced topological pressure for topological dynamical systems
Xing, Zhitao; Chen, Ercai
2015-02-15
In this paper, inspired by the article [J. Jaerisch et al., Stochastics Dyn. 14, 1350016, pp. 1-30 (2014)], we introduce the induced topological pressure for a topological dynamical system. In particular, we prove a variational principle for the induced topological pressure.
Topological Mott insulator by block spin phenomenology
NASA Astrophysics Data System (ADS)
Kim, Yun Ki; Son, Kwang Chul; Koo, Je Huan
2015-11-01
We investigate the relationship between topological Mott insulators and spin glasses. By first explaining the phase of spin glass on the basis of finite sized block spin concepts, we then introduce the three-dimensional insulating phase of a topological insulator with a finite bulk bandgap as the pairing of block spins comprised of many random spins with respective majority spin directions. However, the two-dimensional edge state of the topological insulator may be thought of as the pairing of triplet spins with a zero bandgap. Topological insulators can be transformed into ordinary insulators below a certain temperature. Electric field-induced transitions between normal and topological insulators are possible as explained by means of composite charges.
Intrinsic topological superfluidity - fluctuations and response
NASA Astrophysics Data System (ADS)
Levin, K.; Wu, Chien-Te; Anderson, Brandon; Boyack, Rufus
Recent interest in topological superconductivity is based primarily on exploiting proximity effects to obtain this important phase. However, in cold gases it is possible to contemplate ``intrinsic'' topological superfluidity produced with a synthetic spin-orbit coupling and Zeeman field. It is important for such future experiments to establish how low in temperature one needs to go to reach the ordered phase. Similarly, it will be helpful to have a probe of the normal (pseudogap) phase to determine if the ultimate superfluid order will be topological or trivial. In this talk, we address these issues by considering fluctuation effects in such a superfluid, and calculate the critical transition temperature and response functions. We see qualitative signatures of topological superfluidity in spin and charge response functions. We also explore the suppression of superfluidity due to fluctuations, and importantly find that the temperature scales necessary to reach topological superfluidity are reasonably accessible
Soft topological objects in topological media
NASA Astrophysics Data System (ADS)
Väyrynen, J. I.; Volovik, G. E.
2011-05-01
Topological invariants in terms of the Green's function in momentum and real space determine properties of smooth textures within topological media. In space dimension d = 1 the topological invariant N 3 in terms of the Green's function [InlineMediaObject not available: see fulltext.](ω, k x , x) determines the fermion number of the kink, while in space dimension d = 3 the topological invariant N 5 in terms of the Green's function [InlineMediaObject not available: see fulltext.](ω, k x , k y , k z , z) determines quantization of Hall conductivity in the soliton plane within the topological insulators.
Da Silva, David; Han, Liqi; Faivre, Robert; Costes, Evelyne
2014-01-01
Background and Aims The impact of a fruit tree's architecture on its performance is still under debate, especially with regard to the definition of varietal ideotypes and the selection of architectural traits in breeding programmes. This study aimed at providing proof that a modelling approach can contribute to this debate, by using in silico exploration of different combinations of traits and their consequences on light interception, here considered as one of the key parameters to optimize fruit tree production. Methods The variability of organ geometrical traits, previously described in a bi-parental population, was used to simulate 1- to 5-year-old apple trees (Malus × domestica). Branching sequences along trunks observed during the first year of growth of the same hybrid trees were used to initiate the simulations, and hidden semi-Markov chains previously parameterized were used in subsequent years. Tree total leaf area (TLA) and silhouette to total area ratio (STAR) values were estimated, and a sensitivity analysis was performed, based on a metamodelling approach and a generalized additive model (GAM), to analyse the relative impact of organ geometry and lateral shoot types on STAR. Key Results A larger increase over years in TLA mean and variance was generated by varying branching along trunks than by varying organ geometry, whereas the inverse was observed for STAR, where mean values stabilized from year 3 to year 5. The internode length and leaf area had the highest impact on STAR, whereas long sylleptic shoots had a more significant effect than proleptic shoots. Although the GAM did not account for interactions, the additive effects of the geometrical factors explained >90% of STAR variation, but much less in the case of branching factors. Conclusions This study demonstrates that the proposed modelling approach could contribute to screening architectural traits and their relative impact on tree performance, here viewed through light interception. Even though trait combinations and antagonism will need further investigation, the approach opens up new perspectives for breeding and genetic selection to be assisted by varietal ideotype definition. PMID:24723446
Topological solitons in a gauged C P (2 ) model
NASA Astrophysics Data System (ADS)
Loginov, A. Yu.
2016-03-01
(2 +1 )-dimensional Abelian gauged C P (2 ) model with a self-interaction potential is considered. It is shown that there are topological solitons in this model. The magnetic flux of these solitons can be either quantized or nonquantized. Properties of the topological soliton with quantized magnetic flux are investigated as well as properties of the topological soliton with nonquantized magnetic flux. A comparative analysis of the properties is performed for the topological solitons of both types. Solutions of the model field equations are obtained numerically for the topological solitons of both types. The dependencies on the model parameters are presented for the energy and magnetic flux of the solitons. The stability of the topological solitons of both types to the decay into solitons with smaller topological charges is studied numerically. Possible generalizations of the investigated topological solitons are discussed.
Topological susceptibility with the improved Asqtad action
C. Bernard et al.
2004-01-06
As a test of the chiral properties of the improved Asqtad (staggered fermion) action, we have been measuring the topological susceptibility as a function of quark masses for 2 + 1 dynamical flavors. We report preliminary results, which show reasonable agreement with leading order chiral perturbation theory for lattice spacing less than 0.1 fm. The total topological charge, however, shows strong persistence over Monte Carlo time.
Topological Z2 Gapless Photonic Crystals
NASA Astrophysics Data System (ADS)
Xie, Biye; Wang, Zidan
Topological properties of electronic materials with gapless band structure such as Topological Semimetals(TSMs) and Topological Metals(TMs) have drew lots of attention to both theoretical and experimental physicists recently. Although theoretical prediction of TSMs and TMs have been done well, experimental study of them is quite difficult to perform due to the fact that it is very difficult to control and design certain electronic materials. However, since the topological properties stem from the geometric feature, we can study them in Photonic Crystals(PhCs) which are much easy to be controlled and designed. Here we study 2-dimension PhCs consisting of gyrotropic materials with hexagonal structure. In the Brillouin corner, the dispersion relation has gapless points which are similar to Dirac Cones in electronic materials. We firstly derive the effective Hamiltonian of this system and show that if certain perturbation is added to this effective Hamiltonian, this system belongs to AII class according to Altland and Zirbauer topological classification and is described by a Z2 topological charge. Finally we also propose a way to detect this Z2 topological charge using momentum space Aharonov-Bohm interferometer which is firstly proposed by L.Duca and T.Li,etc.
Topological insulators and superconductors from string theory
Ryu, Shinsei; Takayanagi, Tadashi
2010-10-15
Topological insulators and superconductors in different spatial dimensions and with different discrete symmetries have been fully classified recently, revealing a periodic structure for the pattern of possible types of topological insulators and superconductors, both in terms of spatial dimensions and in terms of symmetry classes. It was proposed that K theory is behind the periodicity. On the other hand, D-branes, a solitonic object in string theory, are also known to be classified by K theory. In this paper, by inspecting low-energy effective field theories realized by two parallel D-branes, we establish a one-to-one correspondence between the K-theory classification of topological insulators/superconductors and D-brane charges. In addition, the string theory realization of topological insulators and superconductors comes naturally with gauge interactions, and the Wess-Zumino term of the D-branes gives rise to a gauge field theory of topological nature, such as ones with the Chern-Simons term or the {theta} term in various dimensions. This sheds light on topological insulators and superconductors beyond noninteracting systems, and the underlying topological field theory description thereof. In particular, our string theory realization includes the honeycomb lattice Kitaev model in two spatial dimensions, and its higher-dimensional extensions. Increasing the number of D-branes naturally leads to a realization of topological insulators and superconductors in terms of holography (AdS/CFT).
Dual-wavelength laser with topological charge
NASA Astrophysics Data System (ADS)
Yu, Haohai; Xu, Miaomiao; Zhao, Yongguang; Wang, Yicheng; Han, Shuo; Zhang, Huaijin; Wang, Zhengping; Wang, Jiyang
2013-09-01
We demonstrate the simultaneous oscillation of different photons with equal orbital angular momentum in solid-state lasers for the first time to our knowledge. Single tunable Hermite-Gaussian (HG0,n) (0 ≤ n ≤ 7) laser modes with dual wavelength were generated using an isotropic cavity. With a mode-converter, the corresponding Laguerre-Gaussian (LG0,n) laser modes were obtained. The oscillating laser modes have two types of photons at the wavelengths of 1077 and 1081 nm and equal orbital angular momentum of nħ per photon. These results identify the possibility of simultaneous oscillation of different photons with equal and controllable orbital angular momentum. It can be proposed that this laser should have promising applications in many fields based on its compact structure, tunable orbital angular momentum, and simultaneous oscillation of different photons with equal orbital angular momentum.
On small beams with large topological charge
NASA Astrophysics Data System (ADS)
Krenn, Mario; Tischler, Nora; Zeilinger, Anton
2016-03-01
Light beams can carry a discrete, in principle unbounded amount of angular momentum. Examples of such beams, the Laguerre-Gauss modes, are frequently expressed as solutions of the paraxial wave equation. The paraxial wave equation is a small-angle approximation of the Helmholtz equation, and is commonly used in beam optics. There, the Laguerre-Gauss modes have well-defined orbital angular momentum (OAM). The paraxial solutions predict that beams with large OAM could be used to resolve arbitrarily small distances—a dubious situation. Here we show how to solve that situation by calculating the properties of beams free from the paraxial approximation. We find the surprising result that indeed one can resolve smaller distances with larger OAM, although with decreased visibility. If the visibility is kept constant (for instance at the Rayleigh criterion, the limit where two points are reasonably distinguishable), larger OAM does not provide an advantage. The drop in visibility is due to a field in the direction of propagation, which is neglected within the paraxial limit. Our findings have implications for imaging techniques and raise questions on the difference between photonic and matter waves, which we briefly discuss in the conclusion.
Deficient topological measures and functionals generated by them
Svistula, Marina G
2013-05-31
This paper looks at the properties of deficient topological measures, which are a generalization of topological measures. Integration of a real function that is continuous on a compact set with respect to a deficient topological measure is also investigated. The notions of r- and l-functionals are introduced and an analogue of the Riesz representation theorem is obtained for them. As corollaries, both well-known and new results for quasi-integrals and topological measures are presented (for example, a new version of the definition of a quasi-integral). Bibliography: 16 titles.
NASA Technical Reports Server (NTRS)
Lieberman, R. N.
1972-01-01
Given a directed graph, a natural topology is defined and relationships between standard topological properties and graph theoretical concepts are studied. In particular, the properties of connectivity and separatedness are investigated. A metric is introduced which is shown to be related to separatedness. The topological notions of continuity and homeomorphism. A class of maps is studied which preserve both graph and topological properties. Applications involving strong maps and contractions are also presented.
Open string amplitudes of closed topological vertex
NASA Astrophysics Data System (ADS)
Takasaki, Kanehisa; Nakatsu, Toshio
2016-01-01
The closed topological vertex is the simplest ‘off-strip’ case of non-compact toric Calabi-Yau threefolds with acyclic web diagrams. By the diagrammatic method of topological vertex, open string amplitudes of topological string theory therein can be obtained by gluing a single topological vertex to an ‘on-strip’ subdiagram of the tree-like web diagram. If non-trivial partitions are assigned to just two parallel external lines of the web diagram, the amplitudes can be calculated with the aid of techniques borrowed from the melting crystal models. These amplitudes are thereby expressed as matrix elements, modified by simple prefactors, of an operator product on the Fock space of 2D charged free fermions. This fermionic expression can be used to derive q-difference equations for generating functions of special subsets of the amplitudes. These q-difference equations may be interpreted as the defining equation of a quantum mirror curve.
Electrically Tunable Magnetism in Magnetic Topological Insulators
NASA Astrophysics Data System (ADS)
Zhang, Shou-Cheng; Wang, Jing; Lian, Biao
2015-03-01
The external controllability of the magnetic properties in topological insulators would be important both for fundamental and practical interests. Here we predict the electric-field control of ferromagnetism in a thin film of insulating magnetic topological insulators. The decrease of band inversion by the application of electric fields results in a reduction of magnetic susceptibility, and hence in the modication of magnetism. Remarkably, the electric field could even induce the magnetic quantum phase transition from ferromagnetism to paramagnetism. We further propose a topological transistor device in which the dissipationless charge transport of chiral edge states is controlled by an electric field. The simultaneous electrical control of magnetic order and chiral edge transport in such a device may lead to electronic and spintronic applications for topological insulators. This work is supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under Contract No. DE-AC02-76SF00515.
A hierarchy of topological tensor network states
NASA Astrophysics Data System (ADS)
Buerschaper, Oliver; Mombelli, Juan Martn; Christandl, Matthias; Aguado, Miguel
2013-01-01
We present a hierarchy of quantum many-body states among which many examples of topological order can be identified by construction. We define these states in terms of a general, basis-independent framework of tensor networks based on the algebraic setting of finite-dimensional Hopf C*-algebras. At the top of the hierarchy we identify ground states of new topological lattice models extending Kitaev's quantum double models [Ann. Phys. 303, 2 (2003), 10.1016/S0003-4916(02)00018-0]. For these states we exhibit the mechanism responsible for their non-zero topological entanglement entropy by constructing an entanglement renormalization flow. Furthermore, we argue that the hierarchy states are related to each other by the condensation of topological charges.
Sufficient symmetry conditions for Topological Quantum Order
Nussinov, Zohar; Ortiz, Gerardo
2009-01-01
We prove sufficient conditions for Topological Quantum Order at zero and finite temperatures. The crux of the proof hinges on the existence of low-dimensional Gauge-Like Symmetries, thus providing a unifying framework based on a symmetry principle. These symmetries may be actual invariances of the system, or may emerge in the low-energy sector. Prominent examples of Topological Quantum Order display Gauge-Like Symmetries. New systems exhibiting such symmetries include Hamiltonians depicting orbital-dependent spin exchange and Jahn–Teller effects in transition metal orbital compounds, short-range frustrated Klein spin models, and p+ip superconducting arrays. We analyze the physical consequences of Gauge-Like Symmetries (including topological terms and charges) and show the insufficiency of the energy spectrum, topological entanglement entropy, maximal string correlators, and fractionalization in establishing Topological Quantum Order. General symmetry considerations illustrate that not withstanding spectral gaps, thermal fluctuations may impose restrictions on suggested quantum computing schemes. Our results allow us to go beyond standard topological field theories and engineer systems with Topological Quantum Order. PMID:19805113
Fractional Topological Insulators in Three Dimensions
Maciejko, Joseph; Zhang Shoucheng; Qi Xiaoliang; Karch, Andreas
2010-12-10
Topological insulators can be generally defined by a topological field theory with an axion angle {theta} of 0 or {pi}. In this work, we introduce the concept of fractional topological insulator defined by a fractional axion angle and show that it can be consistent with time reversal T invariance if ground state degeneracies are present. The fractional axion angle can be measured experimentally by the quantized fractional bulk magnetoelectric polarization P{sub 3}, and a 'halved' fractional quantum Hall effect on the surface with Hall conductance of the form {sigma}{sub H}=(p/q)(e{sup 2}/2h) with p, q odd. In the simplest of these states the electron behaves as a bound state of three fractionally charged 'quarks' coupled to a deconfined non-Abelian SU(3) 'color' gauge field, where the fractional charge of the quarks changes the quantization condition of P{sub 3} and allows fractional values consistent with T invariance.
Topological orders with global gauge anomalies
NASA Astrophysics Data System (ADS)
You, Yi-Zhuang; Xu, Cenke
2015-08-01
By definition, the physics of the d -dimensional (dim) boundary of a (d +1 ) -dim symmetry protected topological (SPT) state cannot be realized as itself on a d -dim lattice. If the symmetry of the system is unitary, then a formal way to determine whether a d -dim theory must be a boundary or not, is to couple this theory to a gauge field (or to "gauge" its symmetry), and check if there is a gauge anomaly. In this paper we discuss the following question: Can the boundary of a SPT state be driven into a fully gapped topological order which preserves all the symmetries? We argue (conjecture) that if the gauge anomaly of the boundary is "perturbative," then the boundary must remain gapless; while if the boundary only has global gauge anomaly but no perturbative anomaly, then it is possible to gap out the boundary by driving it into a topological state, when d ≥2 . We will demonstrate this conjecture with two examples: (1) the 3 d spin-1/2 chiral fermion with the well-known Witten's global anomaly [Phys. Lett. 117, 324 (1982), 10.1016/0370-2693(82)90728-6], which can be realized on the boundary of a 4 d topological superconductor with SU(2) or U (1 ) ⋊Z2 symmetry; and (2) the 4 d boundary of a 5 d topological superconductor with the same symmetry. We show that these boundary systems can be driven into a fully gapped Z2 N topological order with topological degeneracy, but this Z2 N topological order cannot be future driven into a trivial confined phase that preserves all the symmetries due to some special properties of its topological defects. Our study also leads to exotic states of matter in pure 3 d space.
Topological pumping in class-D superconducting wires
NASA Astrophysics Data System (ADS)
Gibertini, Marco; Fazio, Rosario; Polini, Marco; Taddei, Fabio
2013-10-01
We study adiabatic pumping at a normal metal/class-D superconductor hybrid interface when superconductivity is induced through the proximity effect in a spin-orbit coupled nanowire in the presence of a tilted Zeeman field. When the induced order parameter in the nanowire is nonuniform, the phase diagram has isolated trivial regions surrounded by topological ones. We show that in this case the pumped charge is quantized in units of the elementary charge e and has a topological nature.
NASA Astrophysics Data System (ADS)
Huang, Shin-Ming; Tsai, Wei-Feng; Chung, Chung-Hou; Mou, Chung-Yu
2016-02-01
The ground state of the large Hubbard U limit of a honeycomb lattice near half filling is known to be a singlet d +i d -wave superconductor. It is also known that this d +i d superconductor exhibits a chiral p +i p pairing locally at the Dirac cone, characterized by a 2 Z topological invariant. By constructing a dual transformation, we demonstrate that this 2 Z topological superconductor is equivalent to a collection of two topological ferromagnetic insulators. As a result of the duality, the topology of the electronic structures for a d +i d superconductor is controllable via the change of the chemical potential by tuning the gate voltage. In particular, instead of always being a chiral superconductor, we find that the d +i d superconductor undergoes a topological phase transition from a chiral superconductor to a quasihelical superconductor as the gap amplitude or the chemical potential decreases. The quasihelical superconducting phase is found to be characterized by a topological invariant in the pseudospin charge sector with vanishing both the Chern number and the spin Chern number. We further elucidate the topological phase transition by analyzing the relationship between the topological invariant and the rotation symmetry. Due to the angular momentum carried by the gap function and spin-orbit interactions, we show that by placing d +i d superconductors in proximity to ferromagnets, varieties of chiral superconducting phases characterized by higher Chern numbers can be accessed, providing a platform for hosting large numbers of Majorana modes at edges.
Bulk Topological Proximity Effect
NASA Astrophysics Data System (ADS)
Hsieh, Timothy H.; Ishizuka, Hiroaki; Balents, Leon; Hughes, Taylor L.
2016-02-01
Existing proximity effects stem from systems with a local order parameter, such as a local magnetic moment or a local superconducting pairing amplitude. Here, we demonstrate that despite lacking a local order parameter, topological phases also may give rise to a proximity effect of a distinctively inverted nature. We focus on a general construction in which a topological phase is extensively coupled to a second system, and we argue that, in many cases, the inverse topological order will be induced on the second system. To support our arguments, we rigorously establish this "bulk topological proximity effect" for all gapped free-fermion topological phases and representative integrable models of interacting topological phases. We present a terrace construction which illustrates the phenomenological consequences of this proximity effect. Finally, we discuss generalizations beyond our framework, including how intrinsic topological order may also exhibit this effect.
Bulk Topological Proximity Effect.
Hsieh, Timothy H; Ishizuka, Hiroaki; Balents, Leon; Hughes, Taylor L
2016-02-26
Existing proximity effects stem from systems with a local order parameter, such as a local magnetic moment or a local superconducting pairing amplitude. Here, we demonstrate that despite lacking a local order parameter, topological phases also may give rise to a proximity effect of a distinctively inverted nature. We focus on a general construction in which a topological phase is extensively coupled to a second system, and we argue that, in many cases, the inverse topological order will be induced on the second system. To support our arguments, we rigorously establish this "bulk topological proximity effect" for all gapped free-fermion topological phases and representative integrable models of interacting topological phases. We present a terrace construction which illustrates the phenomenological consequences of this proximity effect. Finally, we discuss generalizations beyond our framework, including how intrinsic topological order may also exhibit this effect. PMID:26967436
Kalb, Jeffrey L.; Lee, David S.
2008-01-01
Emerging high-bandwidth, low-latency network technology has made network-based architectures both feasible and potentially desirable for use in satellite payload architectures. The selection of network topology is a critical component when developing these multi-node or multi-point architectures. This study examines network topologies and their effect on overall network performance. Numerous topologies were reviewed against a number of performance, reliability, and cost metrics. This document identifies a handful of good network topologies for satellite applications and the metrics used to justify them as such. Since often multiple topologies will meet the requirements of the satellite payload architecture under development, the choice of network topology is not easy, and in the end the choice of topology is influenced by both the design characteristics and requirements of the overall system and the experience of the developer.
Topological binding and elastic interactions of microspheres and fibres in a nematic liquid crystal.
Nikkhou, M; Škarabot, M; Muševič, I
2015-03-01
We present a detailed analysis of topological binding and elastic interactions between a long, and micrometer-diameter fiber, and a microsphere in a homogeneously aligned nematic liquid crystal. Both objects are surface treated to produce strong perpendicular anchoring of the nematic liquid crystal. We use the opto-thermal micro-quench of the laser tweezers to produce topological defects with prescribed topological charge, such as pairs of a Saturn ring and an anti-ring, hyperbolic and radial hedgehogs on a fiber, as well as zero-charge loops. We study the entanglement and topological charge interaction between the topological defects of the fiber and sphere and we observe a huge variety of different entanglement topologies and defect-mediated elastic bindings. We explain all observed phenomena with simple topological rule: like topological charges repel each other and opposite topological charges attract. These binding mechanisms not only demonstrate the fascinating topology of nematic colloids, but also open a novel route to the assembly of very complex topological networks of fibers, spheres and other objects for applications in liquid crystal photonics. PMID:25813607
Photonic Floquet topological insulators.
Rechtsman, Mikael C; Zeuner, Julia M; Plotnik, Yonatan; Lumer, Yaakov; Podolsky, Daniel; Dreisow, Felix; Nolte, Stefan; Segev, Mordechai; Szameit, Alexander
2013-04-11
Topological insulators are a new phase of matter, with the striking property that conduction of electrons occurs only on their surfaces. In two dimensions, electrons on the surface of a topological insulator are not scattered despite defects and disorder, providing robustness akin to that of superconductors. Topological insulators are predicted to have wide-ranging applications in fault-tolerant quantum computing and spintronics. Substantial effort has been directed towards realizing topological insulators for electromagnetic waves. One-dimensional systems with topological edge states have been demonstrated, but these states are zero-dimensional and therefore exhibit no transport properties. Topological protection of microwaves has been observed using a mechanism similar to the quantum Hall effect, by placing a gyromagnetic photonic crystal in an external magnetic field. But because magnetic effects are very weak at optical frequencies, realizing photonic topological insulators with scatter-free edge states requires a fundamentally different mechanism-one that is free of magnetic fields. A number of proposals for photonic topological transport have been put forward recently. One suggested temporal modulation of a photonic crystal, thus breaking time-reversal symmetry and inducing one-way edge states. This is in the spirit of the proposed Floquet topological insulators, in which temporal variations in solid-state systems induce topological edge states. Here we propose and experimentally demonstrate a photonic topological insulator free of external fields and with scatter-free edge transport-a photonic lattice exhibiting topologically protected transport of visible light on the lattice edges. Our system is composed of an array of evanescently coupled helical waveguides arranged in a graphene-like honeycomb lattice. Paraxial diffraction of light is described by a Schrödinger equation where the propagation coordinate (z) acts as 'time'. Thus the helicity of the waveguides breaks z-reversal symmetry as proposed for Floquet topological insulators. This structure results in one-way edge states that are topologically protected from scattering. PMID:23579677
Photonic Floquet topological insulators
NASA Astrophysics Data System (ADS)
Rechtsman, Mikael C.; Zeuner, Julia M.; Plotnik, Yonatan; Lumer, Yaakov; Podolsky, Daniel; Dreisow, Felix; Nolte, Stefan; Segev, Mordechai; Szameit, Alexander
2013-09-01
Topological insulators are a new phase of matter, with the striking property that conduction of electrons occurs only on the surface. In two dimensions, surface electrons in topological insulators do not scatter despite defects and disorder, providing robustness akin to superconductors. Topological insulators are predicted to have wideranging applications in fault-tolerant quantum computing and spintronics. Recently, large theoretical efforts were directed towards achieving topological insulation for electromagnetic waves. One-dimensional systems with topological edge states have been demonstrated, but these states are zero-dimensional, and therefore exhibit no transport properties. Topological protection of microwaves has been observed using a mechanism similar to the quantum Hall effect, by placing a gyromagnetic photonic crystal in an external magnetic field. However, since magnetic effects are very weak at optical frequencies, realizing photonic topological insulators with scatterfree edge states requires a fundamentally different mechanism - one that is free of magnetic fields. Recently, a number of proposals for photonic topological transport have been put forward. Specifically, one suggested temporally modulating a photonic crystal, thus breaking time-reversal symmetry and inducing one-way edge states. This is in the spirit of the proposed Floquet topological insulators, where temporal variations in solidstate systems induce topological edge states. Here, we propose and experimentally demonstrate the first external field-free photonic topological insulator with scatter-free edge transport: a photonic lattice exhibiting topologically protected transport of visible light on the lattice edges. Our system is composed of an array of evanescently coupled helical waveguides arranged in a graphene-like honeycomb lattice. Paraxial diffraction of light is described by a Schrödinger equation where the propagation coordinate acts as `time'. Thus the waveguides' helicity breaks zreversal symmetry in the sense akin to Floquet Topological Insulators. This structure results in scatter-free, oneway edge states that are topologically protected from scattering.
Topological description of Easter Islander palmar dermatoglyphics.
Goodson, C S; Meier, R J
1986-10-01
A sample of 594 Easter Islander palms was analyzed according to the topological method. Some suggestions for clarification of the topological approach were made, including clearer definition of the palmar triradii and substitution of the term "profile" for "formula." The frequency of Easter Islander profiles was compared against British and Australian Aborigine samples (Loesch, 1974; 1983a,b) and found to be significantly different for two of the ten most common combinations. The individual pattern elements, pattern intensities, a-b count, A-line exit, and atd angle were described, with population comparisons made when they were available. PMID:3799825
The strong, weak and anomalous sides of weak topological insulators
NASA Astrophysics Data System (ADS)
Ringel, Zohar
2013-03-01
Disorder and topology can be thought of as two counter-driving forces. While the former pushes electron wave functions to localize in space, the latter requires them to remain coherent over the entire system. We study the interplay between these two on the surface of a ``weakly'' topological phase- the Weak Topological Insulator. Using arguments based on flux-insertions and locality, we show that such surfaces cannot undergo a localization transition even when the surface is strongly disordered. We also present a numerical study which further quantifies this result. We then reformulate the same notions, in field theory language, using a novel Z2-charge-anomaly. This anomaly generalizes the Z-charge-anomaly associated with edges of the Integer Quantum Hall Effect. Besides unifying various aspects of Topological Insulators, the anomaly allows us to calculate new topological properties of TIs in the presence of electric fields.
Hopf insulators and their topologically protected surface states
NASA Astrophysics Data System (ADS)
Wang, Sheng-Tao; Deng, Dong-Ling; Shen, Chao; Duan, Lu-Ming
2014-03-01
Three-dimensional (3D) topological insulators in general need to be protected by certain kinds of symmetries other than the presumed U(1) charge conservation. A peculiar exception is the Hopf insulators which are 3D topological insulators characterized by an integer Hopf index. To demonstrate the existence and physical relevance of the Hopf insulators, we construct a class of tight-binding model Hamiltonians which realize all kinds of Hopf insulators with arbitrary integer Hopf index. These Hopf insulator phases have topologically protected surface states and we numerically demonstrate the robustness of these topologically protected states under general random perturbations without any symmetry other than the U(1) charge conservation that is implicit in all kinds of topological insulators. NBR-PC (973 Program) 2011CBA00300 (2011CBA00302), the DARPA OLE program, the IARPA MUSIQC program, the ARO and the AFOSR MURI program.
12 CFR 226.4 - Finance charge.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 12 Banks and Banking 3 2010-01-01 2010-01-01 false Finance charge. 226.4 Section 226.4 Banks and... LENDING (REGULATION Z) General § 226.4 Finance charge. (a) Definition. The finance charge is the cost of...) Charges by third parties. The finance charge includes fees and amounts charged by someone other than...
12 CFR 226.4 - Finance charge.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 12 Banks and Banking 3 2013-01-01 2013-01-01 false Finance charge. 226.4 Section 226.4 Banks and...) TRUTH IN LENDING (REGULATION Z) General § 226.4 Finance charge. (a) Definition. The finance charge is... transaction. (1) Charges by third parties. The finance charge includes fees and amounts charged by...
12 CFR 226.4 - Finance charge.
Code of Federal Regulations, 2012 CFR
2012-01-01
... 12 Banks and Banking 3 2012-01-01 2012-01-01 false Finance charge. 226.4 Section 226.4 Banks and... LENDING (REGULATION Z) General § 226.4 Finance charge. (a) Definition. The finance charge is the cost of...) Charges by third parties. The finance charge includes fees and amounts charged by someone other than...
12 CFR 226.4 - Finance charge.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 12 Banks and Banking 3 2014-01-01 2014-01-01 false Finance charge. 226.4 Section 226.4 Banks and...) TRUTH IN LENDING (REGULATION Z) General § 226.4 Finance charge. (a) Definition. The finance charge is... transaction. (1) Charges by third parties. The finance charge includes fees and amounts charged by...
Topological crystalline insulator nanostructures
NASA Astrophysics Data System (ADS)
Shen, Jie; Cha, Judy J.
2014-11-01
Topological crystalline insulators are topological insulators whose surface states are protected by the crystalline symmetry, instead of the time reversal symmetry. Similar to the first generation of three-dimensional topological insulators such as Bi2Se3 and Bi2Te3, topological crystalline insulators also possess surface states with exotic electronic properties such as spin-momentum locking and Dirac dispersion. Experimentally verified topological crystalline insulators to date are SnTe, Pb1-xSnxSe, and Pb1-xSnxTe. Because topological protection comes from the crystal symmetry, magnetic impurities or in-plane magnetic fields are not expected to open a gap in the surface states in topological crystalline insulators. Additionally, because they have a cubic structure instead of a layered structure, branched structures or strong coupling with other materials for large proximity effects are possible, which are difficult with layered Bi2Se3 and Bi2Te3. Thus, additional fundamental phenomena inaccessible in three-dimensional topological insulators can be pursued. In this review, topological crystalline insulator SnTe nanostructures will be discussed. For comparison, experimental results based on SnTe thin films will be covered. Surface state properties of topological crystalline insulators will be discussed briefly.
4D topological mass by gauging spin
NASA Astrophysics Data System (ADS)
Choudhury, I. D.; Diamantini, M. Cristina; Guarnaccia, Giuseppe; Lahiri, A.; Trugenberger, Carlo A.
2015-06-01
We propose a spin gauge field theory in which the curl of a Dirac fermion current density plays the role of the pseudovector charge density. In this field-theoretic model, spin interactions are mediated by a single scalar gauge boson in its antisymmetric tensor formulation. We show that these long range spin interactions induce a gauge invariant photon mass in the one-loop effective action. The fermion loop generates a coupling between photons and the spin gauge boson, which acquires thus charge. This coupling represents also an induced, gauge invariant, topological mass for the photons, leading to the Meissner effect. The one-loop effective equations of motion for the charged spin gauge boson are the London equations. We propose thus spin gauge interactions as an alternative, topological mechanism for superconductivity in which no spontaneous symmetry breaking is involved.
Symmetry protected Josephson supercurrents in three-dimensional topological insulators
NASA Astrophysics Data System (ADS)
Cho, Sungjae; Dellabetta, Brian; Yang, Alina; Schneeloch, John; Xu, Zhijun; Valla, Tonica; Gu, Genda; Gilbert, Matthew J.; Mason, Nadya
2013-04-01
Coupling the surface state of a topological insulator to an s-wave superconductor is predicted to produce the long-sought Majorana quasiparticle excitations. However, superconductivity has not been measured in surface states when the bulk charge carriers are fully depleted, that is, in the true topological regime relevant for investigating Majorana modes. Here we report measurements of d.c. Josephson effects in topological insulator-superconductor junctions as the chemical potential is moved through the true topological regime characterized by the presence of only surface currents. We compare our results with three-dimensional quantum transport simulations, and determine the effects of bulk/surface mixing, disorder and magnetic field; in particular, we show that the supercurrent is largely carried by surface states, due to the inherent topology of the bands, and that it is robust against disorder. Our results thus clarify key open issues regarding the nature of supercurrents in topological insulators.
Topological wave functions and the 4D-5D lift
NASA Astrophysics Data System (ADS)
Gao, Peng; Pioline, Boris
2008-07-01
We revisit the holomorphic anomaly equations satisfied by the topological string amplitude from the perspective of the 4D-5D lift, in the context of ``magic'' Script N = 2 supergravity theories. In particular, we interpret the Gopakumar-Vafa relation between 5D black hole degeneracies and the topological string amplitude as the result of a canonical transformation from 4D to 5D charges. Moreover we use the known Bekenstein-Hawking entropy of 5D black holes to constrain the asymptotic behavior of the topological wave function at finite topological coupling but large Kähler classes. In the process, some subtleties in the relation between 5D black hole degeneracies and the topological string amplitude are uncovered, but not resolved. Finally we extend these considerations to the putative one-parameter generalization of the topological string amplitude, and identify the canonical transformation as a Weyl reflection inside the 3D duality group.
Topological and error-correcting properties for symmetry-protected topological order
NASA Astrophysics Data System (ADS)
Zeng, Bei; Zhou, D. L.
2016-03-01
We study the symmetry-protected topological (SPT) orders for bosonic systems from an information-theoretic viewpoint. We show that with a proper choice of the onsite basis, the degenerate ground-state space of SPT orders (on a manifold with boundary) is a quantum error-correcting code with macroscopic classical distance, hence is stable against any local bit-flip errors. We show that this error-correcting property of the SPT orders has a natural connection to that of the symmetry-breaking orders, whose degenerate ground-state space is a classical error-correcting code with a macroscopic distance, providing a new angle for the hidden symmetry-breaking properties in SPT orders. We further propose new types of topological entanglement entropy that probe the SPT orders hidden in their symmetric ground states, which also signal the topological phase transitions protected by symmetry. Combined with the original definition of topological entanglement entropy that probes the “intrinsic topological orders”, and the recent proposed one that probes the symmetry-breaking orders, the set of different types of topological entanglement entropy may hence distinguish topological orders, SPT orders, and symmetry-breaking orders, which may be mixed up in a single system.
Topological susceptibility near Tc in SU(3) gauge theory
NASA Astrophysics Data System (ADS)
Xiong, Guang-Yi; Zhang, Jian-Bo; Chen, Ying; Liu, Chuan; Liu, Yu-Bin; Ma, Jian-Ping
2016-01-01
Topological charge susceptibility χt for pure gauge SU(3) theory at finite temperature is studied using anisotropic lattices. The over-improved stout-link smoothing method is utilized to calculate the topological charge. Near the phase transition point we find a rapid declining behavior for χt with values decreasing from (188 (1) MeV) 4 to (67 (3) MeV) 4 as the temperature increased from zero temperature to 1.9Tc which demonstrates the existence of topological excitations far above Tc. The 4th order cumulant c4 of topological charge, as well as the ratio c4 /χt is also investigated. Results of c4 show step-like behavior near Tc while the ratio at high temperature agrees with the value as predicted by the diluted instanton gas model.
Virasoro constraints and flavor-topology duality in QCD
Dalmazi, D.; Verbaarschot, J. J. M.
2001-09-01
We derive Virasoro constraints for the zero momentum part of the QCD-like partition functions in the sector of topological charge {nu}. The constraints depend on the topological charge only through the combination N{sub f}+{beta}{nu}/2 where the value of the Dyson index {beta} is determined by the reality type of the fermions. This duality between flavor and topology is inherited by the small-mass expansion of the partition function and all spectral sum rules of inverse powers of the eigenvalues of the Dirac operator. For the special case {beta}=2 but arbitrary topological charge the Virasoro constraints are solved uniquely by a generalized Kontsevich model with the potential V(X)=1/X.
Topological Hamiltonian as an exact tool for topological invariants.
Wang, Zhong; Yan, Binghai
2013-04-17
We propose the concept of 'topological Hamiltonian' for topological insulators and superconductors in interacting systems. The eigenvalues of the topological Hamiltonian are significantly different from the physical energy spectra, but we show that the topological Hamiltonian contains the information of gapless surface states, therefore it is an exact tool for topological invariants. PMID:23507711
Topological structure of the SU(3) vacuum
NASA Astrophysics Data System (ADS)
Smith, Douglas A.; Teper, Michael J.
1998-07-01
We investigate the topological structure of the vacuum in SU(3) lattice gauge theory. We use under-relaxed cooling to remove the high-frequency fluctuations and a variety of ``filters'' to identify the topological charges in the resulting smoothened field configurations. We find a densely packed vacuum with an average instanton size, in the continuum limit, of ρ¯~0.5 fm. The density at large ρ decreases rapidly as 1/ρ~11. At small sizes we see some signs of a trend towards the asymptotic perturbative behavior of D(ρ)~ρ6. We find that an interesting polarization phenomenon occurs: the large topological charges tend to have, on the average, the same sign and are over-screened by the smaller charges which tend to have, again on the average, the opposite sign to the larger instantons. We also calculate the topological susceptibility, χt, for which we obtain a continuum value of χ1/4t~187 MeV. We perform the calculations for various volumes, lattice spacings and numbers of cooling sweeps, so as to obtain some control over the associated systematic errors. The coupling range is 6.0<=β<=6.4 and the lattice volumes range from 163×48 to 323×64.
Yazdani, Ali; Ong, N. Phuan; Cava, Robert J.
2016-05-03
An interconnect is disclosed with enhanced immunity of electrical conductivity to defects. The interconnect includes a material with charge carriers having topological surface states. Also disclosed is a method for fabricating such interconnects. Also disclosed is an integrated circuit including such interconnects. Also disclosed is a gated electronic device including a material with charge carriers having topological surface states.
Considerations for Multiprocessor Topologies
NASA Technical Reports Server (NTRS)
Byrd, Gregory T.; Delagi, Bruce A.
1987-01-01
Choosing a multiprocessor interconnection topology may depend on high-level considerations, such as the intended application domain and the expected number of processors. It certainly depends on low-level implementation details, such as packaging and communications protocols. The authors first use rough measures of cost and performance to characterize several topologies. They then examine how implementation details can affect the realizable performance of a topology.
High-topological-number magnetic skyrmions and topologically protected dissipative structure
NASA Astrophysics Data System (ADS)
Zhang, Xichao; Zhou, Yan; Ezawa, Motohiko
2016-01-01
The magnetic skyrmion with the topological number of unity (Q =1 ) is a well-known nanometric swirling spin structure in the nonlinear σ model with the Dzyaloshinskii-Moriya interaction. Here we show that magnetic skyrmion with the topological number of two (Q =2 ) can be created and stabilized by applying vertical spin-polarized current though it cannot exist as a static stable excitation. Magnetic skyrmion with Q =2 is a nonequilibrium dynamic object, subsisting on a balance between the energy injection from the current and the energy dissipation by the Gilbert damping. Once it is created, it becomes a topologically protected object against fluctuations of various variables including the injected current itself. Hence we may call it a topologically protected dissipative structure. We also elucidate the nucleation and destruction mechanisms of the magnetic skyrmion with Q =2 by studying the evolutions of the magnetization distribution, the topological charge density, as well as the energy density. Our results will be useful for the study of the nontrivial topology of magnetic skyrmions with higher topological numbers.
NASA Astrophysics Data System (ADS)
Metlitski, Max A.; Kane, C. L.; Fisher, Matthew P. A.
2015-09-01
A three-dimensional electron topological insulator (ETI) is a phase of matter protected by particle-number conservation and time-reversal symmetry. It was previously believed that the surface of an ETI must be gapless unless one of these symmetries is broken. A well-known symmetry-preserving, gapless surface termination of an ETI supports an odd number of Dirac cones. In this paper, we deduce a symmetry-respecting, gapped surface termination of an ETI, which carries an intrinsic two-dimensional (2d) topological order, Moore-Read×U (1) -2 . The Moore-Read sector supports non-Abelian charge 1 /4 anyons, while the Abelian, U (1) -2 , (antisemion) sector is electrically neutral. Time-reversal symmetry is implemented in this surface phase in a highly nontrivial way. Moreover, it is impossible to realize this phase strictly in 2d, simultaneously preserving its implementation of both the particle-number and time-reversal symmetries. A one-dimensional (1d) edge on the ETI surface between the topologically ordered phase and the topologically trivial time-reversal-broken phase with a Hall conductivity σx y=1 /2 carries a right-moving neutral Majorana mode, a right-moving bosonic charge mode, and a left-moving bosonic neutral mode. The topologically ordered phase is separated from the surface superconductor by a direct second-order phase transition in the X Y* universality class, which is driven by the condensation of a charge 1 /2 boson, when approached from the topologically ordered side, and proliferation of a flux 4 π (2 h c /e ) vortex, when approached from the superconducting side. In addition, we prove that time-reversal invariant (interacting) electron insulators with no intrinsic topological order and electromagnetic response characterized by a θ angle, θ =π , do not exist if the electrons transform as Kramers singlets under time reversal.
- criticality of topological black holes in Lovelock-Born-Infeld gravity
NASA Astrophysics Data System (ADS)
Mo, Jie-Xiong; Liu, Wen-Biao
2014-04-01
To understand the effect of third order Lovelock gravity, - criticality of topological AdS black holes in Lovelock-Born-Infeld gravity is investigated. The thermodynamics is further explored with some more extensions and in some more detail than the previous literature. A detailed analysis of the limit case is performed for the seven-dimensional black holes. It is shown that, for the spherical topology, - criticality exists for both the uncharged and the charged cases. Our results demonstrate again that the charge is not the indispensable condition of - criticality. It may be attributed to the effect of higher derivative terms of the curvature because similar phenomenon was also found for Gauss-Bonnet black holes. For , there would be no - criticality. Interesting findings occur in the case , in which positive solutions of critical points are found for both the uncharged and the charged cases. However, the - diagram is quite strange. To check whether these findings are physical, we give the analysis on the non-negative definiteness condition of the entropy. It is shown that, for any nontrivial value of , the entropy is always positive for any specific volume . Since no - criticality exists for in Einstein gravity and Gauss-Bonnet gravity, we can relate our findings with the peculiar property of third order Lovelock gravity. The entropy in third order Lovelock gravity consists of extra terms which are absent in the Gauss-Bonnet black holes, which makes the critical points satisfy the constraint of non-negative definiteness condition of the entropy. We also check the Gibbs free energy graph and "swallow tail" behavior can be observed. Moreover, the effect of nonlinear electrodynamics is also included in our research.
A new class of non-topological solitons
NASA Technical Reports Server (NTRS)
Frieman, Joshua A.; Lynn, Bryan W.
1989-01-01
A class of non-topological solitons was constructed in renormalizable scalar field theories with nonlinear self-interactions. For large charge Q, the soliton mass increases linearly with Q, i.e., the soliton mass density is approximately independent of charge. Such objects could be naturally produced in a phase transition in the early universe or in the decay of superconducting cosmic strings.
Petkova, V. B.
2013-10-15
Areview of the notion, properties and the use of topological defects in 2d conformal field theories is presented. An emphasis is made on the recent interpretation of such operators in non-rational theories, as describing Wilson-'t Hooft loop operators of N = 2 supersymmetric 4d topological theories.
Periodic table for topological insulators and superconductors
Kitaev, Alexei
2009-05-14
Gapped phases of noninteracting fermions, with and without charge conservation and time-reversal symmetry, are classified using Bott periodicity. The symmetry and spatial dimension determines a general universality class, which corresponds to one of the 2 types of complex and 8 types of real Clifford algebras. The phases within a given class are further characterized by a topological invariant, an element of some Abelian group that can be 0, Z, or Z{sub 2}. The interface between two infinite phases with different topological numbers must carry some gapless mode. Topological properties of finite systems are described in terms of K-homology. This classification is robust with respect to disorder, provided electron states near the Fermi energy are absent or localized. In some cases (e.g., integer quantum Hall systems) the K-theoretic classification is stable to interactions, but a counterexample is also given.
Bosonic topological phase in a paired superfluid
NASA Astrophysics Data System (ADS)
Gazit, Snir; Vishwanath, Ashvin
2016-03-01
We study an effective model of two interacting species of bosons in two dimensions, which is amenable to sign problem free Monte Carlo simulations. In addition to conventional ground states, we access a paired superfluid which is also a topological phase, protected by the remaining U (1 ) ×Z2 symmetry. This phase arises from the condensation of a composite object, the bound state of vortices and antivortices of one species, to a boson of the second species. We introduce a bulk response function, the Ising analog of the quantized Hall effect, to diagnose the topological phase. The interplay of broken symmetry and topology leads to interesting effects such as fractionally charged vortices in the paired superfluid. Possible extensions towards realistic models of cold atomic bosons are discussed.
Dynamical gap generation in topological insulators
NASA Astrophysics Data System (ADS)
Cea, Paolo
2016-04-01
We developed a quantum field theoretical description for the surface states of three-dimensional topological insulators. Within the relativistic quantum field theory formulation, we investigated the dynamics of low-lying surface states in an applied transverse magnetic field. We argued that, by taking into account quantum fluctuations, in three-dimensional topological insulators there is dynamical generation of a gap by a rearrangement of the Dirac sea. By comparing with available experimental data we found that our theoretical results allowed a consistent and coherent description of the Landau level spectrum of the surface low-lying excitations. Finally, we showed that the recently detected zero-Hall plateau at the charge neutral point could be accounted for by chiral edge states residing at the magnetic domain boundaries between the top and bottom surfaces of the three-dimensional topological insulator.
Superconducting doped topological materials
NASA Astrophysics Data System (ADS)
Sasaki, Satoshi; Mizushima, Takeshi
2015-07-01
Recently, the search for Majorana fermions (MFs) has become one of the most important and exciting issues in condensed matter physics since such an exotic quasiparticle is expected to potentially give rise to unprecedented quantum phenomena whose functional properties will be used to develop future quantum technology. Theoretically, the MFs may reside in various types of topological superconductor materials that is characterized by the topologically protected gapless surface state which are essentially an Andreev bound state. Superconducting doped topological insulators and topological crystalline insulators are promising candidates to harbor the MFs. In this review, we discuss recent progress and understanding on the research of MFs based on time-reversal-invariant superconducting topological materials to deepen our understanding and have a better outlook on both the search for and realization of MFs in these systems. We also discuss some advantages of these bulk systems to realize MFs including remarkable superconducting robustness against nonmagnetic impurities.
Topological nonsymmorphic crystalline superconductors
NASA Astrophysics Data System (ADS)
Wang, Qing-Ze; Liu, Chao-Xing
2016-01-01
Topological superconductors possess a nodeless superconducting gap in the bulk and gapless zero energy modes, known as "Majorana zero modes," at the boundary of a finite system. In this work, we introduce a new class of topological superconductors, which are protected by nonsymmorphic crystalline symmetry and thus dubbed "topological nonsymmorphic crystalline superconductors." We construct an explicit Bogoliubov-de Gennes type of model for this superconducting phase in the D class and show how Majorana zero modes in this model are protected by glide plane symmetry. Furthermore, we generalize the classification of topological nonsymmorphic crystalline superconductors to the classes with time reversal symmetry, including the DIII and BDI classes, in two dimensions. Our theory provides guidance to search for new topological superconducting materials with nonsymmorphic crystal structures.
NASA Astrophysics Data System (ADS)
Dzero, Maxim; Xia, Jing; Galitski, Victor; Coleman, Piers
2016-03-01
This article reviews recent theoretical and experimental work on a new class of topological material -- topological Kondo insulators, which develop through the interplay of strong correlations and spin-orbit interactions. The history of Kondo insulators is reviewed along with the theoretical models used to describe these heavy fermion compounds. The Fu-Kane method of topological classification of insulators is used to show that hybridization between the conduction electrons and localized f electrons in these systems gives rise to interaction-induced topological insulating behavior. Finally, some recent experimental results are discussed, which appear to confirm the theoretical prediction of the topological insulating behavior in samarium hexaboride, where the long-standing puzzle of the residual low-temperature conductivity has been shown to originate from robust surface states.
Dynamic topology representing networks.
Si, J; Lin, S; Vuong, M A
2000-07-01
In the present paper, we propose a new algorithm, namely the Dynamic Topology Representing Networks (DTRN) for learning both topology and clustering information from input data. In contrast to other models with adaptive architecture of this kind, the DTRN algorithm adaptively grows the number of output nodes by applying a vigilance test. The clustering procedure is based on a winner-take-quota learning strategy in conjunction with an annealing process in order to minimize the associated mean square error. A competitive Hebbian rule is applied to learn the global topology information concurrently with the clustering process. The topology information learned is also utilized for dynamically deleting the nodes and for the annealing process. Properties of the DTRN algorithm will be discussed. Extensive simulations will be provided to characterize the effectiveness of the new algorithm in topology preserving, learning speed, and classification tasks as compared to other algorithms of the same nature. PMID:10987515
Study of charges transferability for use in force fields
NASA Astrophysics Data System (ADS)
Maciel, Glauciete S.; Garcia, Edgardo
2006-03-01
This Letter examines the topological neighborhood effects on atomic partial charges and their transferability. To determine neighborhood effects, we used Breneman and Wiberg's CHELPG charges calculated at B3LYP/6-31G* theory level and AM1 geometries for a test set of 324 molecules of insecticides, ferroelectric liquid crystals (FLC) and antiinflammatories. The Qcode atomic descriptor was applied to represent topological neighborhood. Calculated molecular dipole moments using averaged charges with various neighbor numbers indicate that partial charges have a strong dependence with the molecular topology. Five or more neighbors are demonstrated to be typically needed for accurate partial charges transferability.
Colossal magnetoresistance in topological Kondo insulator
NASA Astrophysics Data System (ADS)
Slieptsov, Igor O.; Karnaukhov, Igor N.
2016-04-01
Abnormal electronic properties of complex systems require new ideas concerning explanation of their behavior and possibility of realization. In this acticle we show that a colossal magnetoresistance is realized in the state of the topological Kondo insulator, that is similar to the Kondo insulator state in the Kondo lattice. The mechanism of the phenomenon is the following: in the spin gapless phase an external magnetic field induces the gap in the spectrum of spin excitations, the gap in the spectrum of fermions is opened due to a hybridization between spin and fermion subsystems at half-filling, as the result the magnetic field leads to metal–insulator (or bad metal–insulator) phase transition. A model of the topological Kondo lattice defined on a honeycomb lattice is studied for the case when spinless fermion bands are half-filled. It is shown that the hybridization between local moments and itinerant fermions should be understood as the hybridization between corresponding Majorana fermions of the spin and charge sectors. The system is a topological insulator, single fermion and spin excitations at low energies are massive. We will show that a spin gap induces a gap in the charge channel, it leads to an appearance of a topological insulator state with chiral gapless edge modes and the Chern number one or two depending on the exchange integrals’ values. The relevance of this to the traditional Kondo insulator state is discussed.
Topological Pair-Density-Wave Superconducting States
NASA Astrophysics Data System (ADS)
Soto Garrido, Rodrigo; Cho, Gil Young; Fradkin, Eduardo
2015-03-01
We show that the pair-density-wave (PDW) superconducting state emergent in extended Heisenberg-Hubbard models in two-leg ladders is topological in the presence of an Ising spin symmetry. This topological PDW state supports a Majorana zero mode (MZM) at an open boundary and at a junction with a uniform one-dimensional d-wave superconductor. Similarly to a conventional finite-momentum paired state, the order parameter of the topological PDW state is a charge- 2 e field with finite momentum, and a subleading charge 4 e uniform SC order. However, the topological PDW order parameter here is a quartic electron operator and conventional mean-field theory cannot be applied to study this state. We use bosonization to show that the 1D PDW state has a MZM at a boundary. This work was supported in part by the NSF Grants DMR-1064319 and DMR 1408713 at UIUC, PHY11-25915 at KITP and DOE Award No. DE-FG02-07ER46453.
Gauge symmetries, topology, and quantisation
NASA Astrophysics Data System (ADS)
Balachandran, A. P.
1994-10-01
The following two loosely connected sets of topics are reviewed in these lecture notes: 1) Gauge invariance, its treatment in field theories and its implications for internal symmetries and edge states such as those in the quantum Hall effect. 2) Quantisation on multiply connected spaces and a topological proof the spin-statistics theorem which avoids quantum field theory and relativity. Under 1), after explaining the meaning of gauge invariance and the theory of constraints, we discuss boundary conditions on gauge transformations and the definition of internal symmetries in gauge field theories. We then show how the edge states in the quantum Hall effect can be derived from the Chern-Simons action using the preceding ideas. Under 2), after explaining the significance of fibre bundles for quantum physics, we review quantisation on multiply connected spaces in detail, explaining also mathematical ideas such as those of the universal covering space and the fundamental group. These ideas are then used to prove the aforementioned topological spin-statistics theorem.
Topological dynamics in supramolecular rotors.
Palma, Carlos-Andres; Bjrk, Jonas; Rao, Francesco; Khne, Dirk; Klappenberger, Florian; Barth, Johannes V
2014-08-13
Artificial molecular switches, rotors, and machines are set to establish design rules and applications beyond their biological counterparts. Herein we exemplify the role of noncovalent interactions and transient rearrangements in the complex behavior of supramolecular rotors caged in a 2D metal-organic coordination network. Combined scanning tunneling microscopy experiments and molecular dynamics modeling of a supramolecular rotor with respective rotation rates matching with 0.2 kcal mol(-1) (9 meV) precision, identify key steps in collective rotation events and reconfigurations. We notably reveal that stereoisomerization of the chiral trimeric units entails topological isomerization whereas rotation occurs in a topology conserving, two-step asynchronous process. In supramolecular constructs, distinct displacements of subunits occur inducing a markedly lower rotation barrier as compared to synchronous mechanisms of rigid rotors. Moreover, the chemical environment can be instructed to control the system dynamics. Our observations allow for a definition of mechanical cooperativity based on a significant reduction of free energy barriers in supramolecules compared to rigid molecules. PMID:25078022
Topological Phase Transition without Gap Closing
Ezawa, Motohiko; Tanaka, Yukio; Nagaosa, Naoto
2013-01-01
Topological phase transition is accompanied with a change of topological numbers. According to the bulk-edge correspondence, the gap closing and the breakdown of the adiabaticity are necessary at the phase transition point to make the topological number ill-defined. However, the gap closing is not always needed. In this paper, we show that two topological distinct phases can be continuously connected without gap closing, provided the symmetry of the system changes during the process. Here we propose the generic principles how this is possible by demonstrating various examples such as 1D polyacetylene with the charge-density-wave order, 2D silicene with the antiferromagnetic order, 2D silicene or quantum well made of HgTe with superconducting proximity effects and 3D superconductor Cu doped Bi2Se3. It is argued that such an unusual phenomenon can occur when we detour around the gap closing point provided the connection of the topological numbers is lost along the detour path. PMID:24071900
Topological pair-density-wave superconducting states.
Cho, Gil Young; Soto-Garrido, Rodrigo; Fradkin, Eduardo
2014-12-19
We show that the pair-density-wave (PDW) superconducting state emergent in extended Heisenberg-Hubbard models in two-leg ladders is topological in the presence of an Ising spin symmetry and supports a Majorana zero mode (MZM) at an open boundary and at a junction with a uniform d-wave one-dimensional superconductor. Similarly to a conventional finite-momentum paired state, the order parameter of the PDW state is a charge-2e field with finite momentum. However, the order parameter here is a quartic electron operator and conventional mean-field theory cannot be applied to study this state. We use bosonization to show that the 1D PDW state has a MZM at a boundary. This superconducting state is an exotic topological phase supporting Majorana fermions with finite-momentum pairing fields and charge-4e superconductivity. PMID:25554900
Topological Pair-Density-Wave Superconducting States
NASA Astrophysics Data System (ADS)
Cho, Gil Young; Soto-Garrido, Rodrigo; Fradkin, Eduardo
2014-12-01
We show that the pair-density-wave (PDW) superconducting state emergent in extended Heisenberg-Hubbard models in two-leg ladders is topological in the presence of an Ising spin symmetry and supports a Majorana zero mode (MZM) at an open boundary and at a junction with a uniform d -wave one-dimensional superconductor. Similarly to a conventional finite-momentum paired state, the order parameter of the PDW state is a charge-2 e field with finite momentum. However, the order parameter here is a quartic electron operator and conventional mean-field theory cannot be applied to study this state. We use bosonization to show that the 1D PDW state has a MZM at a boundary. This superconducting state is an exotic topological phase supporting Majorana fermions with finite-momentum pairing fields and charge-4 e superconductivity.
Higgsless superconductivity from topological defects in compact BF terms
NASA Astrophysics Data System (ADS)
Diamantini, M. Cristina; Trugenberger, Carlo A.
2015-02-01
We present a new Higgsless model of superconductivity, inspired from anyon superconductivity but P- and T-invariant and generalisable to any dimension. While the original anyon superconductivity mechanism was based on incompressible quantum Hall fluids as average field states, our mechanism involves topological insulators as average field states. In D space dimensions it involves a (D - 1)-form fictitious pseudovector gauge field which originates from the condensation of topological defects in compact low-energy effective BF theories. In the average field approximation, the corresponding uniform emergent charge creates a gap for the (D - 2)-dimensional branes via the Magnus force, the dual of the Lorentz force. One particular combination of intrinsic and emergent charge fluctuations that leaves the total charge distribution invariant constitutes an isolated gapless mode leading to superfluidity. The remaining massive modes organise themselves into a D-dimensional charged, massive vector. There is no massive Higgs scalar as there is no local order parameter. When electromagnetism is switched on, the photon acquires mass by the topological BF mechanism. Although the charge of the gapless mode (2) and the topological order (4) are the same as those of the standard Higgs model, the two models of superconductivity are clearly different since the origins of the gap, reflected in the high-energy sectors are totally different. In 2D this type of superconductivity is explicitly realised as global superconductivity in Josephson junction arrays. In 3D this model predicts a possible phase transition from topological insulators to Higgsless superconductors.
Topological color code and symmetry-protected topological phases
NASA Astrophysics Data System (ADS)
Yoshida, Beni
2015-06-01
We study (d -1 ) -dimensional excitations in the d -dimensional color code that are created by transversal application of the Rd phase operators on connected subregions of qubits. We find that such excitations are the superpositions of electric charges and can be characterized by the fixed-point wave functions of (d -1 ) -dimensional bosonic symmetry-protected topological (SPT) phases with (Z2) ⊗d symmetry. While these SPT excitations are localized on (d -1 ) -dimensional boundaries, their creation requires operations acting on all qubits inside the boundaries, reflecting the nontriviality of emerging SPT wave functions. Moreover, these SPT excitations can be physically realized as transparent gapped domain walls which exchange excitations in the color code. Namely, in the three-dimensional color code, the domain wall, associated with the transversal R3 operator, exchanges a magnetic flux and a composite of a magnetic flux and the looplike SPT excitation, revealing rich possibilities of boundaries in higher-dimensional TQFTs. We also find that magnetic fluxes and the looplike SPT excitations exhibit nontrivial three-loop braiding statistics in three dimensions as a result of the fact that the R3 phase operator belongs to the third level of the Clifford hierarchy. We believe that the connection between SPT excitations, fault-tolerant logical gates and gapped domain walls, established in this paper, can be generalized to a large class of topological quantum codes and TQFTs.
Manipulating Topological States by Imprinting Non-Collinear Spin Textures
Streubel, Robert; Han, Luyang; Im, Mi-Young; Kronast, Florian; Rößler, Ulrich K.; Radu, Florin; Abrudan, Radu; Lin, Gungun; Schmidt, Oliver G.; Fischer, Peter; Makarov, Denys
2015-01-01
Topological magnetic states, such as chiral skyrmions, are of great scientific interest and show huge potential for novel spintronics applications, provided their topological charges can be fully controlled. So far skyrmionic textures have been observed in noncentrosymmetric crystalline materials with low symmetry and at low temperatures. We propose theoretically and demonstrate experimentally the design of spin textures with topological charge densities that can be tailored at ambient temperatures. Tuning the interlayer coupling in vertically stacked nanopatterned magnetic heterostructures, such as a model system of a Co/Pd multilayer coupled to Permalloy, the in-plane non-collinear spin texture of one layer can be imprinted into the out-of-plane magnetised material. We observe distinct spin textures, e.g. vortices, magnetic swirls with tunable opening angle, donut states and skyrmion core configurations. We show that applying a small magnetic field, a reliable switching between topologically distinct textures can be achieved at remanence. PMID:25739643
Manipulating topological states by imprinting non-collinear spin textures
Streubel, Robert; Han, Luyang; Im, Mi -Young; Kronast, Florian; Rößler, Ulrich K.; Radu, Florin; Abrudan, Radu; Schmidt, Oliver G.; Fischer, Peter; Makarov, Denys
2015-03-05
Topological magnetic states, such as chiral skyrmions, are of great scientific interest and show huge potential for novel spintronics applications, provided their topological charges can be fully controlled. So far skyrmionic textures have been observed in noncentrosymmetric crystalline materials with low symmetry and at low temperatures. We propose theoretically and demonstrate experimentally the design of spin textures with topological charge densities that can be tailored at ambient temperatures. Tuning the interlayer coupling in vertically stacked nanopatterned magnetic heterostructures, such as a model system of a Co/Pd multilayer coupled to Permalloy, the in-plane non-collinear spin texture of one layer can be imprinted into the out-of-plane magnetised material. We observe distinct spin textures, e.g. vortices, magnetic swirls with tunable opening angle, donut states and skyrmion core configurations. We show that applying a small magnetic field, a reliable switching between topologically distinct textures can be achieved at remanence
Effect of improving the lattice gauge action on QCD topology
Grandy, J.; Kilcup, G.
1996-08-19
We use lattice topology as a laboratory to-compare the Wilson action (WA) with the Symanzik-Weisz (SW) action constructed from a combination of (1 x 1) and (1 x 2) Wilson loops, and the estimate of the renormalization trajectory (RT)[1] from a renormalization group transformation (RGT) which also includes higher representations of the (1 x 1) loop. Topological charges are computed using the geometric (Luscher`s) and plaquette methods on the uncooled lattice, and also by using cooling to remove ultraviolet artifacts. We show that as the action improves by approaching the RT, the topological charges for individual configurations, computed using these three methods become more highly correlated, suggesting that artificial lattice renormalizations to the topological susceptibility can be suppressed by improving the action.
Manipulating topological states by imprinting non-collinear spin textures
Streubel, Robert; Han, Luyang; Im, Mi -Young; Kronast, Florian; Rößler, Ulrich K.; Radu, Florin; Abrudan, Radu; Lin, Gungun; Schmidt, Oliver G.; Fischer, Peter; et al
2015-03-05
Topological magnetic states, such as chiral skyrmions, are of great scientific interest and show huge potential for novel spintronics applications, provided their topological charges can be fully controlled. So far skyrmionic textures have been observed in noncentrosymmetric crystalline materials with low symmetry and at low temperatures. We propose theoretically and demonstrate experimentally the design of spin textures with topological charge densities that can be tailored at ambient temperatures. Tuning the interlayer coupling in vertically stacked nanopatterned magnetic heterostructures, such as a model system of a Co/Pd multilayer coupled to Permalloy, the in-plane non-collinear spin texture of one layer can bemore » imprinted into the out-of-plane magnetised material. We observe distinct spin textures, e.g. vortices, magnetic swirls with tunable opening angle, donut states and skyrmion core configurations. We show that applying a small magnetic field, a reliable switching between topologically distinct textures can be achieved at remanence« less
NASA Astrophysics Data System (ADS)
Knitter, Sebastian; Fatt Liew, Seng; Xiong, Wen; Guy, Mikhael I.; Solomon, Glenn S.; Cao, Hui
2016-01-01
We introduce a topological defect to a regular photonic crystal defect cavity with anisotropic unit cell. Spatially localized resonances are formed and have high quality factor. Unlike the regular photonic crystal defect states, the localized resonances in the topological defect structures support powerflow vortices. Experimentally we realize lasing in the topological defect cavities with optical pumping. This work shows that the spatially inhomogeneous variation of the unit cell orientation adds another degree of freedom to the control of lasing modes, enabling the manipulation of the field pattern and energy flow landscape.
Topological solitons in 8-spinor mie electrodynamics
Rybakov, Yu. P.
2013-10-15
We investigate the effective 8-spinor field model suggested earlier as the generalization of nonlinear Mie electrodynamics. We first study in pure spinorial model the existence of topological solitons endowed with the nontrivial Hopf invariant Q{sub H}, which can be interpreted as the lepton number. Electromagnetic field being included as the perturbation, we estimate the energy and the spin of the localized charged configuration.
Multi-terminal Josephson junctions as topological matter
NASA Astrophysics Data System (ADS)
Riwar, Roman-Pascal; Houzet, Manuel; Meyer, Julia S.; Nazarov, Yuli V.
2016-04-01
Topological materials and their unusual transport properties are now at the focus of modern experimental and theoretical research. Their topological properties arise from the bandstructure determined by the atomic composition of a material and as such are difficult to tune and naturally restricted to <=3 dimensions. Here we demonstrate that n-terminal Josephson junctions with conventional superconductors may provide novel realizations of topology in n-1 dimensions, which have similarities, but also marked differences with existing 2D or 3D topological materials. For n>=4, the Andreev subgap spectrum of the junction can accommodate Weyl singularities in the space of the n-1 independent superconducting phases, which play the role of bandstructure quasimomenta. The presence of these Weyl singularities enables topological transitions that are manifested experimentally as changes of the quantized transconductance between two voltage-biased leads, the quantization unit being 4e2/h, where e is the electric charge and h is the Planck constant.
Ground-state degeneracy of topological phases on open surfaces.
Hung, Ling-Yan; Wan, Yidun
2015-02-20
We relate the ground state degeneracy of a non-Abelian topological phase on a surface with boundaries to the anyon condensates that break the topological phase into a trivial phase. Specifically, we propose that gapped boundary conditions of the surface are in one-to-one correspondence with the sets of condensates, each being able to completely break the phase, and we substantiate this by examples. The ground state degeneracy resulting from a particular boundary condition coincides with the number of confined topological sectors due to the corresponding condensation. These lead to a generalization of the Laughlin-Tao-Wu charge-pumping argument for Abelian fractional quantum Hall states to encompass non-Abelian topological phases, in the sense that an anyon loop of a confined anyon winding a nontrivial cycle can pump a condensed anyon from one boundary to another. Such generalized pumping may find applications in quantum control of anyons, eventually realizing topological quantum computation. PMID:25763964
Twisted gauge theory model of topological phases in three dimensions
NASA Astrophysics Data System (ADS)
Wan, Yidun; Wang, Juven C.; He, Huan
2015-07-01
We propose an exactly solvable lattice Hamiltonian model of topological phases in 3 +1 dimensions, based on a generic finite group G and a 4-cocycle ω over G . We show that our model has topologically protected degenerate ground states and obtain the formula of its ground state degeneracy on the 3-torus. In particular, the ground state spectrum implies the existence of purely three-dimensional looplike quasiexcitations specified by two nontrivial flux indices and one charge index. We also construct other nontrivial topological observables of the model, namely the S L (3 ,Z ) generators as the modular S and T matrices of the ground states, which yield a set of topological quantum numbers classified by ω and quantities derived from ω . Our model fulfills a Hamiltonian extension of the (3 +1 )-dimensional Dijkgraaf-Witten topological gauge theory with a gauge group G . This work is presented to be accessible for a wide range of physicists and mathematicians.
Topological black holes in Horava-Lifshitz gravity
Cai Ronggen; Cao Liming; Ohta, Nobuyoshi
2009-07-15
We find topological (charged) black holes whose horizon has an arbitrary constant scalar curvature 2k in Horava-Lifshitz theory. Without loss of generality, one may take k=1, 0, and -1. The black hole solution is asymptotically anti-de Sitter with a nonstandard asymptotic behavior. Using the Hamiltonian approach, we define a finite mass associated with the solution. We discuss the thermodynamics of the topological black holes and find that the black hole entropy has a logarithmic term in addition to an area term. We find a duality in Hawking temperature between topological black holes in Horava-Lifshitz theory and Einstein's general relativity: the temperature behaviors of black holes with k=1, 0, and -1 in Horava-Lifshitz theory are, respectively, dual to those of topological black holes with k=-1, 0, and 1 in Einstein's general relativity. The topological black holes in Horava-Lifshitz theory are thermodynamically stable.
Destroying a topological quantum bit by condensing Ising vortices.
Hao, Zhihao; Inglis, Stephen; Melko, Roger
2014-01-01
The imminent realization of topologically protected qubits in fabricated systems will provide not only an elementary implementation of fault-tolerant quantum computing architecture, but also an experimental vehicle for the general study of topological order. The simplest topological qubit harbours what is known as a Z2 liquid phase, which encodes information via a degeneracy depending on the system's topology. Elementary excitations of the phase are fractionally charged objects called spinons, or Ising flux vortices called visons. At zero temperature, a Z2 liquid is stable under deformations of the Hamiltonian until spinon or vison condensation induces a quantum-phase transition destroying the topological order. Here we use quantum Monte Carlo to study a vison-induced transition from a Z2 liquid to a valence-bond solid in a quantum dimer model on the kagome lattice. Our results indicate that this critical point is beyond the description of the standard Landau paradigm. PMID:25488132
Multi-terminal Josephson junctions as topological matter
Riwar, Roman-Pascal; Houzet, Manuel; Meyer, Julia S.; Nazarov, Yuli V.
2016-01-01
Topological materials and their unusual transport properties are now at the focus of modern experimental and theoretical research. Their topological properties arise from the bandstructure determined by the atomic composition of a material and as such are difficult to tune and naturally restricted to ≤3 dimensions. Here we demonstrate that n-terminal Josephson junctions with conventional superconductors may provide novel realizations of topology in n−1 dimensions, which have similarities, but also marked differences with existing 2D or 3D topological materials. For n≥4, the Andreev subgap spectrum of the junction can accommodate Weyl singularities in the space of the n−1 independent superconducting phases, which play the role of bandstructure quasimomenta. The presence of these Weyl singularities enables topological transitions that are manifested experimentally as changes of the quantized transconductance between two voltage-biased leads, the quantization unit being 4e2/h, where e is the electric charge and h is the Planck constant. PMID:27040917
Multi-terminal Josephson junctions as topological matter.
Riwar, Roman-Pascal; Houzet, Manuel; Meyer, Julia S; Nazarov, Yuli V
2016-01-01
Topological materials and their unusual transport properties are now at the focus of modern experimental and theoretical research. Their topological properties arise from the bandstructure determined by the atomic composition of a material and as such are difficult to tune and naturally restricted to ≤3 dimensions. Here we demonstrate that n-terminal Josephson junctions with conventional superconductors may provide novel realizations of topology in n-1 dimensions, which have similarities, but also marked differences with existing 2D or 3D topological materials. For n≥4, the Andreev subgap spectrum of the junction can accommodate Weyl singularities in the space of the n-1 independent superconducting phases, which play the role of bandstructure quasimomenta. The presence of these Weyl singularities enables topological transitions that are manifested experimentally as changes of the quantized transconductance between two voltage-biased leads, the quantization unit being 4e(2)/h, where e is the electric charge and h is the Planck constant. PMID:27040917
Experimental Discovery of Topological Insulators and Related Superconductors
Hasan, M Zahid
2010-09-15
Most quantum states of condensed matter are categorized by the symmetries they break. The remarkable discovery of charge Quantum Hall effects (1980s) revealed that there exists an organizational principle of matter based only on the topological distinctions, but in the presence of time-reversal symmetry breaking. In the past few years, theoretical developments suggest that new classes of topological states of matter might exist that are purely topological in nature in the sense that they do not break time-reversal symmetry, and hence can be realized without any applied magnetic field: "Quantum Hall-like effects without Magnetic Fields." This talk describes our discovery of new topologically ordered states of matter (topological insulators) and discusses the unusual electro-magnetic, spin, and superconducting properties this novel phase of quantum matter might exhibit and their potential applications.
Jauregui, Luis A; Pettes, Michael T; Rokhinson, Leonid P; Shi, Li; Chen, Yong P
2016-04-01
The spin-helical Dirac fermion topological surface states in a topological insulator nanowire or nanoribbon promise novel topological devices and exotic physics such as Majorana fermions. Here, we report local and non-local transport measurements in Bi2Te3 topological insulator nanoribbons that exhibit quasi-ballistic transport over ∼2 μm. The conductance versus axial magnetic flux Φ exhibits Aharonov-Bohm oscillations with maxima occurring alternately at half-integer or integer flux quanta (Φ0 = h/e, where h is Planck's constant and e is the electron charge) depending periodically on the gate-tuned Fermi wavevector (kF) with period 2π/C (where C is the nanoribbon circumference). The conductance versus gate voltage also exhibits kF-periodic oscillations, anti-correlated between Φ = 0 and Φ0/2. These oscillations enable us to probe the Bi2Te3 band structure, and are consistent with the circumferentially quantized topological surface states forming a series of one-dimensional subbands, which undergo periodic magnetic field-induced topological transitions with the disappearance/appearance of the gapless Dirac point with a one-dimensional spin helical mode. PMID:26780658
NASA Astrophysics Data System (ADS)
Jauregui, Luis A.; Pettes, Michael T.; Rokhinson, Leonid P.; Shi, Li; Chen, Yong P.
2016-04-01
The spin-helical Dirac fermion topological surface states in a topological insulator nanowire or nanoribbon promise novel topological devices and exotic physics such as Majorana fermions. Here, we report local and non-local transport measurements in Bi2Te3 topological insulator nanoribbons that exhibit quasi-ballistic transport over ∼2 μm. The conductance versus axial magnetic flux Φ exhibits Aharonov–Bohm oscillations with maxima occurring alternately at half-integer or integer flux quanta (Φ0 = h/e, where h is Planck's constant and e is the electron charge) depending periodically on the gate-tuned Fermi wavevector (kF) with period 2π/C (where C is the nanoribbon circumference). The conductance versus gate voltage also exhibits kF-periodic oscillations, anti-correlated between Φ = 0 and Φ0/2. These oscillations enable us to probe the Bi2Te3 band structure, and are consistent with the circumferentially quantized topological surface states forming a series of one-dimensional subbands, which undergo periodic magnetic field-induced topological transitions with the disappearance/appearance of the gapless Dirac point with a one-dimensional spin helical mode.
Topologically nontrivial narrow bands in ultrathin SnTe films with defect superstructures.
Kim, Minsung; Ihm, Jisoon
2014-06-11
It is shown that a two-dimensional topological insulator can be realized and the band topology (equivalently, the edge states) may be further controlled by charge doping in an ultrathin SnTe film with a defect superstructure. Based on first-principles density functional theory (DFT), we predict that a Sn-Te bilayer, if exfoliated from three-dimensional bulk SnTe in the (1 1 1) direction, has a trivial band topology in its pristine form, but is made topologically nontrivial by introducing an appropriate array of defects. The emergence of the topological state is ascribed to the formation of topologically nontrivial narrow bands near the Fermi level by spin–orbit splitting of defect-induced bands. In addition, we demonstrate that a transition between a topological insulator and a normal insulator is possible under the electron or hole doping which can be useful for controlling the topological edge states. PMID:25932473
Supersymmetric black holes with lens-space topology.
Kunduri, Hari K; Lucietti, James
2014-11-21
We present a new supersymmetric, asymptotically flat, black hole solution to five-dimensional supergravity. It is regular on and outside an event horizon of lens-space topology L(2,1). It is the first example of an asymptotically flat black hole with lens-space topology. The solution is characterized by a charge, two angular momenta, and a magnetic flux through a noncontractible disk region ending on the horizon, with one constraint relating these. PMID:25479484
Influence of topology on the scale setting
NASA Astrophysics Data System (ADS)
Bergner, G.; Montvay, I.; Giudice, P.; Münster, G.; Piemonte, S.
2015-11-01
Recently a new method to set the scale in lattice gauge theories, based on the gradient flow generated by the Wilson action, has been proposed, and the systematic errors of the new scales t0 and w0 have been investigated by various groups. The Wilson flow provides also an interesting alternative smoothing procedure particularly useful for the measurement of the topological charge as a pure gluonic observable. We show the viability of this method for N=1 supersymmetric Yang-Mills theory by analysing the configurations produced by the DESY-Muenster Collaboration. The relation between the scale and the topological charge has been investigated showing a strong correlation. We have found that the scale has a linear dependence on the topological charge, the slope of which increases decreasing the volume and the gluino mass. Moreover we have investigated this dependence as a function of the reference parameter used to define the scale: the tuning of this parameter turns out to be fundamental for a more reliable scale setting. Similar conclusions hold for the Sommer parameter r0.
Layered Topological Crystalline Insulators.
Kim, Youngkuk; Kane, C L; Mele, E J; Rappe, Andrew M
2015-08-21
Topological crystalline insulators (TCIs) are insulating materials whose topological property relies on generic crystalline symmetries. Based on first-principles calculations, we study a three-dimensional (3D) crystal constructed by stacking two-dimensional TCI layers. Depending on the interlayer interaction, the layered crystal can realize diverse 3D topological phases characterized by two mirror Chern numbers (MCNs) (μ1,μ2) defined on inequivalent mirror-invariant planes in the Brillouin zone. As an example, we demonstrate that new TCI phases can be realized in layered materials such as a PbSe (001) monolayer/h-BN heterostructure and can be tuned by mechanical strain. Our results shed light on the role of the MCNs on inequivalent mirror-symmetric planes in reciprocal space and open new possibilities for finding new topological materials. PMID:26340198
Layered Topological Crystalline Insulators
NASA Astrophysics Data System (ADS)
Kim, Youngkuk; Kane, C. L.; Mele, E. J.; Rappe, Andrew M.
2015-08-01
Topological crystalline insulators (TCIs) are insulating materials whose topological property relies on generic crystalline symmetries. Based on first-principles calculations, we study a three-dimensional (3D) crystal constructed by stacking two-dimensional TCI layers. Depending on the interlayer interaction, the layered crystal can realize diverse 3D topological phases characterized by two mirror Chern numbers (MCNs) (μ1,μ2 ) defined on inequivalent mirror-invariant planes in the Brillouin zone. As an example, we demonstrate that new TCI phases can be realized in layered materials such as a PbSe (001) monolayer/h -BN heterostructure and can be tuned by mechanical strain. Our results shed light on the role of the MCNs on inequivalent mirror-symmetric planes in reciprocal space and open new possibilities for finding new topological materials.
Topological currents in black phosphorus with broken inversion symmetry
NASA Astrophysics Data System (ADS)
Low, Tony; Jiang, Yongjin; Guinea, Francisco
2015-12-01
We examine the nature of topological currents in black phosphorus when its inversion symmetry is deliberately broken. Here, the conduction- and valence-band edges are located at the Γ point of the rectangular Brillouin zone, and they exhibit strong anisotropy along its two crystal axes. We will show below that these salient features lead to linear transverse neutral topological currents, accompanied also by nonlinear transverse charge currents at the Fermi surface. These topological currents are maximal when the in-plane electric field is applied along the zigzag crystal axes but zero along the armchair direction.
Universal Finite-Size Scaling around Topological Quantum Phase Transitions
NASA Astrophysics Data System (ADS)
Gulden, Tobias; Janas, Michael; Wang, Yuting; Kamenev, Alex
2016-01-01
The critical point of a topological phase transition is described by a conformal field theory, where finite-size corrections to energy are uniquely related to its central charge. We investigate the finite-size scaling away from criticality and find a scaling function, which discriminates between phases with different topological indices. This function appears to be universal for all five Altland-Zirnbauer symmetry classes with nontrivial topology in one spatial dimension. We obtain an analytic form of the scaling function and compare it with numerical results.
Photonic Floquet Topological Insulators
NASA Astrophysics Data System (ADS)
Rechtsman, Mikael; Zeuner, Julia; Plotnik, Yonatan; Segev, Mordechai; Szameit, Alexander
2013-03-01
The topological insulator is a fundamentally new phase of matter, with the property that the conduction of electrons occurs only on the surface, not in the bulk. Perhaps the most fascinating and technologically important aspect of this material is ``topological protection,'' the total lack of scattering of electrons by disorder. This effect occurs at room temperature and without an external magnetic field, unlike in quantum Hall systems, which require extremely low temperatures and a strong field. Topological protection is predicted to have wide-ranging applications in fault-tolerant quantum computing and spintronics. Recently, a large theoretical effort has been directed towards achieving topological protection of light at optical frequencies for applications in optical isolation and robust photon transport. Here, we theoretically propose and experimentally demonstrate the topological protection of light, without the need for an external field. The system is composed of an array of spiralling waveguides, evanescently coupled to one another, and arranged in a honeycomb lattice. The chirality of the waveguides results in scatter-free, one-way edge states that are topologically protected from scattering.
NASA Astrophysics Data System (ADS)
Budich, Jan Carl; Diehl, Sebastian
2015-04-01
We investigate the topological properties of density matrices, motivated by the question to what extent phenomena such as topological insulators and superconductors can be generalized to mixed states in the framework of open quantum systems. The notion of geometric phases has been extended from pure to mixed states by Uhlmann [Rep. Math. Phys. 24, 229 (1986), 10.1016/0034-4877(86)90055-8], who discovered an emergent gauge theory over the density matrices based on their pure state representation in a larger Hilbert space. However, since the uniquely defined square root √{ρ } of a density matrix ρ provides a global gauge, this construction is always topologically trivial. Here, we study a more restrictive gauge structure which can be topologically nontrivial and is capable of resolving homotopically distinct mappings of density matrices subject to various spectral constraints. Remarkably, in this framework, topological invariants can be directly defined and calculated for mixed states. In the limit of pure states, the well-known system of topological invariants for gapped band structures at zero temperature is reproduced. We compare our construction with recent approaches to Chern insulators at finite temperature.
1996-07-01
The time dependence of B{sub d}{sup 0}-B{sub d}{sup 0} mixing has been measured using a sample of 150,000 hadronic Z{sup 0} decays collected by the SLD experiment at the SLC between 1993 and 1995. The analysis identifies the semileptonic decays of B mesons with high (p, p{sub t}) leptons and reconstructs the B meson decay length and charge by vertexing the lepton with a partially reconstructed D meson. Vertex charge is used to enrich the selection of neutral over charged B mesons. This method results in a sample of 581 neutral decays with high charge purity. The B candidate is tagged at production with a combined tag that exploits the large polarized b forward-backward asymmetry in conjunction with the opposite hemisphere b jet charge. The final state is tagged by the sign of the high (p, p{sub t}) lepton. From their preliminary analysis the authors find a mass difference between the two B{sub d}{sup 0} mass eigenstates of, {Delta}m{sub d} = 0.452 {+-} 0.074(stat) {+-} 0.049(syst) ps{sup {minus}1}.
NASA Astrophysics Data System (ADS)
He, Cheng; Lin, Liang; Sun, Xiao-Chen; Liu, Xiao-Ping; Lu, Ming-Hui; Chen, Yan-Feng
2014-01-01
As exotic phenomena in optics, topological states in photonic crystals have drawn much attention due to their fundamental significance and great potential applications. Because of the broken time-reversal symmetry under the influence of an external magnetic field, the photonic crystals composed of magneto-optical materials will lead to the degeneracy lifting and show particular topological characters of energy bands. The upper and lower bulk bands have nonzero integer topological numbers. The gapless edge states can be realized to connect two bulk states. This topological photonic states originated from the topological property can be analogous to the integer quantum Hall effect in an electronic system. The gapless edge state only possesses a single sign of gradient in the whole Brillouin zone, and thus the group velocity is only in one direction leading to the one-way energy flow, which is robust to disorder and impurity due to the nontrivial topological nature of the corresponding electromagnetic states. Furthermore, this one-way edge state would cross the Brillouin center with nonzero group velocity, where the negative-zero-positive phase velocity can be used to realize some interesting phenomena such as tunneling and backward phase propagation. On the other hand, under the protection of time-reversal symmetry, a pair of gapless edge states can also be constructed by using magnetic-electric coupling meta-materials, exhibiting Fermion-like spin helix topological edge states, which can be regarded as an optical counterpart of topological insulator originating from the spin-orbit coupling. The aim of this article is to have a comprehensive review of recent research literatures published in this emerging field of photonic topological phenomena. Photonic topological states and their related phenomena are presented and analyzed, including the chiral edge states, polarization dependent transportation, unidirectional waveguide and nonreciprocal optical transmission, all of which might lead to novel applications such as one-way splitter, optical isolator and delay line. In addition, the possible prospect and development of related topics are also discussed.
Geometry of complex networks and topological centrality
NASA Astrophysics Data System (ADS)
Ranjan, Gyan; Zhang, Zhi-Li
2013-09-01
We explore the geometry of complex networks in terms of an n-dimensional Euclidean embedding represented by the Moore-Penrose pseudo-inverse of the graph Laplacian (L). The squared distance of a node i to the origin in this n-dimensional space (lii+), yields a topological centrality index, defined as C∗(i)=1/lii+. In turn, the sum of reciprocals of individual node centralities, ∑i1/C∗(i)=∑ilii+, or the trace of L, yields the well-known Kirchhoff index (K), an overall structural descriptor for the network. To put into context this geometric definition of centrality, we provide alternative interpretations of the proposed indices that connect them to meaningful topological characteristics - first, as forced detour overheads and frequency of recurrences in random walks that has an interesting analogy to voltage distributions in the equivalent electrical network; and then as the average connectedness of i in all the bi-partitions of the graph. These interpretations respectively help establish the topological centrality (C∗(i)) of node i as a measure of its overall position as well as its overall connectedness in the network; thus reflecting the robustness of i to random multiple edge failures. Through empirical evaluations using synthetic and real world networks, we demonstrate how the topological centrality is better able to distinguish nodes in terms of their structural roles in the network and, along with Kirchhoff index, is appropriately sensitive to perturbations/re-wirings in the network.
Alles, B.; D'Elia, M.; Di Giacomo, A.; Pica, C.
2006-11-01
A Ginsparg-Wilson based calibration of the topological charge is used to calculate the renormalization constants which appear in the field-theoretical determination of the topological susceptibility on the lattice. A systematic comparison is made with calculations based on cooling. The two methods agree within present statistical errors (3%-4%). We also discuss the independence of the multiplicative renormalization constant Z from the background topological charge used to determine it.
LHCb Topological Trigger Reoptimization
NASA Astrophysics Data System (ADS)
Likhomanenko, Tatiana; Ilten, Philip; Khairullin, Egor; Rogozhnikov, Alex; Ustyuzhanin, Andrey; Williams, Michael
2015-12-01
The main b-physics trigger algorithm used by the LHCb experiment is the so- called topological trigger. The topological trigger selects vertices which are a) detached from the primary proton-proton collision and b) compatible with coming from the decay of a b-hadron. In the LHC Run 1, this trigger, which utilized a custom boosted decision tree algorithm, selected a nearly 100% pure sample of b-hadrons with a typical efficiency of 60-70%; its output was used in about 60% of LHCb papers. This talk presents studies carried out to optimize the topological trigger for LHC Run 2. In particular, we have carried out a detailed comparison of various machine learning classifier algorithms, e.g., AdaBoost, MatrixNet and neural networks. The topological trigger algorithm is designed to select all ’interesting” decays of b-hadrons, but cannot be trained on every such decay. Studies have therefore been performed to determine how to optimize the performance of the classification algorithm on decays not used in the training. Methods studied include cascading, ensembling and blending techniques. Furthermore, novel boosting techniques have been implemented that will help reduce systematic uncertainties in Run 2 measurements. We demonstrate that the reoptimized topological trigger is expected to significantly improve on the Run 1 performance for a wide range of b-hadron decays.
Detectability of Torus Topology
NASA Astrophysics Data System (ADS)
Fabre, Ophélia; Prunet, Simon; Uzan, Jean-Philippe
2014-05-01
The global shape, or topology, of the universe is not constrained by the equations of General Relativity, which only describe the local universe. As a consequence, the boundaries of space are not fixed and topologies different from the trivial infinite Euclidean space are possible. The cosmic microwave background (CMB) is the most efficient tool to study topology and test alternative models. Multi-connected topologies, such as the 3-torus, are of great interest because they are anisotropic and allow us to test a possible violation of isotropy in CMB data. We show that the correlation function of the coefficients of the expansion of the temperature and polarization anisotropies in spherical harmonics encodes a topological signature. This signature can be used to distinguish an infinite space from a multi-connected space on sizes larger than the diameter of the last scattering surface (D LSS ). With the help of the Kullback-Leibler divergence, we set the size of the edge of the biggest distinguishable torus with CMB temperature fluctuations and E-modes of polarization to 1.15 D LSS . CMB temperature fluctuations allow us to detect universes bigger than the observable universe, whereas E-modes are efficient to detect universes smaller than the observable universe.
Polydispersity-driven topological defects as order-restoring excitations.
Yao, Zhenwei; Olvera de la Cruz, Monica
2014-04-01
The engineering of defects in crystalline matter has been extensively exploited to modify the mechanical and electrical properties of many materials. Recent experiments on manipulating extended defects in graphene, for example, show that defects direct the flow of electric charges. The fascinating possibilities offered by defects in two dimensions, known as topological defects, to control material properties provide great motivation to perform fundamental investigations to uncover their role in various systems. Previous studies mostly focus on topological defects in 2D crystals on curved surfaces. On flat geometries, topological defects can be introduced via density inhomogeneities. We investigate here topological defects due to size polydispersity on flat surfaces. Size polydispersity is usually an inevitable feature of a large variety of systems. In this work, simulations show well-organized induced topological defects around an impurity particle of a wrong size. These patterns are not found in systems of identical particles. Our work demonstrates that in polydispersed systems topological defects play the role of restoring order. The simulations show a perfect hexagonal lattice beyond a small defective region around the impurity particle. Elasticity theory has demonstrated an analogy between the elementary topological defects named disclinations to electric charges by associating a charge to a disclination, whose sign depends on the number of its nearest neighbors. Size polydispersity is shown numerically here to be an essential ingredient to understand short-range attractions between like-charge disclinations. Our study suggests that size polydispersity has a promising potential to engineer defects in various systems including nanoparticles and colloidal crystals. PMID:24706918
Topology of three-dimensional separated flows
NASA Technical Reports Server (NTRS)
Tobak, M.; Peake, D. J.
1981-01-01
Based on the hypothesis that patterns of skin-friction lines and external streamlines reflect the properties of continuous vector fields, topology rules define a small number of singular points (nodes, saddle points, and foci) that characterize the patterns on the surface and on particular projections of the flow (e.g., the crossflow plane). The restricted number of singular points and the rules that they obey are considered as an organizing principle whose finite number of elements can be combined in various ways to connect together the properties common to all steady three dimensional viscous flows. Introduction of a distinction between local and global properties of the flow resolves an ambiguity in the proper definition of a three dimensional separated flow. Adoption of the notions of topological structure, structural stability, and bifurcation provides a framework to describe how three dimensional separated flows originate and succeed each other as the relevant parameters of the problem are varied.
Wannier Center Sheets in Topological Insulators
NASA Astrophysics Data System (ADS)
Taherinejad, Maryam; Garrity, Kevin; Vanderbilt, David
2014-03-01
The electronic ground state in a periodic crystalline insulator can be described by hybrid Wannier functions | Wnlz(kx ,ky) > which are maximally localized in one direction and Bloch-like in the other two. In 3D insulators the Wannier charge centers (WCCs), defined as zn(kx ,ky) = < Wn 0(kx ,ky) | z& circ; |Wn 0(kx ,ky) > , are functions of momentum in two dimensions and can be plotted as sheets over the 2D Brillouin zone. We show that the symmetry group of the WCCs zn(kx ,ky) includes all the symmetries of surface energy bands ɛn(kx ,ky) . More importantly, the WCCs contain the same kind of topological information as is carried in the surface energy bands, with the crucial advantage that the topological properties of the bulk can be deduced from bulk properties alone. The distinct topological behavior of these WCC sheets in trivial, Chern, weak, strong, and crystalline topological insulators are demonstrated using different tight-binding models. The WCC sheets calculated from first-principles calculations in Z2-even Sb2Se3, weak Z2-odd KHgSb, and strong Z2-odd Bi2Se3 confirm the results from the tight-binding models. Supported by NSF Grant DMR-10-05838.
Topology optimized microbioreactors.
Schäpper, Daniel; Lencastre Fernandes, Rita; Lantz, Anna Eliasson; Okkels, Fridolin; Bruus, Henrik; Gernaey, Krist V
2011-04-01
This article presents the fusion of two hitherto unrelated fields--microbioreactors and topology optimization. The basis for this study is a rectangular microbioreactor with homogeneously distributed immobilized brewers yeast cells (Saccharomyces cerevisiae) that produce a recombinant protein. Topology optimization is then used to change the spatial distribution of cells in the reactor in order to optimize for maximal product flow out of the reactor. This distribution accounts for potentially negative effects of, for example, by-product inhibition. We show that the theoretical improvement in productivity is at least fivefold compared with the homogeneous reactor. The improvements obtained by applying topology optimization are largest where either nutrition is scarce or inhibition effects are pronounced. PMID:21404253
NASA Astrophysics Data System (ADS)
Pugh, David John Rhydwyn
1990-09-01
This report describes work done in collaboration with Mike Teper using Phillips and Stone's geometric algorithm to measure the topology of gauge fields on the lattice. The algorithm has been around for a number of years, and in that time has been used for exhaustive calculations of the density of topological fluctuations in the SU(2) gauge vacuum [4-6]. At first sight these appear to show good scaling; better in fact than any other quantity investigated so far. Unfortunately the results disagree by an order of magnitude with other methods, and it was in order to resolve the inconsistency that this work was carried out. Having programmed the geometric algorithm ourselves and examined the results in detail [1,2,8,9], we believe it to be dominated by lattice artifacts, and therefore not a good measure of the physical topology. Instead we suggest it is used in conjunction with some smoothening process such as blocking.
NASA Astrophysics Data System (ADS)
He, Yuan-Yao; Wu, Han-Qing; You, Yi-Zhuang; Xu, Cenke; Meng, Zi Yang; Lu, Zhong-Yi
2016-03-01
It is expected that the interplay between nontrivial band topology and strong electron correlation will lead to very rich physics. Thus a controlled study of the competition between topology and correlation is of great interest. Here, employing large-scale quantum Monte Carlo simulations, we provide a concrete example of the Kane-Mele-Hubbard model on an AA-stacking bilayer honeycomb lattice with interlayer antiferromagnetic interaction. Our simulation identified several different phases: a quantum spin Hall insulator (QSH), an x y -plane antiferromagnetic Mott insulator, and an interlayer dimer-singlet insulator. Most importantly, a bona fide topological phase transition between the QSH and the dimer-singlet insulators, purely driven by the interlayer antiferromagnetic interaction, is found. At the transition, the spin and charge gap of the system close while the single-particle excitations remain gapped, which means that this transition has no mean-field analog and it can be viewed as a transition between bosonic symmetry-protected topological (SPT) states. At one special point, this transition is described by a (2 +1 )d O (4 ) nonlinear sigma model with exact S O (4 ) symmetry and a topological term at exactly Θ =π . The relevance of this work towards more general interacting SPT states is discussed.
Andreev Bound States in a One-Dimensional Topological Superconductor
NASA Astrophysics Data System (ADS)
Liu, Xiong-Jun
2012-09-01
We study the charge character of the Andreev bound states (ABSs) in one-dimensional topological superconductors with spatial inversion symmetry (SIS) breaking. Despite the absence of the SIS, we show a hidden symmetry for the Bogoliubov-de Gennes equations around Fermi points in addition to the particle-hole symmetry. This hidden symmetry protects that the charge of the ABSs is solely dependent on the corresponding Fermi velocities. On the other hand, if the SIS is present, the ABSs are charge neutral, similar to Majorana fermions. We also propose that the charge of the ABSs can be experimentally measured in the tunneling transport spectroscopy from the resonant differential tunneling conductance.
Probing the Chiral Anomaly with Nonlocal Transport in Three-Dimensional Topological Semimetals
NASA Astrophysics Data System (ADS)
Parameswaran, S. A.; Grover, T.; Abanin, D. A.; Pesin, D. A.; Vishwanath, A.
2014-07-01
Weyl semimetals are three-dimensional crystalline systems where pairs of bands touch at points in momentum space, termed Weyl nodes, that are characterized by a definite topological charge: the chirality. Consequently, they exhibit the Adler-Bell-Jackiw anomaly, which in this condensed-matter realization implies that the application of parallel electric (E) and magnetic (B) fields pumps electrons between nodes of opposite chirality at a rate proportional to E .B. We argue that this pumping is measurable via nonlocal transport experiments, in the limit of weak internode scattering. Specifically, we show that as a consequence of the anomaly, applying a local magnetic field parallel to an injected current induces a valley imbalance that diffuses over long distances. A probe magnetic field can then convert this imbalance into a measurable voltage drop far from source and drain. Such nonlocal transport vanishes when the injected current and magnetic field are orthogonal and therefore serves as a test of the chiral anomaly. We further demonstrate that a similar effect should also characterize Dirac semimetals—recently reported to have been observed in experiments—where the coexistence of a pair of Weyl nodes at a single point in the Brillouin zone is protected by a crystal symmetry. Since the nodes are analogous to valley degrees of freedom in semiconductors, the existence of the anomaly suggests that valley currents in three-dimensional topological semimetals can be controlled using electric fields, which has potential practical "valleytronic" applications.
Quantum Phase Slips in Topological Josephson Junction Rings
NASA Astrophysics Data System (ADS)
Rodriguez Mota, Rosa; Vishveshwara, Smitha; Pereg-Barnea, Tami
We study quantum phase slip processes (QPS) in a ring of N topological superconducting islands joined by Josephson junctions and threaded by magnetic flux. In this array, neighboring islands interact through the usual charge 2e Josephson tunneling and the Majorana assisted charge e tunneling. When the charging energy associated with the island's capacitance is zero, the energy vs. flux relation of the system is characterized by parabolas centered around even or odd multiples of the superconducting flux quantum, depending on the parity of the system. For small but non-zero charging energy, quantum fluctuations can lead to tunneling between these classical states. In this work, we calculate the amplitude of these tunneling processes, commonly known as quantum phase slips. We also add gate voltages to our system and study how the amplitude of QPS in these topological Josephson array is modified by Aharanov-Casher interference effects.
Rendering the Topological Spines
Nieves-Rivera, D.
2015-05-05
Many tools to analyze and represent high dimensional data already exits yet most of them are not flexible, informative and intuitive enough to help the scientists make the corresponding analysis and predictions, understand the structure and complexity of scientific data, get a complete picture of it and explore a greater number of hypotheses. With this in mind, N-Dimensional Data Analysis and Visualization (ND²AV) is being developed to serve as an interactive visual analysis platform with the purpose of coupling together a number of these existing tools that range from statistics, machine learning, and data mining, with new techniques, in particular with new visualization approaches. My task is to create the rendering and implementation of a new concept called topological spines in order to extend ND²AV's scope. Other existing visualization tools create a representation preserving either the topological properties or the structural (geometric) ones because it is challenging to preserve them both simultaneously. Overcoming such challenge by creating a balance in between them, the topological spines are introduced as a new approach that aims to preserve them both. Its render using OpenGL and C++ and is currently being tested to further on be implemented on ND²AV. In this paper I will present what are the Topological Spines and how they are rendered.
Topological Crystalline Insulators
NASA Astrophysics Data System (ADS)
Hsieh, Timothy
2015-03-01
Topological crystalline insulators (TCI) are new phases of matter in which nontrivial band topology and crystal symmetry unite to protect metallic states on the boundary. Remarkably, TCIs have been predicted and observed in the conveniently simple rocksalt SnTe class of IV-VI semiconductors. Despite the simple crystal structure, the interplay between topology and crystal symmetry in these materials have led to a rich variety of new phenomena, including the coexistence of massless and massive Dirac fermions arising from ferroelectric distortion and strain-induced flat band superconductivity. These new physical mechanisms are not only of intrinsic interest but may also find application in new transistor devices. After discussing the topological nature and potential uses of IV-VI family TCIs, I will present recent predictions of TCIs in several anti-perovskite materials. The origin of TCI in this new class of materials is strikingly different and involves the band inversion of two J = 3/2 quartets of Dirac fermions, which together form a ``Dirac octet.'' As interactions play a significant role in many anti-perovskites, this prediction serves as first step toward realizing TCIs in strongly correlated systems. This work is supported by NSF Graduate Research Fellowship No. 0645960 and DOE Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-SC0010526.
Order, topology and preference
NASA Technical Reports Server (NTRS)
Sertel, M. R.
1971-01-01
Some standard order-related and topological notions, facts, and methods are brought to bear on central topics in the theory of preference and the theory of optimization. Consequences of connectivity are considered, especially from the viewpoint of normally preordered spaces. Examples are given showing how the theory of preference, or utility theory, can be applied to social analysis.
Synthesising Topological Links
Baas, Nils A.; Seeman, Nadrian C.; Stacey, Andrew
2014-01-01
We discuss the chemical synthesis of topological links, in particular higher order links which have the Brunnian property (namely that removal of any one component unlinks the entire system). Furthermore, we suggest how to obtain both two dimensional and three dimensional objects (surfaces and solids, respectively) which also have this Brunnian property. PMID:25678732
Symmetry Protected Josephson Supercurrents in Three-Dimensional Topological Insulators
NASA Astrophysics Data System (ADS)
Cho, Sungjae; Dellabetta, Brian; Yang, Alina; Schneeloch, John; Xu, Zhijun; Valla, Tonica; Gu, Genda; Gilbert, Matthew; Mason, Nadya
2013-03-01
Coupling the surface state of a topological insulator (TI) to an s-wave superconductor is predicted to produce the long-sought Majorana quasiparticle excitations. However, superconductivity has not been measured in surface states when the bulk charge carriers are fully depleted, i.e., in the true topological regime relevant for investigating Majorana modes. Here, we report measurements of DC Josephson effects in TI-superconductor junctions as the chemical potential is moved through the true topological regime characterized by the presence of only surface currents. We compare our results to 3D quantum transport simulations, and determine the effects of bulk/surface mixing, disorder, and magnetic field; in particular, we show that the supercurrent is largely carried by surface states, due to the inherent topology of the bands, and that it is robust against disorder. Our results thus clarify key open issues regarding the nature of supercurrents in TIs.
TOPPER: Topology Prediction of Transmembrane Protein Based on Evidential Reasoning
Deng, Xinyang; Liu, Qi; Hu, Yong; Deng, Yong
2013-01-01
The topology prediction of transmembrane protein is a hot research field in bioinformatics and molecular biology. It is a typical pattern recognition problem. Various prediction algorithms are developed to predict the transmembrane protein topology since the experimental techniques have been restricted by many stringent conditions. Usually, these individual prediction algorithms depend on various principles such as the hydrophobicity or charges of residues. In this paper, an evidential topology prediction method for transmembrane protein is proposed based on evidential reasoning, which is called TOPPER (topology prediction of transmembrane protein based on evidential reasoning). In the proposed method, the prediction results of multiple individual prediction algorithms can be transformed into BPAs (basic probability assignments) according to the confusion matrix. Then, the final prediction result can be obtained by the combination of each individual prediction base on Dempster's rule of combination. The experimental results show that the proposed method is superior to the individual prediction algorithms, which illustrates the effectiveness of the proposed method. PMID:23401665
Anomalous Quasiparticles on the Domain Wall Between Topological Insulators and Spin Ice Compounds
NASA Astrophysics Data System (ADS)
Kanazawa, I.; Sasaki, T.
We have discussed the behavior of anomalous quasiparticle with fractional electronic charge on the domain wall between topological insulators and spin ice compounds from the standpoint of the field-theoretical formula.
NASA Astrophysics Data System (ADS)
Xu, B.; Jiang, W. S.; Zhu, Q. S.
2015-05-01
In this work, we concentrate on the hierarchy and completeness of roof topology, and the aim is to avoid or correct the errors in roof topology. The hierarchy of topology is expressed by the hierarchical roof topology graph (HRTG) in accord with the definition of CityGML LOD (level of details). We decompose the roof topology graph (RTG) with a progressive approach while maintain the integrality and consistency of the data set simultaneously. Common feathers like collinear ridges or boundaries are calculated integrally to maintain their completeness. The roof items will only detected locally to decrease the error caused by data spare or mutual interference. Finally, a topology completeness test is adopted to detect and correct errors in roof topology, which results in a complete and hierarchical building model. Experiments shows that our methods have obvious improvements to the RTG based reconstruction method, especially for sparse data or roof topology with ambiguous.
Topological defects at finite temperature
Bazeia, D.; Eboli, O.J.P.; Guerra, J.M. Jr.; Marques, G.C.
1987-11-15
We obtain the phase diagram of gauge theories by studying the influence of topologically nontrivial boundary conditions. For this reason, we develop a scheme for computing the free energy of topological defects at finite temperature. As an application, the free energy of topological defects for the minimal SU(5) model are evaluated in the semiclassical approximation.
Noncommuting Momenta of Topological Solitons
NASA Astrophysics Data System (ADS)
Watanabe, Haruki; Murayama, Hitoshi
2014-05-01
We show that momentum operators of a topological soliton may not commute among themselves when the soliton is associated with the second cohomology H2 of the target space. The commutation relation is proportional to the winding number, taking a constant value within each topological sector. The noncommutativity makes it impossible to specify the momentum of a topological soliton, and induces a Magnus force.
Topological spin transport by Brownian diffusion of domain walls
NASA Astrophysics Data System (ADS)
Kim, Se Kwon; Takei, So; Tserkovnyak, Yaroslav
2015-12-01
We propose thermally populated domain walls (DWs) in an easy-plane ferromagnetic insulator as robust spin carriers between two metals. The chirality of a DW, which serves as a topological charge, couples to the metal spin accumulation via spin-transfer torque and results in the chirality-dependent thermal nucleation rates of DWs at the interface. After overpopulated DWs of a particular (net) chirality diffuse and leave the ferromagnet at the other interface, they reemit the spin current by spin pumping. The conservation of the topological charge supports an algebraic decay of spin transport as the length of the ferromagnet increases; this is analogous to the decaying behavior of superfluid spin transport but contrasts with the exponential decay of magnon spin transport. We envision that similar spin transport with algebraic decay may be implemented in materials with exotic spin phases by exploiting topological characteristics and the associated conserved quantities of their excitations.
Topological Photonic Quasicrystals: Fractal Topological Spectrum and Protected Transport
NASA Astrophysics Data System (ADS)
Bandres, Miguel A.; Rechtsman, Mikael C.; Segev, Mordechai
2016-01-01
We show that it is possible to have a topological phase in two-dimensional quasicrystals without any magnetic field applied, but instead introducing an artificial gauge field via dynamic modulation. This topological quasicrystal exhibits scatter-free unidirectional edge states that are extended along the system's perimeter, contrary to the states of an ordinary quasicrystal system, which are characterized by power-law decay. We find that the spectrum of this Floquet topological quasicrystal exhibits a rich fractal (self-similar) structure of topological "minigaps," manifesting an entirely new phenomenon: fractal topological systems. These topological minigaps form only when the system size is sufficiently large because their gapless edge states penetrate deep into the bulk. Hence, the topological structure emerges as a function of the system size, contrary to periodic systems where the topological phase can be completely characterized by the unit cell. We demonstrate the existence of this topological phase both by using a topological index (Bott index) and by studying the unidirectional transport of the gapless edge states and its robustness in the presence of defects. Our specific model is a Penrose lattice of helical optical waveguides—a photonic Floquet quasicrystal; however, we expect this new topological quasicrystal phase to be universal.
Electromagnetic effect on disordered surface of topological insulators
NASA Astrophysics Data System (ADS)
Taguchi, Katsuhisa; Shintani, Kunitaka; Tanaka, Yukio
2016-02-01
We theoretically study electromagnetic effects due to magnetization on disordered surface of topological insulators with attaching a ferromagnetic insulator junction by using the result of the magnetization dynamics induced charge flow. We find that the electric polarization is induced by not only the magnetization but also the spatial derivative of the magnetization with the diffusion on the disordered surface.
Combinational reasoning of quantitative fuzzy topological relations for simple fuzzy regions.
Liu, Bo; Li, Dajun; Xia, Yuanping; Ruan, Jian; Xu, Lili; Wu, Huanyi
2015-01-01
In recent years, formalization and reasoning of topological relations have become a hot topic as a means to generate knowledge about the relations between spatial objects at the conceptual and geometrical levels. These mechanisms have been widely used in spatial data query, spatial data mining, evaluation of equivalence and similarity in a spatial scene, as well as for consistency assessment of the topological relations of multi-resolution spatial databases. The concept of computational fuzzy topological space is applied to simple fuzzy regions to efficiently and more accurately solve fuzzy topological relations. Thus, extending the existing research and improving upon the previous work, this paper presents a new method to describe fuzzy topological relations between simple spatial regions in Geographic Information Sciences (GIS) and Artificial Intelligence (AI). Firstly, we propose a new definition for simple fuzzy line segments and simple fuzzy regions based on the computational fuzzy topology. And then, based on the new definitions, we also propose a new combinational reasoning method to compute the topological relations between simple fuzzy regions, moreover, this study has discovered that there are (1) 23 different topological relations between a simple crisp region and a simple fuzzy region; (2) 152 different topological relations between two simple fuzzy regions. In the end, we have discussed some examples to demonstrate the validity of the new method, through comparisons with existing fuzzy models, we showed that the proposed method can compute more than the existing models, as it is more expressive than the existing fuzzy models. PMID:25775452
EDITORIAL: Topological data analysis Topological data analysis
NASA Astrophysics Data System (ADS)
2011-12-01
Inverse problems can be defined as the area of mathematics that attempts to reconstruct a physical or mathematical object from derived data. Frequently, this means the evaluation of parameters or other numerical quantities (such as eigenvalues) that characterize or provide information about the system. There are, however, other aspects of a system that are important, but are not as readily summarized by numerical quantities. If one considers observations of diabetic patients (using metabolic quantities), one will find that the data breaks up into components, or pieces, corresponding to distinct forms of the disease. The decomposition of data sets into disjoint pieces, or clustering, is an aspect of the study of the shape of the data, albeit one that has been extensively studied. A more complex notion of shape appears in observations of a predator-prey system governed by a Lotka-Volterra equation. One would find that exact observations, consisting of (prey population, predator population) pairs, appear to lie along a simple closed curve in the plane. The fact that the data lies along such a closed curve is an important piece of information, since it suggests that the system displays recurrent behavior. If one did not know, a priori, that the system is governed by a Lotka-Volterra equation, then it would not be immediately obvious that the system is undergoing recurrent motion, and this deduction would constitute a significant insight. In this case, it is again the shape of the data, namely the fact that it lies on a simple closed curve, which is the key insight. Shape is a somewhat nebulous concept, which at first blush may be too intuitive to make precise mathematically, and describe quantitatively. Within pure mathematics, the disciplines of topology and differential geometry are designed exactly to address this problem. They provide explicit signatures which, in precise senses, quantify and describe the shape of a geometric object. In addition, they provide methods for discretizing and compressing the information present in a geometric object so as to provide a useful, small representation of the object. The articles in this special issue are concerned with the applications of topology to the analysis of data sets. The adaptation of topological techniques from pure mathematics to the study of data from real systems is a project which has been undertaken during the past two decades, and the present volume contains various contributions to that project. At the current state of development, homology and persistence are two of the most popular topological techniques used in this context. Homology goes back to the beginnings of topology in Poincaré's influential papers. It is the idea that the connectivity of a space is determined by its cycles of different dimensions, and that these cycles organize themselves into abelian groups, called homology groups. Better known than these groups are their ranks, the Betti numbers of the space, which are non-negative integers that count the number of independent cycles in each dimension. To give an example, the zeroth Betti number counts the components, and the first counts the loops. A crucial feature of homology groups is that, given a reasonably explicit description of a space, their computation is an exercise in linear algebra. Even better known than the Betti numbers is the Euler characteristic, which we know from Poincaré's work, is equal to the alternating sum of the Betti numbers, which can be computed without computing the homology groups themselves. To give evidence that these numbers have relevant practical applications, we mention that integrating the Euler characteristic over a domain with sensor information can be used to count objects in the domain. This alone would not explain the popularity of homology groups, which we see rooted in the fact that they hit a sweet-spot that offers relatively strong discriminative power, and a clear intuitive meaning, all at a surprisingly low computational cost. Even these desirable qualities would not be sufficient if it were not possible to overcome a serious shortcoming, namely the high sensitivity of homology to minor mistakes in the data collection. Because of the finite nature of most data sets, the notion of shape within data sets is inevitably stochastic. To some extent this is because of the uncertainty of what a shape in nature is, but more importantly, the available data can only be used to give an estimate for the probability of a given shape. This has led to the study of persistent homology, in which the invariants are in the form of 'persistence diagrams' or 'barcodes'. These invariants quantify the stability of geometric features with respect to perturbations that, in turn, provide a basis for discriminating between artifacts caused by noise or undersampling and real phenomena. Several papers in this volume deal with questions about these diagrams, and some deal with probabilistic issues related to the occurrence of these diagrams. Our hope is that the papers in this volume will provide exposure of these techniques to both a wider audience of mathematicians and also potential users of the techniques. Charles Epstein, Gunnar Carlsson and Herbert Edelsbrunner Guest Editors
EDITORIAL: Topological data analysis Topological data analysis
NASA Astrophysics Data System (ADS)
Epstein, Charles; Carlsson, Gunnar; Edelsbrunner, Herbert
2011-12-01
Inverse problems can be defined as the area of mathematics that attempts to reconstruct a physical or mathematical object from derived data. Frequently, this means the evaluation of parameters or other numerical quantities (such as eigenvalues) that characterize or provide information about the system. There are, however, other aspects of a system that are important, but are not as readily summarized by numerical quantities. If one considers observations of diabetic patients (using metabolic quantities), one will find that the data breaks up into components, or pieces, corresponding to distinct forms of the disease. The decomposition of data sets into disjoint pieces, or clustering, is an aspect of the study of the shape of the data, albeit one that has been extensively studied. A more complex notion of shape appears in observations of a predator-prey system governed by a Lotka-Volterra equation. One would find that exact observations, consisting of (prey population, predator population) pairs, appear to lie along a simple closed curve in the plane. The fact that the data lies along such a closed curve is an important piece of information, since it suggests that the system displays recurrent behavior. If one did not know, a priori, that the system is governed by a Lotka-Volterra equation, then it would not be immediately obvious that the system is undergoing recurrent motion, and this deduction would constitute a significant insight. In this case, it is again the shape of the data, namely the fact that it lies on a simple closed curve, which is the key insight. Shape is a somewhat nebulous concept, which at first blush may be too intuitive to make precise mathematically, and describe quantitatively. Within pure mathematics, the disciplines of topology and differential geometry are designed exactly to address this problem. They provide explicit signatures which, in precise senses, quantify and describe the shape of a geometric object. In addition, they provide methods for discretizing and compressing the information present in a geometric object so as to provide a useful, small representation of the object. The articles in this special issue are concerned with the applications of topology to the analysis of data sets. The adaptation of topological techniques from pure mathematics to the study of data from real systems is a project which has been undertaken during the past two decades, and the present volume contains various contributions to that project. At the current state of development, homology and persistence are two of the most popular topological techniques used in this context. Homology goes back to the beginnings of topology in Poincaré's influential papers. It is the idea that the connectivity of a space is determined by its cycles of different dimensions, and that these cycles organize themselves into abelian groups, called homology groups. Better known than these groups are their ranks, the Betti numbers of the space, which are non-negative integers that count the number of independent cycles in each dimension. To give an example, the zeroth Betti number counts the components, and the first counts the loops. A crucial feature of homology groups is that, given a reasonably explicit description of a space, their computation is an exercise in linear algebra. Even better known than the Betti numbers is the Euler characteristic, which we know from Poincaré's work, is equal to the alternating sum of the Betti numbers, which can be computed without computing the homology groups themselves. To give evidence that these numbers have relevant practical applications, we mention that integrating the Euler characteristic over a domain with sensor information can be used to count objects in the domain. This alone would not explain the popularity of homology groups, which we see rooted in the fact that they hit a sweet-spot that offers relatively strong discriminative power, and a clear intuitive meaning, all at a surprisingly low computational cost. Even these desirable qualities would not be sufficient if it were not possible to overcome a serious shortcoming, namely the high sensitivity of homology to minor mistakes in the data collection. Because of the finite nature of most data sets, the notion of shape within data sets is inevitably stochastic. To some extent this is because of the uncertainty of what a shape in nature is, but more importantly, the available data can only be used to give an estimate for the probability of a given shape. This has led to the study of persistent homology, in which the invariants are in the form of 'persistence diagrams' or 'barcodes'. These invariants quantify the stability of geometric features with respect to perturbations that, in turn, provide a basis for discriminating between artifacts caused by noise or undersampling and real phenomena. Several papers in this volume deal with questions about these diagrams, and some deal with probabilistic issues related to the occurrence of these diagrams. Our hope is that the papers in this volume will provide exposure of these techniques to both a wider audience of mathematicians and also potential users of the techniques.
NASA Technical Reports Server (NTRS)
Hunt, W. D.; Brennan, K. F.; Summers, C. J.; Cameron, Thomas P.
1996-01-01
This thesis addresses the acoustoelectric issues concerning the amplification of surface acoustic waves (SAWs) and the reflection of SAWs from slanted reflector gratings on GaAs, with application to a novel acoustic charge transport (ACT) device architecture. First a simple model of the SAWAMP was developed, which was subsequently used to define the epitaxially grown material structure necessary to provide simultaneously high resistance and high electron mobility. In addition, a segmented SAWAMP structure was explored with line widths on the order of an acoustic wavelength. This resulted in the demonstration of SAWAMPS with an order of magnitude less voltage and power requirements than previously reported devices. A two-dimensional model was developed to explain the performance of devices with charge confinement layers less then 0.5 mm, which was experimentally verified. This model was extended to predict a greatly increased gain from the addition of a ZnO overlay. These overlays were experimentally attempted, but no working devices were reported due to process incompatibilities. In addition to the SAWAMP research, the reflection of SAWs from slanted gratings on GaAs was also studied and experimentally determined reflection coefficients for both 45 deg grooves and Al stripes on GaAs have been reported for the first time. The SAWAMp and reflector gratings were combined to investigate the integrated ring oscillator for application to the proposed ACT device and design parameters for this device have been provided.
Circuital characterisation of space-charge motion with a time-varying applied bias
Kim, Chul; Moon, Eun-Yi; Hwang, Jungho; Hong, Hiki
2015-01-01
Understanding the behaviour of space-charge between two electrodes is important for a number of applications. The Shockley-Ramo theorem and equivalent circuit models are useful for this; however, fundamental questions of the microscopic nature of the space-charge remain, including the meaning of capacitance and its evolution into a bulk property. Here we show that the microscopic details of the space-charge in terms of resistance and capacitance evolve in a parallel topology to give the macroscopic behaviour via a charge-based circuit or electric-field-based circuit. We describe two approaches to this problem, both of which are based on energy conservation: the energy-to-current transformation rule, and an energy-equivalence-based definition of capacitance. We identify a significant capacitive current due to the rate of change of the capacitance. Further analysis shows that Shockley-Ramo theorem does not apply with a time-varying applied bias, and an additional electric-field-based current is identified to describe the resulting motion of the space-charge. Our results and approach provide a facile platform for a comprehensive understanding of the behaviour of space-charge between electrodes. PMID:26133999
Circuital characterisation of space-charge motion with a time-varying applied bias.
Kim, Chul; Moon, Eun-Yi; Hwang, Jungho; Hong, Hiki
2015-01-01
Understanding the behaviour of space-charge between two electrodes is important for a number of applications. The Shockley-Ramo theorem and equivalent circuit models are useful for this; however, fundamental questions of the microscopic nature of the space-charge remain, including the meaning of capacitance and its evolution into a bulk property. Here we show that the microscopic details of the space-charge in terms of resistance and capacitance evolve in a parallel topology to give the macroscopic behaviour via a charge-based circuit or electric-field-based circuit. We describe two approaches to this problem, both of which are based on energy conservation: the energy-to-current transformation rule, and an energy-equivalence-based definition of capacitance. We identify a significant capacitive current due to the rate of change of the capacitance. Further analysis shows that Shockley-Ramo theorem does not apply with a time-varying applied bias, and an additional electric-field-based current is identified to describe the resulting motion of the space-charge. Our results and approach provide a facile platform for a comprehensive understanding of the behaviour of space-charge between electrodes. PMID:26133999
Circuital characterisation of space-charge motion with a time-varying applied bias
NASA Astrophysics Data System (ADS)
Kim, Chul; Moon, Eun-Yi; Hwang, Jungho; Hong, Hiki
2015-07-01
Understanding the behaviour of space-charge between two electrodes is important for a number of applications. The Shockley-Ramo theorem and equivalent circuit models are useful for this; however, fundamental questions of the microscopic nature of the space-charge remain, including the meaning of capacitance and its evolution into a bulk property. Here we show that the microscopic details of the space-charge in terms of resistance and capacitance evolve in a parallel topology to give the macroscopic behaviour via a charge-based circuit or electric-field-based circuit. We describe two approaches to this problem, both of which are based on energy conservation: the energy-to-current transformation rule, and an energy-equivalence-based definition of capacitance. We identify a significant capacitive current due to the rate of change of the capacitance. Further analysis shows that Shockley-Ramo theorem does not apply with a time-varying applied bias, and an additional electric-field-based current is identified to describe the resulting motion of the space-charge. Our results and approach provide a facile platform for a comprehensive understanding of the behaviour of space-charge between electrodes.
Seeing the magnetic monopole through the mirror of topological surface states
Qi, Xiao-Liang; Li, Rundong; Zang, Jiadong; Zhang, Shou-Cheng; /Stanford U., Phys. Dept. /Fudan U.
2010-03-25
Existence of the magnetic monopole is compatible with the fundamental laws of nature, however, this illusive particle has yet to be detected experimentally. In this work, we show that an electric charge near the topological surface state induces an image magnetic monopole charge due to the topological magneto-electric effect. The magnetic field generated by the image magnetic monopole can be experimentally measured, and the inverse square law of the field dependence can be determined quantitatively. We propose that this effect can be used to experimentally realize a gas of quantum particles carrying fractional statistics, consisting of the bound states of the electric charge and the image magnetic monopole charge.
DNA topology and transcription
Kouzine, Fedor; Levens, David; Baranello, Laura
2014-01-01
Chromatin is a complex assembly that compacts DNA inside the nucleus while providing the necessary level of accessibility to regulatory factors conscripted by cellular signaling systems. In this superstructure, DNA is the subject of mechanical forces applied by variety of molecular motors. Rather than being a rigid stick, DNA possesses dynamic structural variability that could be harnessed during critical steps of genome functioning. The strong relationship between DNA structure and key genomic processes necessitates the study of physical constrains acting on the double helix. Here we provide insight into the source, dynamics, and biology of DNA topological domains in the eukaryotic cells and summarize their possible involvement in gene transcription. We emphasize recent studies that might inspire and impact future experiments on the involvement of DNA topology in cellular functions. PMID:24755522
Quist, Daniel A.; Gavrilov, Eugene M.; Fisk, Michael E.
2008-01-15
A method enables the topology of an acyclic fully propagated network to be discovered. A list of switches that comprise the network is formed and the MAC address cache for each one of the switches is determined. For each pair of switches, from the MAC address caches the remaining switches that see the pair of switches are located. For each pair of switches the remaining switches are determined that see one of the pair of switches on a first port and the second one of the pair of switches on a second port. A list of insiders is formed for every pair of switches. It is determined whether the insider for each pair of switches is a graph edge and adjacent ones of the graph edges are determined. A symmetric adjacency matrix is formed from the graph edges to represent the topology of the data link network.
Topological States of Heterostructures
NASA Astrophysics Data System (ADS)
Usanmaz, Demet; Nath, Pinku; Plata, Jose J.; Buongiorno Nardelli, Marco; Fornari, Marco; Curtarolo, Stefano
Topological insulators (TIs) have exotic properties, such as having insulating behavior in the bulk and metallic states at the surface [1]. Observations of metallic states rely on the spin-orbit induced band inversion in bulk materials and are protected by time-reversal symmetry or crystal symmetry [ 2 ]. These remarkable characteristics of TIs give rise to various applications from spintronics to quantum computers. In order to broaden the range of applications of TIs and make it more effective, an exploration of high quality heterostructures are required. Creating heterostructures of TIs has recently demonstrated to be advantageous for controlling electronic properties [3]. Inspired by these interesting properties, we have investigated the topological interface states of heterostructures.
Modulated Floquet topological insulators.
Katan, Yaniv Tenenbaum; Podolsky, Daniel
2013-01-01
The application of spatially uniform light on conventional insulators can induce Floquet spectra with characteristics akin to those of topological insulators. We demonstrate that spatial modulation of light allows for remarkable control of the properties in these systems. We provide configurations to generate one-dimensional bulk modes, photoinduced currents, as well as fractionalized excitations. We show a close analogy to p-wave superconductors and use this analogy to explain our results. PMID:23383821
Topological confinement and superconductivity
Al-hassanieh, Dhaled A; Batista, Cristian D
2008-01-01
We derive a Kondo Lattice model with a correlated conduction band from a two-band Hubbard Hamiltonian. This mapping allows us to describe the emergence of a robust pairing mechanism in a model that only contains repulsive interactions. The mechanism is due to topological confinement and results from the interplay between antiferromagnetism and delocalization. By using Density-Matrix-Renormalization-Group (DMRG) we demonstrate that this mechanism leads to dominant superconducting correlations in aID-system.
Photonic topological insulators
NASA Astrophysics Data System (ADS)
Rechtsman, Mikael; Zeuner, Julia; Plotnik, Yonatan; Lumer, Yaakov; Nolte, Stefan; Segev, Mordechai; Szameit, Alexander
2013-05-01
We present the first experimental observation of Photonic Topological Insulators (Photonic TIs). TIs are a new state of matter, which are bulk insulators, but conduct electrons on the surface. In photonic TIs, the propagating waves are electromagnetic, rather than electronic (in our case, visible light). Beyond their fundamental signifiucance, photonic TIs have also been suggested for a number of applications, including highly robust optical delay lines, on-chip optical diodes, and spin-cloaked photon sources. In solid-state TIs, topological protection is achieved by virtue of the Kramers degeneracy, which does not apply to photons. Therefore, for a non-fermionic TI, another mechanism is required. Our system is composed of an array of helical waveguides arranged in a honeycomb lattice. The helicity induces a fictitious, time-varying electric field, and the structure becomes equivalent to a Floquet TI (proposed by Lindner et al.). By probing the diffraction of light through the lattice, we demonstrate topologically-protected edge states, scatter-free propagation around corners and upon encountering defects. Our setting will allow for the probing of mean-field interactions in TIs through optical nonlinearities, as well as the effects of controllable disorder.
Anderson topological superconductor
NASA Astrophysics Data System (ADS)
Borchmann, Jan; Farrell, Aaron; Pereg-Barnea, T.
2016-03-01
In this paper we study the phase diagram of a disordered, spin-orbit coupled superconductor with s -wave or d +i d -wave pairing symmetry in symmetry class D . We analyze the topological phase transitions by applying three different methods, which include a disorder averaged entanglement entropy, a disorder averaged real-space Chern number, and an evaluation of the momentum space Chern number in a disorder averaged effective model. We find evidence for a disorder-induced topological state. While in the clean limit there is a single phase transition from a trivial phase with a Chern number C =4 to a topological phase with C =1 , in the disordered system there is an intermediate phase with C =3 . The phase transition from the trivial C =4 phase into the intermediate phase with C =3 is seen in the real-space calculation of the Chern number. In spite of this, this phase transition is not detectable in the entanglement entropy. A second phase transition from the disorder-induced C =3 into the C =1 phase is seen in all three quantities.
Estrada, Rolando; Tomasi, Carlo; Schmidler, Scott C.; Farsiu, Sina
2015-01-01
Tree-like structures are fundamental in nature, and it is often useful to reconstruct the topology of a tree—what connects to what—from a two-dimensional image of it. However, the projected branches often cross in the image: the tree projects to a planar graph, and the inverse problem of reconstructing the topology of the tree from that of the graph is ill-posed. We regularize this problem with a generative, parametric tree-growth model. Under this model, reconstruction is possible in linear time if one knows the direction of each edge in the graph—which edge endpoint is closer to the root of the tree—but becomes NP-hard if the directions are not known. For the latter case, we present a heuristic search algorithm to estimate the most likely topology of a rooted, three-dimensional tree from a single two-dimensional image. Experimental results on retinal vessel, plant root, and synthetic tree datasets show that our methodology is both accurate and efficient. PMID:26353004
Transformable topological mechanical metamaterials
NASA Astrophysics Data System (ADS)
Rocklin, D. Zeb; Zhou, Shangnan; Sun, Kai; Mao, Xiaoming
We present a class of mechanical metamaterials characterized by a uniform soft deformation--a large, zero-energy homogeneous elastic deformation mode of the structure--that may be used to induce topological transitions and dramatically change mechanical and acoustic properties of the structure. We show that the existence of such a mode determines certain exotic mechanical and acoustic properties of the structure and its activation can reversibly alter and tune these properties. This serves as the basis for a design principle for mechanical metamaterials with tunable properties. When the structure's uniform mode is primarily dilational (shearing) its surface (bulk) possesses phonon modes with vanishing speed of sound. Maxwell lattices comprise a subclass of such material which, owing to their critical coordination number (four, in 2D), necessarily possess such a uniform zero mode, often termed a Guest mode, and which may be topologically polarized, such that zero modes are moved from one edge to another. We show that activating the deformation can alter the shear/dilational character of the mode and topologically polarize the structure, thereby altering the bulk and surface properties at no significant energy cost. arXiv:1510.06389 [cond-mat.soft] NWO, Delta Institute of Physics, ICAM fellowship (DZR) and NSF Grant PHY-1402971 at University of Michigan (KS).
Designing topologicality using oxides
NASA Astrophysics Data System (ADS)
Pardo, Victor
In this talk we will describe a series of ab intio calculations carried out on different oxide-based systems and their nanostructures that show emerging non-trivial topological properties or nodal Fermi surfaces. We will show that various well-known oxide structures with the appropriate filling host Dirac points at the Fermi level that could eventually respond to spin-orbit coupling. In particular, we will focus on the results obtained in rutile multilayers, perovskite bilayers grown along the polar (111) direction and corundum-based multilayers. Topologically non-trivial phases occur in various limits of spin-orbit coupling strength and on-site Coulomb repulsion, using different fillings of the d-shell for various 3d and 5d elements in the active layers. The different systems will be discussed and compared to try to understand the key ingredients that lead to non-trivial topological properties in oxides and how these can be enhanced or tuned. We acknowledge support of the MINECO through the Ramon y Cajal Program and Project No. MAT2013-44673-R and Xunta de Galicia through Project No. EM2013/037.
Transportation Network Topologies
NASA Technical Reports Server (NTRS)
Holmes, Bruce J.; Scott, John
2004-01-01
A discomforting reality has materialized on the transportation scene: our existing air and ground infrastructures will not scale to meet our nation's 21st century demands and expectations for mobility, commerce, safety, and security. The consequence of inaction is diminished quality of life and economic opportunity in the 21st century. Clearly, new thinking is required for transportation that can scale to meet to the realities of a networked, knowledge-based economy in which the value of time is a new coin of the realm. This paper proposes a framework, or topology, for thinking about the problem of scalability of the system of networks that comprise the aviation system. This framework highlights the role of integrated communication-navigation-surveillance systems in enabling scalability of future air transportation networks. Scalability, in this vein, is a goal of the recently formed Joint Planning and Development Office for the Next Generation Air Transportation System. New foundations for 21st thinking about air transportation are underpinned by several technological developments in the traditional aircraft disciplines as well as in communication, navigation, surveillance and information systems. Complexity science and modern network theory give rise to one of the technological developments of importance. Scale-free (i.e., scalable) networks represent a promising concept space for modeling airspace system architectures, and for assessing network performance in terms of scalability, efficiency, robustness, resilience, and other metrics. The paper offers an air transportation system topology as framework for transportation system innovation. Successful outcomes of innovation in air transportation could lay the foundations for new paradigms for aircraft and their operating capabilities, air transportation system architectures, and airspace architectures and procedural concepts. The topology proposed considers air transportation as a system of networks, within which strategies for scalability of the topology may be enabled by technologies and policies. In particular, the effects of scalable ICNS concepts are evaluated within this proposed topology. Alternative business models are appearing on the scene as the old centralized hub-and-spoke model reaches the limits of its scalability. These models include growth of point-to-point scheduled air transportation service (e.g., the RJ phenomenon and the Southwest Effect). Another is a new business model for on-demand, widely distributed, air mobility in jet taxi services. The new businesses forming around this vision are targeting personal air mobility to virtually any of the thousands of origins and destinations throughout suburban, rural, and remote communities and regions. Such advancement in air mobility has many implications for requirements for airports, airspace, and consumers. These new paradigms could support scalable alternatives for the expansion of future air mobility to more consumers in more places.
Transportation Network Topologies
NASA Technical Reports Server (NTRS)
Holmes, Bruce J.; Scott, John M.
2004-01-01
A discomforting reality has materialized on the transportation scene: our existing air and ground infrastructures will not scale to meet our nation's 21st century demands and expectations for mobility, commerce, safety, and security. The consequence of inaction is diminished quality of life and economic opportunity in the 21st century. Clearly, new thinking is required for transportation that can scale to meet to the realities of a networked, knowledge-based economy in which the value of time is a new coin of the realm. This paper proposes a framework, or topology, for thinking about the problem of scalability of the system of networks that comprise the aviation system. This framework highlights the role of integrated communication-navigation-surveillance systems in enabling scalability of future air transportation networks. Scalability, in this vein, is a goal of the recently formed Joint Planning and Development Office for the Next Generation Air Transportation System. New foundations for 21PstP thinking about air transportation are underpinned by several technological developments in the traditional aircraft disciplines as well as in communication, navigation, surveillance and information systems. Complexity science and modern network theory give rise to one of the technological developments of importance. Scale-free (i.e., scalable) networks represent a promising concept space for modeling airspace system architectures, and for assessing network performance in terms of scalability, efficiency, robustness, resilience, and other metrics. The paper offers an air transportation system topology as framework for transportation system innovation. Successful outcomes of innovation in air transportation could lay the foundations for new paradigms for aircraft and their operating capabilities, air transportation system architectures, and airspace architectures and procedural concepts. The topology proposed considers air transportation as a system of networks, within which strategies for scalability of the topology may be enabled by technologies and policies. In particular, the effects of scalable ICNS concepts are evaluated within this proposed topology. Alternative business models are appearing on the scene as the old centralized hub-and-spoke model reaches the limits of its scalability. These models include growth of point-to-point scheduled air transportation service (e.g., the RJ phenomenon and the 'Southwest Effect'). Another is a new business model for on-demand, widely distributed, air mobility in jet taxi services. The new businesses forming around this vision are targeting personal air mobility to virtually any of the thousands of origins and destinations throughout suburban, rural, and remote communities and regions. Such advancement in air mobility has many implications for requirements for airports, airspace, and consumers. These new paradigms could support scalable alternatives for the expansion of future air mobility to more consumers in more places.
Topological order in interacting one-dimensional Bose Systems
NASA Astrophysics Data System (ADS)
Grusdt, Fabian; Höning, Michael; Fleischhauer, Michael
2015-05-01
We discuss topological aspects of one-dimensional inversion-symmetric systems of interacting bosons, which can be implemented in current experiments with ultra cold atoms. We consider both integer and fractional fillings of a topologically non-trivial Bloch band. Our starting point is the chiral-symmetric Su-Schrieffer-Heeger (SSH) model of non-interacting fermions, which can be realized by hard-core bosons. When the hard-core constraint is removed, we obtain a bosonic system with inversion-symmetry protected topological order. Because the chiral symmetry is broken by finite interactions, the bulk-boundary correspondence of the SSH model is no longer valid. Nevertheless we show that the fractional part of the charge which is localized at the edge can distinguish topologically trivial- from non-trivial states. We generalize our analysis by including nearest neighbor interactions and present a topological classification of the resulting quarter-filling Mott insulating phase. In this case fractionally charged bulk excitations exist, which we identify in the grand-canonical phase diagram. F.G. acknowledges support from the Graduate School of Material Science MAINZ.
Topological aspects of fermions on hyperdiamond
Saidi, E. H.; Fassi-Fehri, O.; Bousmina, M.
2012-07-15
Motivated by recent results on the index of the Dirac operator D={gamma}{sup {mu}}D{sub {mu}} of QCD on lattice and also by results on topological features of electrons and holes of two-dimensional graphene, we compute in this paper the index of D for fermions living on a family of even-dimensional lattices denoted as L{sub 2N} and describing the 2N-dimensional generalization of the graphene honeycomb. The calculation of this topological index is done by using the direct method based on solving explicitly the gauged Dirac equation and also by using specific properties of the lattices L{sub 2N}, which are shown to be intimately linked with the weight lattices of SU(2N+ 1). The index associated with the two leading N= 1 and N= 2 elements of this family describe precisely the chiral anomalies of graphene and QCD{sub 4}. Comments on the method using the spectral flow approach as well as the computation of the topological charges on 2-cycles of 2N-dimensional compact supercell in L{sub 2N} and applications to QCD{sub 4} are also given.
Topological aspects of fermions on hyperdiamond
NASA Astrophysics Data System (ADS)
Saidi, E. H.; Fassi-Fehri, O.; Bousmina, M.
2012-07-01
Motivated by recent results on the index of the Dirac operator D = γμDμ of QCD on lattice and also by results on topological features of electrons and holes of two-dimensional graphene, we compute in this paper the index of D for fermions living on a family of even-dimensional lattices denoted as {L}_{2N} and describing the 2N-dimensional generalization of the graphene honeycomb. The calculation of this topological index is done by using the direct method based on solving explicitly the gauged Dirac equation and also by using specific properties of the lattices {L} _{2N}, which are shown to be intimately linked with the weight lattices of SU(2N + 1). The index associated with the two leading N = 1 and N = 2 elements of this family describe precisely the chiral anomalies of graphene and QCD4. Comments on the method using the spectral flow approach as well as the computation of the topological charges on 2-cycles of 2N-dimensional compact supercell in {L}_{2N} and applications to QCD4 are also given.
A battery charger and state of charge indicator
NASA Astrophysics Data System (ADS)
Latos, T. S.
1984-04-01
A battery charger which has a full wave rectifier in series with a transformer isolated 20 kHz dc-dc converter with high frequency switches, which are programmed to actively shape the input dc line current to be a mirror image of the ac line voltage is discussed. The power circuit operates at 2 kW peak and 1 kW average power. The BC/SCI has two major subsystems: (1) the battery charger power electronics with its controls; and (2) a microcomputer subsystem which is used to acquire battery terminal data and exercise the state of charge software programs. The state of charge definition employed is the energy remaining in the battery when extracted at a 10 kW rate divided by the energy capacity of a fully charged new battery. The battery charger circuit is an isolated boost converter operating at an internal frequency of 20 kHz. The switches selected for the battery charger are the single most important item in determining its efficiency. The combination of voltage and current requirements dictate the use of high power NPN Darlington switching transistors. The power circuit topology is a three switch design which utilizes a power FET on the center tap of the isolation transformer and the power Darlingtons on each of the two ends. An analog control system is employed to accomplish active input current waveshaping as well as the necessary regulation.
Battery charger and state of charge indicator. Final report
Latos, T.S.
1984-04-15
The battery charger has a full-wave rectifier in series with a transformer isolated 20 kHz dc-dc converter with high frequency switches which are programmed to actively shape the input ac line current to be a mirror image of the ac line voltage. The power circuit is capable of operating at 2 kW peak and 1 kW average power. The BC/SCI has two major subsystems: (1) the battery charger power electronics with its controls; and (2) a microcomputer subsystem which is used to acquire battery terminal data and exercise the state-of-charge software programs. The state-of-charge definition employed is the energy remaining in the battery when extracted at a 10 kW rate divided by the energy capacity of a fully charged new battery. The battery charger circuit is an isolated boost converter operating at an internal frequency of 20 kHz. The switches selected for the battery charger are the single most important item in determining its efficiency. The combination of voltage and current requirements dictated the use of high power NPN Darlington switching transistors. The power circuit topology developed is a three switch design utilizing a power FET on the center tap of the isolation transformer and the power Darlingtons on each of the two ends. An analog control system is employed to accomplish active input current waveshaping as well as the necessary regulation.
A Battery Charger and State of Charge Indicator
NASA Technical Reports Server (NTRS)
Latos, T. S.
1984-01-01
A battery charger which has a full wave rectifier in series with a transformer isolated 20 kHz dc-dc converter with high frequency switches, which are programmed to actively shape the input dc line current to be a mirror image of the ac line voltage is discussed. The power circuit operates at 2 kW peak and 1 kW average power. The BC/SCI has two major subsystems: (1) the battery charger power electronics with its controls; and (2) a microcomputer subsystem which is used to acquire battery terminal data and exercise the state of charge software programs. The state of charge definition employed is the energy remaining in the battery when extracted at a 10 kW rate divided by the energy capacity of a fully charged new battery. The battery charger circuit is an isolated boost converter operating at an internal frequency of 20 kHz. The switches selected for the battery charger are the single most important item in determining its efficiency. The combination of voltage and current requirements dictate the use of high power NPN Darlington switching transistors. The power circuit topology is a three switch design which utilizes a power FET on the center tap of the isolation transformer and the power Darlingtons on each of the two ends. An analog control system is employed to accomplish active input current waveshaping as well as the necessary regulation.
Topological phases with generalized global symmetries
NASA Astrophysics Data System (ADS)
Yoshida, Beni
2016-04-01
We present simple lattice realizations of symmetry-protected topological phases with q -form global symmetries where charged excitations have q spatial dimensions. Specifically, we construct d space-dimensional models supported on a (d +1 ) -colorable graph by using a family of unitary phase gates, known as multiqubit control-Z gates in quantum information community. In our construction, charged excitations of different dimensionality may coexist and form a short-range entangled state which is protected by symmetry operators of different dimensionality. Nontriviality of proposed models, in a sense of quantum circuit complexity, is confirmed by studying protected boundary modes, gauged models, and corresponding gapped domain walls. We also comment on applications of our construction to quantum error-correcting codes, and discuss corresponding fault-tolerant logical gates.
Bulk-Edge Correspondence in 2+1-Dimensional Abelian Topological Phases
NASA Astrophysics Data System (ADS)
Plamadeala, Eugeniu; Cheng, Meng; Mulligan, Michael; Nayak, Chetan; Cano, Jennifer; Yard, Jon
2014-03-01
The same bulk two-dimensional topological phase can have multiple distinct, fully-chiral edge phases. We show that this can occur in the integer quantum Hall and Abelian fractional quantum Hall states. We give a general criterion for the existence of multiple distinct chiral edge phases for the same bulk phase and discuss experimental consequences. We show that fermionic systems can have edge phases with only bosonic low-energy excitations and discuss a fermionic generalization of the relation between bulk topological spins and the central charge. The latter follows from our demonstration that every fermionic topological phase can be represented as a bosonic topological phase, together with some number of filled Landau levels. Our analysis shows that every Abelian topological phase can be decomposed into a tensor product of theories associated with prime numbers p in which every quasiparticle has a topological spin that is a pn-th root of unity for some n.
Predicting, Realizing and Exploiting Exotic Topological Phases of Quantum Matter
NASA Astrophysics Data System (ADS)
Bansil, Arun
The revolution started by the discovery of topological insulators a few years ago has turned out to be the proverbial tip of the much larger iceberg of exotic phases harbored by quantum matter. Consideration of electronic states protected by time-reversal, crystalline and particle-hole symmetries has led to the prediction of many novel 3D materials, which can support Weyl, Dirac and Majorana fermions, and to new types of insulators such as topological crystalline insulators and topological Kondo insulators, as well as 2D quantum spin Hall insulators with large band gaps capable of surviving room temperature thermal excitations. In this talk, I will discuss our recent theoretical work aimed at predicting topological materials beyond the standard topological insulators and identify cases where robust experimental evidence has been obtained toward their successful materials realization. I will also comment on the potential of topological materials as next generation platforms for manipulating spin and charge transport and other applications. Work supported by the Materials Science & Engineering Division, Basic Energy Sciences, U.S.D.O.E.
Numerical Study of a Bosonic Topological Insulator in three dimensions
NASA Astrophysics Data System (ADS)
Geraedts, Scott; Motrunich, Olexei
2014-03-01
We construct a model which realizes a (3+1)-dimensional symmetry-protected topological phase of bosons with U(1) charge conservation and time reversal symmetry, envisioned by A. Vishwanath and T. Senthil [PRX 4 011016]. Our model works by introducing an additional O(3) degree of freedom, and binding its hedgehogs to a species of charged bosons; the continuous symmetry is thus enlarged to SO(3) U(1) . We study the model using Monte Carlo and determine its bulk phase diagram; the phase where the bound states of hedgehogs and charges condense is the topological phase. We also study surface phase diagram on a (2+1)-dimensional boundary between the topological and trivial insulators. The theory for the surface is the same as for a (2+1)D hedgehog-suppressed non-linear sigma model, which confirms the proposed so-called NCCP1 field theory. We apply a Zeeman field to the surface, which breaks time reversal on the surface only, and observe a surface Hall conductivity which is half of a quantized value allowed for bosons in strictly (2+1)D, thus establishing topological nature of the (3+1)D bulk phase. Support from NSF Grant DMR-1206096; Caltech Institute of Quantum Imformation and Matter, and an NSERC PGS fellowship.
Topological compositeness of quarks, leptons and electroweak bosons
NASA Astrophysics Data System (ADS)
Chew, G. F.; Finkelstein, J.; Nicolescu, B.; Poénaru, V.
1982-12-01
Topological Particle Theory yields a unified particle description in terms of two topological constituents, which we call the I-triangle and the Y-triangle. Each triangle is a charge doublet; the I-triangle has spin 1/2 while the Y-triangle has spin 0. Leptons arebar I bar Y; electroweak vector bosons areI bar I; hadrons areI bar I (mesons),I I I bar Y (baryons), orI I bar Y Y bar I bar I (baryoniums). An as-yet-undiscovered singlet neutral electroweak scalar boson is predicted, corresponding toY bar Y
Topological insulator-graphene junction for spin transport
NASA Astrophysics Data System (ADS)
Li, H.; Zhang, H. B.; Shao, J. M.; Zhang, Y. Y.; Yao, D. X.; Yang, G. W.
2012-12-01
Considering that the strong spin-orbit interaction of a topological insulator (TI) makes it possible to generate large spin polarization and that graphene with weak spin-orbit coupling can transmit spin information over large distances, we propose a topological insulator-graphene junction (TIG) for spin and charge transport. We find that the TI in the TIG can inject a finite electrically induced net spin current into the graphene without any of the conditions necessary in traditional spin-generation devices. The magnitude of the spin current can be tuned with an applied bias voltage. These findings are useful for developing spintronics.
Helical Spin Order from Topological Dirac and Weyl Semimetals.
Sun, Xiao-Qi; Zhang, Shou-Cheng; Wang, Zhong
2015-08-14
We study dynamical mass generation and the resultant helical spin orders in topological Dirac and Weyl semimetals, including the edge states of quantum spin Hall insulators, the surface states of weak topological insulators, and the bulk materials of Weyl semimetals. In particular, the helical spin textures of Weyl semimetals manifest the spin-momentum locking of Weyl fermions in a visible manner. The spin-wave fluctuations of the helical order carry electric charge density; therefore, the spin textures can be electrically controlled in a simple and predictable manner. PMID:26317739
Optically engineering the topological properties of a spin Hall insulator.
Dóra, Balázs; Cayssol, Jérôme; Simon, Ferenc; Moessner, Roderich
2012-02-01
Time-periodic perturbations can be used to engineer topological properties of matter by altering the Floquet band structure. This is demonstrated for the helical edge state of a spin Hall insulator in the presence of monochromatic circularly polarized light. The inherent spin structure of the edge state is influenced by the Zeeman coupling and not by the orbital effect. The photocurrent (and the magnetization along the edge) develops a finite, helicity-dependent expectation value and turns from dissipationless to dissipative with increasing radiation frequency, signalling a change in the topological properties. The connection with Thouless' charge pumping and nonequilibrium zitterbewegung is discussed, together with possible experiments. PMID:22400947
The topology of gyroscopic metamaterials
NASA Astrophysics Data System (ADS)
Nash, Lisa M.; Kleckner, Dustin; Read, Alismari; Vitelli, Vincenzo; Turner, Ari M.; Irvine, William T. M.
Mechanical metamaterials can have topologically protected states, much like their electronic and optical counterparts. We recently demonstrated this in experiment by building a meta-material composed of coupled gyroscopes on a honeycomb lattice. This system breaks time-reversal symmetry and exhibits topologically protected one-way edge modes. In this talk we will explore the relationship between the topology of the band structure and the geometry of the lattice.
Code of Federal Regulations, 2014 CFR
2014-01-01
... PASSENGER FACILITY CHARGES (PFC'S) General § 158.3 Definitions. The following definitions apply in this part... revenue generated by a public airport (1) through any lease, rent, fee, PFC or other charge collected... assistance, or with PFC revenue under this part, or conveyed to such public agency under the provisions...
Code of Federal Regulations, 2012 CFR
2012-01-01
... PASSENGER FACILITY CHARGES (PFC'S) General § 158.3 Definitions. The following definitions apply in this part... revenue generated by a public airport (1) through any lease, rent, fee, PFC or other charge collected... assistance, or with PFC revenue under this part, or conveyed to such public agency under the provisions...
Code of Federal Regulations, 2010 CFR
2010-01-01
... PASSENGER FACILITY CHARGES (PFC'S) General § 158.3 Definitions. The following definitions apply in this part... revenue generated by a public airport (1) through any lease, rent, fee, PFC or other charge collected... assistance, or with PFC revenue under this part, or conveyed to such public agency under the provisions...
Code of Federal Regulations, 2011 CFR
2011-01-01
... PASSENGER FACILITY CHARGES (PFC'S) General § 158.3 Definitions. The following definitions apply in this part... revenue generated by a public airport (1) through any lease, rent, fee, PFC or other charge collected... assistance, or with PFC revenue under this part, or conveyed to such public agency under the provisions...
Code of Federal Regulations, 2013 CFR
2013-01-01
... PASSENGER FACILITY CHARGES (PFC'S) General § 158.3 Definitions. The following definitions apply in this part... revenue generated by a public airport (1) through any lease, rent, fee, PFC or other charge collected... assistance, or with PFC revenue under this part, or conveyed to such public agency under the provisions...
Generating charge from diffeomorphisms
NASA Astrophysics Data System (ADS)
Hansen, James; Kraus, Per
2006-12-01
We unravel some subtleties involving the definition of sphere angular momentum charges in AdSq Sp spacetimes, or equivalently, R-symmetry charges in the dual boundary CFT. In the AdS3 context, it is known that charges can be generated by coordinate transformations, even though the underlying theory is diffeomorphism invariant. This is the bulk version of spectral flow in the boundary CFT. We trace this behavior back to special properties of the p-form field strength supporting the solution, and derive the explicit formulas for angular momentum charges. This analysis also reveals the higher dimensional origin of three dimensional Chern-Simons terms and of chiral anomalies in the boundary theory.
Bombin, H.
2010-03-15
We introduce a family of two-dimensional (2D) topological subsystem quantum error-correcting codes. The gauge group is generated by two-local Pauli operators, so that two-local measurements are enough to recover the error syndrome. We study the computational power of code deformation in these codes and show that boundaries cannot be introduced in the usual way. In addition, we give a general mapping connecting suitable classical statistical mechanical models to optimal error correction in subsystem stabilizer codes that suffer from depolarizing noise.
Topological Confinement and Superconductivity
NASA Astrophysics Data System (ADS)
Al-Hassanieh, Khaled; Batista, Cristian; Sengupta, Pinaki; Feiguin, Adrian
2009-03-01
We derive a Kondo Lattice model with a correlated conduction band from a two-band Hubbard Hamiltonian. This mapping allows us to describe the emergence of a robust pairing mechanism in a model that only contains repulsive interactions. The mechanism is due to topological con?nement and results from the interplay between antiferromagnetism and delocalization. By using Density-Matrix-Renormalization Group (DMRG) we demonstrate that this mechanism leads to dominant superconducting correlations in a 1D-system. [1] K. A. Al-Hassanieh, C. D. Batista, P. Sengupta, and A. E. Feiguin, preprint arXiv:0808.3735.
NASA Astrophysics Data System (ADS)
Berski, Slawomir; Gordon, Agnieszka J.; Latajka, Zdzislaw
2013-04-01
The complicated nature of the chemical bonding in cis and trans isomers of F-O-N=O is discussed based on the results obtained from the topological analysis of electron localization function (η) (ELF), electron localizability index (Y_D^σ), and electron density (ρ). The calculations have been performed for correlated wavefunctions using the CCSD and CASSCF methods. The F-O1 bond with non-bonding basins, V(F) and V'(O1), belongs to the protocovalent type (η,Y_D^σ) and its total population ranges between 0.2 and 0.4e. The central N-O1 bond in the cis form is protocovalent (η, Y_D^σ) with two basins, V(N) and V(O1). The total population oscillates between 0.7 and 0.9e. In the trans isomer, topology of ELF depends on used method. At the CCSD level only one non-bonding basin, V(N), is observed (η). Its population is about 0.5e. According to the definition of a heteronuclear charge-shift (CS) bond, only N-O1 bond in trans-FONO belongs to the CS class. A relation between η- and ρ-topology and N-O1 bond length is discussed.
Visualizing vector field topology in fluid flows
NASA Technical Reports Server (NTRS)
Helman, James L.; Hesselink, Lambertus
1991-01-01
Methods of automating the analysis and display of vector field topology in general and flow topology in particular are discussed. Two-dimensional vector field topology is reviewed as the basis for the examination of topology in three-dimensional separated flows. The use of tangent surfaces and clipping in visualizing vector field topology in fluid flows is addressed.
25 CFR 700.105 - Utility charges.
Code of Federal Regulations, 2014 CFR
2014-04-01
... 25 Indians 2 2014-04-01 2014-04-01 false Utility charges. 700.105 Section 700.105 Indians THE OFFICE OF NAVAJO AND HOPI INDIAN RELOCATION COMMISSION OPERATIONS AND RELOCATION PROCEDURES General Policies and Instructions Definitions § 700.105 Utility charges. Utility charges means the cost for heat, lighting, hot water, electricity, natural...
25 CFR 700.105 - Utility charges.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 25 Indians 2 2010-04-01 2010-04-01 false Utility charges. 700.105 Section 700.105 Indians THE OFFICE OF NAVAJO AND HOPI INDIAN RELOCATION COMMISSION OPERATIONS AND RELOCATION PROCEDURES General Policies and Instructions Definitions § 700.105 Utility charges. Utility charges means the cost for...
12 CFR 1026.4 - Finance charge.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 12 Banks and Banking 9 2014-01-01 2014-01-01 false Finance charge. 1026.4 Section 1026.4 Banks and Banking BUREAU OF CONSUMER FINANCIAL PROTECTION TRUTH IN LENDING (REGULATION Z) § 1026.4 Finance charge. (a) Definition. The finance charge is the cost of consumer credit as a dollar amount. It includes...
12 CFR 1026.4 - Finance charge.
Code of Federal Regulations, 2012 CFR
2012-01-01
... 12 Banks and Banking 8 2012-01-01 2012-01-01 false Finance charge. 1026.4 Section 1026.4 Banks and Banking BUREAU OF CONSUMER FINANCIAL PROTECTION TRUTH IN LENDING (REGULATION Z) General § 1026.4 Finance charge. (a) Definition. The finance charge is the cost of consumer credit as a dollar amount. It...
12 CFR 1026.4 - Finance charge.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 12 Banks and Banking 8 2013-01-01 2013-01-01 false Finance charge. 1026.4 Section 1026.4 Banks and Banking BUREAU OF CONSUMER FINANCIAL PROTECTION TRUTH IN LENDING (REGULATION Z) General § 1026.4 Finance charge. (a) Definition. The finance charge is the cost of consumer credit as a dollar amount. It...
NASA Astrophysics Data System (ADS)
Maas, Axel
2015-03-01
Two popular perspectives on the non-perturbative domain of Yang-Mills theories are either in terms of the gluons themselves or in terms of collective gluonic excitations, i.e. topological excitations. If both views are correct, then they are only two different representations of the same underlying physics. One possibility to investigate this connection is by the determination of gluon correlation functions in topological background fields, as created by the smearing of lattice configurations. This is performed here for the minimal Landau gauge gluon propagator, ghost propagator, and running coupling, both in momentum and position space for SU(2) Yang-Mills theory. The results show that the salient low-momentum features of the propagators are qualitatively retained under smearing at sufficiently small momenta, in agreement with an equivalence of both perspectives. However, the mid-momentum behavior is significantly affected. These results are also relevant for the construction of truncations in functional methods, as they provide hints on necessary properties to be retained in truncations.
Topological invariants in interacting topological insulators: Success and Breakdown
NASA Astrophysics Data System (ADS)
He, Yuan-Yao; Wu, Han-Qing; Meng, Zi Yang; Lu, Zhong-Yi
The content of this talk is twofold. In the first part, we provide a paradigm of efficient numerical evaluation scheme for topological invariants via zero-frequency single-particle Green's function in quantum Monte Carlo (QMC) simulations. Especially, we introduce a periodization process to overcome the ubiquitous finite-size effect and make use of symmetry properties of the underlying systems to reduce the computational effort. This scheme is tested to be successful on models of interacting topological insulators, where there is single-particle gap closing at the transition. In the second part, we apply the above scheme to wider classes of interacting topological insulators, in which the breakdown of constructing topological invariant via single-particle Green's functions is presented. These systems host novel interaction-driven topological phase transitions without symmetry breaking, and hence fermionic degree of freedom is not involved at the critical point, instead, collective bosonic mode become critical.
Optical and Casimir effects in topological materials
NASA Astrophysics Data System (ADS)
Wilson, Justin H.
Two major electromagnetic phenomena, magneto-optical effects and the Casimir effect, have seen much theoretical and experimental use for many years. On the other hand, recently there has been an explosion of theoretical and experimental work on so-called topological materials, and a natural question to ask is how such electromagnetic phenomena change with these novel materials. Specifically, we will consider are topological insulators and Weyl semimetals. When Dirac electrons on the surface of a topological insulator are gapped or Weyl fermions in the bulk of a Weyl semimetal appear due to time-reversal symmetry breaking, there is a resulting quantum anomalous Hall effect (2D in one case and bulk 3D in the other, respectively). For topological insulators, we investigate the role of localized in-gap states which can leave their own fingerprints on the magneto-optics and can therefore be probed. We have shown that these states resonantly contribute to the Hall conductivity and are magneto-optically active. For Weyl semimetals we investigate the Casimir force and show that with thickness, chemical potential, and magnetic field, a repulsive and tunable Casimir force can be obtained. Additionally, various values of the parameters can give various combinations of traps and antitraps. We additionally probe the topological transition called a Lifshitz transition in the band structure of a material and show that in a Casimir experiment, one can observe a non-analytic "kink'' in the Casimir force across such a transition. The material we propose is a spin-orbit coupled semiconductor with large g-factor that can be magnetically tuned through such a transition. Additionally, we propose an experiment with a two-dimensional metal where weak localization is tuned with an applied field in order to definitively test the effect of diffusive electrons on the Casimir force---an issue that is surprisingly unresolved to this day. Lastly, we show how the time-continuous coherent state path integral breaks down for both the single-site Bose-Hubbard model and the spin path integral. Specifically, when the Hamiltonian is quadratic in a generator of the algebra used to construct coherent states, the path integral fails to produce correct results following from an operator approach. We note that the problems do not arise in the time-discretized version of the path integral, as expected.
The quantum spin Hall effect and the topological magneto-electric effect
NASA Astrophysics Data System (ADS)
Zhang, Shoucheng
2009-03-01
Search for topologically non-trivial states of matter has become a important goal for condensed matter physics. Recently, a new class of topological insulators has been proposed. These topological insulators have an insulating gap in the bulk, but have topologically protected edge states due to the time reversal symmetry. In two dimensions the edge states give rise to the quantum spin Hall (QSH) effect, in the absence of any external magnetic field. I shall review the theoretical prediction[1] of the QSH state in HgTe/CdTe semiconductor quantum wells, and its recent experimental observation [2]. The QSH effect can be generalized to three dimensions as the topological magneto-electric effect (TME) of the topological insulators [4]. I shall also present realistic experimental proposals to observe fractional charge [3], spin-charge separation and the deconfinement of the magnetic monopoles in these novel topological states of matter. [4pt] [1] A. Bernevig, T. Hughes and S. C. Zhang, Science, 314, 1757, (2006) [0pt] [2] M. Koenig et al, Science 318, 766, (2007) [0pt] [3] X. Qi, T. Hughes and S. C. Zhang, Nature Physics, 4, 273 (2008) [0pt] [4] Xiao-Liang Qi, Taylor Hughes and Shou-Cheng Zhang, ``Topological Field Theory of Time-Reversal Invariant Insulators", Phys. Rev B. 78, 195424 (2008)
On topological terms in the O(3) nonlinear sigma model
NASA Astrophysics Data System (ADS)
Tsurumaru, Toyohiro; Tsutsui, Izumi
1999-08-01
Topological terms in the O(3) nonlinear sigma model in (1+1) and (2+1) dimensions are re-examined based on the description of the SU(2)-valued field g. We first show that the topological soliton term in (1+1) dimensions arises from the unitary representations of the group characterizing the global structure of the symmetry inherent in the description, in a manner analogous to the appearance of the θ-term in Yang-Mills theory in (3+1) dimensions. We then present a detailed argument as to why the conventional Hopf term, which is the topological counterpart in (2+1) dimensions and has been widely used to realize fractional spin and statistics, is ill-defined unless the soliton charge vanishes. We show how this restriction can be lifted by means of a procedure proposed recently, and provide its physical interpretation as well.
Quantum algorithm for topological and geometric analysis of data
NASA Astrophysics Data System (ADS)
Lloyd, Seth; Zanardi, Paolo; Garnerone, Silvano
2015-03-01
Topological methods for analyzing data sets provide a powerful technique for extracting useful information from data. Data that represents geometric features of the world typically gives a distorted picture of those features, if only because the devices and systems that sense the world and that generate the data by their very nature induce distortions. By definition, topological features are those that persist under continuous distortions of the data. Topological methods can therefore identify features of the real system from which the data was collected, but that have been distorted by the data collection process. Persistent homology is a sophisticated tool for identifying such topological features -connected components, holes, or voids - and for determining how such features persist as the data is viewed at different scales. This talk presents quantum machine learning algorithms for calculating Betti numbers in persistent homology, and for finding eigenvectors and eigenvalues of the combinatorial Laplacian (the quantities that famously allow one to ``hear the shape of a drum''). The algorithms provide an exponential speedup over classical algorithms for topological and geometrical data analysis.
Concept Model on Topological Learning
NASA Astrophysics Data System (ADS)
Ae, Tadashi; Kioi, Kazumasa
2010-11-01
We discuss a new model for concept based on topological learning, where the learning process on the neural network is represented by mathematical topology. The topological learning of neural networks is summarized by a quotient of input space and the hierarchical step induces a tree where each node corresponds to a quotient. In general, the concept acquisition is a difficult problem, but the emotion for a subject is represented by providing the questions to a person. Therefore, a kind of concept is captured by such data and the answer sheet can be mapped into a topology consisting of trees. In this paper, we will discuss a way of mapping the emotional concept to a topological learning model.
Transportation Network Topologies
NASA Technical Reports Server (NTRS)
Alexandrov, Natalia (Editor)
2004-01-01
The existing U.S. hub-and-spoke air transportation system is reaching saturation. Major aspects of the current system, such as capacity, safety, mobility, customer satisfaction, security, communications, and ecological effects, require improvements. The changing dynamics - increased presence of general aviation, unmanned autonomous vehicles, military aircraft in civil airspace as part of homeland defense - contributes to growing complexity of airspace. The system has proven remarkably resistant to change. NASA Langley Research Center and the National Institute of Aerospace conducted a workshop on Transportation Network Topologies on 9-10 December 2003 in Williamsburg, Virginia. The workshop aimed to examine the feasibility of traditional methods for complex system analysis and design as well as potential novel alternatives in application to transportation systems, identify state-of-the-art models and methods, conduct gap analysis, and thus to lay a foundation for establishing a focused research program in complex systems applied to air transportation.
Gear tooth topological modification
NASA Technical Reports Server (NTRS)
Kish, Jules G. (Inventor); Isabelle, Charles (Inventor)
1994-01-01
The topology of parallel axis gears, such as spur and helical gears is modified to produce quieter and more smoothly operating gear sets with more uniform load distribution. A finite element analysis of the gear in its operating mode is made to produce a plot of radial and tangential deflections of the pinion and gear tooth surfaces which will occur when the gears are loaded during operation. The resultant plot is then inverted to produce a plot, or set of coordinates, which will define the path of travel of the gear tooth grinding wheel, which path is a mirror image of the plot of the finite element analysis. The resulting gears, when subjected to operating loads, will thus be deflected tangentially and radially to their optimum operating, or theoretical true involute, positions so as to produce quieter, smoother, and more evenly loaded gear trains.
Topological phases reviewed: The Aharonov Bohm, Aharonov Casher, and He McKellar Wilkens phases
McKellar, B. H. J.; He, X-G.; Klein, A. G.
2014-03-05
There are three topological phases related to electromagnetic interactions in quantum mechanics: 1. The Aharonov Bohm phase acquired when a charged particle encircles a magnetic field but travels through a field free region. 2. The Aharonov Casher phase acquired when a magnetic dipole encircles electric charges but travels through a charge free region. 3. The He McKellar Wilkens phase acquired when an electric dipole encircles magnetic charges but travels through a charge free region. We review the conditions under which these phases are indeed topological and their experimental realisation. Because the He McKellar Wilkens phase has been recently observed we pay particular attention to how the basic concept of 'an electric dipole encircles magnetic charges' was realised experimentally, and discuss possible future experimental realisations.
Topological phases reviewed: The Aharonov Bohm, Aharonov Casher, and He McKellar Wilkens phases
NASA Astrophysics Data System (ADS)
McKellar, B. H. J.; He, X.-G.; Klein, A. G.
2014-03-01
There are three topological phases related to electromagnetic interactions in quantum mechanics: 1. The Aharonov Bohm phase acquired when a charged particle encircles a magnetic field but travels through a field free region. 2. The Aharonov Casher phase acquired when a magnetic dipole encircles electric charges but travels through a charge free region. 3. The He McKellar Wilkens phase acquired when an electric dipole encircles magnetic charges but travels through a charge free region. We review the conditions under which these phases are indeed topological and their experimental realisation. Because the He McKellar Wilkens phase has been recently observed we pay particular attention to how the basic concept of "an electric dipole encircles magnetic charges" was realised experimentally, and discuss possible future experimental realisations.
Liu, Qihang; Zhang, Xiuwen; Abdalla, L B; Fazzio, Adalberto; Zunger, Alex
2015-02-11
The study of topological insulators has generally involved search of materials that have this property as an innate quality, distinct from normal insulators. Here we focus on the possibility of converting a normal insulator into a topological one by application of an external electric field that shifts different bands by different energies and induces a specific band inversion, which leads to a topological state. Phosphorene is a two-dimensional (2D) material that can be isolated through mechanical exfoliation from layered black phosphorus, but unlike graphene and silicene, single-layer phosphorene has a large band gap (1.5-2.2 eV). Thus, it was unsuspected to exhibit band inversion and the ensuing topological insulator behavior. Using first-principles calculations with applied perpendicular electric field F⊥ on few-layer phosphorene we predict a continuous transition from the normal insulator to a topological insulator and eventually to a metal as a function of F⊥. The tuning of topological behavior with electric field would lead to spin-separated, gapless edge states, that is, quantum spin Hall effect. This finding opens the possibility of converting normal insulating materials into topological ones via electric field and making a multifunctional "field effect topological transistor" that could manipulate simultaneously both spin and charge carrier. We use our results to formulate some design principles for looking for other 2D materials that could have such an electrical-induced topological transition. PMID:25607525
Measuring the topological susceptibility in a fixed sector
NASA Astrophysics Data System (ADS)
Bautista, Irais; Bietenholz, Wolfgang; Dromard, Arthur; Gerber, Urs; Gonglach, Lukas; Hofmann, Christoph P.; Mejía-Díaz, Héctor; Wagner, Marc
2015-12-01
For field theories with a topological charge Q , it is often of interest to measure the topological susceptibility χt=(⟨Q2⟩-⟨Q ⟩2)/V . If we manage to perform a Monte Carlo simulation where Q changes frequently, χt can be evaluated directly. However, for local update algorithms and fine lattices, the autocorrelation time with respect to Q tends to be extremely long, which invalidates the direct approach. Nevertheless, the measurement of χt is still feasible, even when the entire Markov chain is topologically frozen. We test a method for this purpose, based on the correlation of the topological charge density, as suggested by Aoki, Fukaya, Hashimoto and Onogi. Our studies in nonlinear σ -models and in two-dimensional Abelian gauge theory yield accurate results for χt, which confirm that the method is applicable. We also obtain promising results in four-dimensional SU(2) Yang-Mills theory, which suggest the applicability of this method in QCD.
Entangled networks, synchronization, and optimal network topology.
Donetti, Luca; Hurtado, Pablo I; Muñoz, Miguel A
2005-10-28
A new family of graphs, entangled networks, with optimal properties in many respects, is introduced. By definition, their topology is such that it optimizes synchronizability for many dynamical processes. These networks are shown to have an extremely homogeneous structure: degree, node distance, betweenness, and loop distributions are all very narrow. Also, they are characterized by a very interwoven (entangled) structure with short average distances, large loops, and no well-defined community structure. This family of nets exhibits an excellent performance with respect to other flow properties such as robustness against errors and attacks, minimal first-passage time of random walks, efficient communication, etc. These remarkable features convert entangled networks in a useful concept, optimal or almost optimal in many senses, and with plenty of potential applications in computer science or neuroscience. PMID:16383953
Z2 anomaly and boundaries of topological insulators
NASA Astrophysics Data System (ADS)
Ringel, Zohar; Stern, Ady
2013-09-01
We study the edge and surface theories of topological insulators from the perspective of anomalies and identify a Z2 anomaly associated with charge conservation. The anomaly is manifested through a two-point correlation function involving creation and annihilation operators on two decoupled boundaries. Although charge conservation on each boundary requires this quantity to vanish, we find that it diverges. A corollary result is that under an insertion of a flux quantum, the ground state evolves to an exactly orthogonal state independent of the rate at which the flux is inserted. The anomaly persists in the presence of disorder and imposes sharp restrictions on possible low-energy theories. Being formulated in a many-body, field-theoretical language, the anomaly allows one to test the robustness of topological insulators to interactions in a concise way.
Topological States in Partially-PT-Symmetric Azimuthal Potentials.
Kartashov, Yaroslav V; Konotop, Vladimir V; Torner, Lluis
2015-11-01
We introduce partially-parity-time (pPT)-symmetric azimuthal potentials composed from individual PT-symmetric cells located on a ring, where two azimuthal directions are nonequivalent in a sense that in such potential excitations carrying topological dislocations exhibit different dynamics for different directions of energy circulation in the initial field distribution. Such nonconservative ratchetlike structures support rich families of stable vortex solitons in cubic nonlinear media, whose properties depend on the sign of the topological charge due to the nonequivalence of azimuthal directions. In contrast, oppositely charged vortex solitons remain equivalent in similar fully-PT-symmetric potentials. The vortex solitons in the pPT- and PT-symmetric potentials are shown to feature qualitatively different internal current distributions, which are described by different discrete rotation symmetries of the intensity profiles. PMID:26588383
Topological States in Partially-PT -Symmetric Azimuthal Potentials
NASA Astrophysics Data System (ADS)
Kartashov, Yaroslav V.; Konotop, Vladimir V.; Torner, Lluis
2015-11-01
We introduce partially-parity-time (p PT ) -symmetric azimuthal potentials composed from individual PT -symmetric cells located on a ring, where two azimuthal directions are nonequivalent in a sense that in such potential excitations carrying topological dislocations exhibit different dynamics for different directions of energy circulation in the initial field distribution. Such nonconservative ratchetlike structures support rich families of stable vortex solitons in cubic nonlinear media, whose properties depend on the sign of the topological charge due to the nonequivalence of azimuthal directions. In contrast, oppositely charged vortex solitons remain equivalent in similar fully-P T -symmetric potentials. The vortex solitons in the p P T - and P T -symmetric potentials are shown to feature qualitatively different internal current distributions, which are described by different discrete rotation symmetries of the intensity profiles.
The Dynamics of Network Topology
NASA Astrophysics Data System (ADS)
Voicu, Ramiro; Legrand, Iosif; Newman, Harvey; Barczyk, Artur; Grigoras, Costin; Dobre, Ciprian
2011-12-01
Network monitoring is vital to ensure proper network operation over time, and is tightly integrated with all the data intensive processing tasks used by the LHC experiments. In order to build a coherent set of network management services it is very important to collect in near real-time information about the network topology, the main data flows, traffic volume and the quality of connectivity. A set of dedicated modules were developed in the MonALISA framework to periodically perform network measurements tests between all sites. We developed global services to present in near real-time the entire network topology used by a community. For any LHC experiment such a network topology includes several hundred of routers and tens of Autonomous Systems. Any changes in the global topology are recorded and this information is can be easily correlated with traffic patterns. The evolution in time of global network topology is shown a dedicated GUI. Changes in the global topology at this level occur quite frequently and even small modifications in the connectivity map may significantly affect the network performance. The global topology graphs are correlated with active end to end network performance measurements, done with the Fast Data Transfer application, between all sites. Access to both real-time and historical data, as provided by MonALISA, is also important for developing services able to predict the usage pattern, to aid in efficiently allocating resources globally.
Topological Phase Transition in Antimony
NASA Astrophysics Data System (ADS)
Wong, Man-Hong; Bian, Guang; Xu, Caizhi; Miller, Thomas; Chiang, Tai-Chang
2014-03-01
Spin-orbit coupling (SOC) is believed to cause the parity exchange that drives normal band insulators into the topological regime. Changing the strength of the effective SOC can also induce quantum phase transitions in materials. We performed a first-principles calculation to elucidate the quantum phase transition from a topologically trivial to nontrivial system in a 15-bilayer Sb film. We increased the k-space sampling relative to previous studies and varied the effective SOC in order to observe the changes in the bulk band gap and topological surface states. A transition from a metal to a semimetal is observed as the SOC is tuned from 0% to 100%. At a SOC value near 300%, a transition from a nontrivial topological semimetal to a topological insulator occurs. Varying the effective SOC strength can be realized experimentally by alloy substitution with elements in the same column in the periodic table. Increasing the effective SOC of the Sb film to values above 100% is a model of the Bi1-xSbx alloy, the first three-dimensional topological insulator. Further studies using this method on different systems may lead to the discovery of new topological insulators. This work is supported by the U.S. Department of Energy (Grant No. DE-FG02-07ER46383 for T-CC).
Aspects of photonic topological insulators
NASA Astrophysics Data System (ADS)
Rechtsman, Mikael
2015-03-01
Great excitement surrounding optical topological protection has recently emerged from the promise of endowing photonic devices with quantum Hall-like robustness. Here, I will present the prediction and realization of a photonic topological insulator for light. Topological insulators (TIs) are solid-state materials that are insulators in the bulk, but conduct electricity along their surfaces - and are intrinsically robust to disorder. In particular, when a surface electron in a TI encounters a defect, it simply goes around it without scattering, always exhibiting - quite strikingly - perfect transmission. The structure is composed of an array of coupled helical waveguides; the helicity generates an artificial circularly-polarized force on the photons that breaks time-reversal symmetry. This leads to bands with non-zero Chern number, and thus topologically-protected edge states (protected in the quantum Hall sense - not by any symmetry). Due to the time-dependent force, the band structure must be solved in the Floquet sense; the result bears close resemblance to that of the quantum anomalous Hall effect. I will also present experimental results on the first realization of a ``topological Anderson insulator'' (in a similar setting), where the addition of disorder can make a trivial system topological. Time permitting, I will discuss the question of what it means to have topological interface states in non-Hermitian systems, and show new experiments exploring their properties.
Topology of the resonating valence-bond state - Solitons and high-T(c) superconductivity
NASA Astrophysics Data System (ADS)
Kivelson, Steven A.; Rokhsar, Daniel S.; Sethna, James P.
1987-06-01
The topological order in the resonating valence-bond state is studied. The elementary excitations have reversed charge-statistics relations: there are neutral spin-1/2 fermions and charge + or - e spinless bosons, analogous to the solitons in polyacetylene. The charged excitations are very light, and form a degenerate Bose gas even at high temperatures. This model is discussed in the context of the recently discovered oxide superconductors.
Semilinear (topological) spaces and applications
NASA Technical Reports Server (NTRS)
Prakash, P.; Sertel, M. R.
1971-01-01
Semivector spaces are defined and some of their algebraic aspects are developed including some structure theory. These spaces are then topologized to obtain semilinear topological spaces for which a hierarchy of local convexity axioms is identified. A number of fixed point and minmax theorems for spaces with various local convexity properties are established. The spaces of concern arise naturally as various hyperspaces of linear and semilinear (topological) spaces. It is indicated briefly how all this can be applied in socio-economic analysis and optimization.
Experimental Evidence for Topological Doping in the Cuprates
Tranquada, J. M.
1999-04-06
Some recent experiments that provide support for the concept of topological doping in cuprate superconductors are discussed. Consistent with the idea of charge segregation, it is argued that the scattering associated with the ''resonance'' peak found in YBa{sub 2}Cu{sub 3}O{sub 6+x} and Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8+{delta}} comes from the Cu spins and not from the doped holes.
Topologically induced local P and CP violation in hot QCD
Kharzeev,D.E.
2009-02-01
Very stringent experimental bounds exist on the amount of P and CP violation in strong interactions. Nevertheless, the presence of non-Abelian topological solutions and the axial anomaly make the issue of CP invariance in QCD non-trivial ('the strong CP problem'). Even in the absence of a global P and CP violation the fluctuations of topological charge in the QCD vacuum are expected to play an important role in the breaking of chiral symmetry, and in the mass spectrum and other properties of hadrons. Here I argue that topological fluctuations in hot QCD matter can become directly observable in the presence of a very intense external magnetic field by inducing local P- and CP-odd effects. These local parity-violating phenomena can be described by using the Maxwell-Chern-Simons, or axion, electrodynamics as an effective theory. Local P and CP violation in hot QCD matter can be observed in experiment through the 'chiral magnetic effect' - the separation of electric charge along the axis of magnetic field that is created by the colliding relativistic ions. There is a recent evidence for the electric charge separation relative to the reaction plane of heavy ion collisions from the STAR Collaboration at RHIC.
Stable topological insulators achieved using high energy electron beams.
Zhao, Lukas; Konczykowski, Marcin; Deng, Haiming; Korzhovska, Inna; Begliarbekov, Milan; Chen, Zhiyi; Papalazarou, Evangelos; Marsi, Marino; Perfetti, Luca; Hruban, Andrzej; Wołoś, Agnieszka; Krusin-Elbaum, Lia
2016-01-01
Topological insulators are potentially transformative quantum solids with metallic surface states which have Dirac band structure and are immune to disorder. Ubiquitous charged bulk defects, however, pull the Fermi energy into the bulk bands, denying access to surface charge transport. Here we demonstrate that irradiation with swift (∼2.5 MeV energy) electron beams allows to compensate these defects, bring the Fermi level back into the bulk gap and reach the charge neutrality point (CNP). Controlling the beam fluence, we tune bulk conductivity from p- (hole-like) to n-type (electron-like), crossing the Dirac point and back, while preserving the Dirac energy dispersion. The CNP conductance has a two-dimensional character on the order of ten conductance quanta and reveals, both in Bi2Te3 and Bi2Se3, the presence of only two quantum channels corresponding to two topological surfaces. The intrinsic quantum transport of the topological states is accessible disregarding the bulk size. PMID:26961901
Stable topological insulators achieved using high energy electron beams
NASA Astrophysics Data System (ADS)
Zhao, Lukas; Konczykowski, Marcin; Deng, Haiming; Korzhovska, Inna; Begliarbekov, Milan; Chen, Zhiyi; Papalazarou, Evangelos; Marsi, Marino; Perfetti, Luca; Hruban, Andrzej; Wołoś, Agnieszka; Krusin-Elbaum, Lia
2016-03-01
Topological insulators are potentially transformative quantum solids with metallic surface states which have Dirac band structure and are immune to disorder. Ubiquitous charged bulk defects, however, pull the Fermi energy into the bulk bands, denying access to surface charge transport. Here we demonstrate that irradiation with swift (~2.5 MeV energy) electron beams allows to compensate these defects, bring the Fermi level back into the bulk gap and reach the charge neutrality point (CNP). Controlling the beam fluence, we tune bulk conductivity from p- (hole-like) to n-type (electron-like), crossing the Dirac point and back, while preserving the Dirac energy dispersion. The CNP conductance has a two-dimensional character on the order of ten conductance quanta and reveals, both in Bi2Te3 and Bi2Se3, the presence of only two quantum channels corresponding to two topological surfaces. The intrinsic quantum transport of the topological states is accessible disregarding the bulk size.
Stable topological insulators achieved using high energy electron beams
Zhao, Lukas; Konczykowski, Marcin; Deng, Haiming; Korzhovska, Inna; Begliarbekov, Milan; Chen, Zhiyi; Papalazarou, Evangelos; Marsi, Marino; Perfetti, Luca; Hruban, Andrzej; Wołoś, Agnieszka; Krusin-Elbaum, Lia
2016-01-01
Topological insulators are potentially transformative quantum solids with metallic surface states which have Dirac band structure and are immune to disorder. Ubiquitous charged bulk defects, however, pull the Fermi energy into the bulk bands, denying access to surface charge transport. Here we demonstrate that irradiation with swift (∼2.5 MeV energy) electron beams allows to compensate these defects, bring the Fermi level back into the bulk gap and reach the charge neutrality point (CNP). Controlling the beam fluence, we tune bulk conductivity from p- (hole-like) to n-type (electron-like), crossing the Dirac point and back, while preserving the Dirac energy dispersion. The CNP conductance has a two-dimensional character on the order of ten conductance quanta and reveals, both in Bi2Te3 and Bi2Se3, the presence of only two quantum channels corresponding to two topological surfaces. The intrinsic quantum transport of the topological states is accessible disregarding the bulk size. PMID:26961901
Conserved charges in 3D gravity
Blagojevic, M.; Cvetkovic, B.
2010-06-15
The covariant canonical expression for the conserved charges, proposed by Nester, is tested on several solutions in three-dimensional gravity with or without torsion and topologically massive gravity. In each of these cases, the calculated values of energy momentum and angular momentum are found to satisfy the first law of black hole thermodynamics.
Unusual spin dynamics in topological insulators.
Dóra, Balázs; Simon, Ferenc
2015-01-01
The dynamic spin susceptibility (DSS) has a ubiquitous Lorentzian form around the Zeeman energy in conventional materials with weak spin orbit coupling, whose spectral width characterizes the spin relaxation rate. We show that DSS has an unusual non-Lorentzian form in topological insulators, which are characterized by strong SOC, and the anisotropy of the DSS reveals the orientation of the underlying spin texture of topological states. At zero temperature, the high frequency part of DSS is universal and increases in certain directions as ω(d-1) with d = 2 and 3 for surface states and Weyl semimetals, respectively, while for helical edge states, the interactions renormalize the exponent as d = 2K - 1 with K the Luttinger-liquid parameter. As a result, spin relaxation rate cannot be deduced from the DSS in contrast to the case of usual metals, which follows from the strongly entangled spin and charge degrees of freedom in these systems. PMID:26439629
New topological excitations in quantum Hall systems
NASA Astrophysics Data System (ADS)
Lyanda-Geller, Yuli; Lin, Tsuging; Simion, George; Watson, John D.; Manfra, Michael J.; Csathy, Gabor; Rokhinson, Leonid
2014-03-01
We discover new topological excitations of two dimensional electrons in the quantum Hall regime. The strain dependence of resistivity observed experimentally is shown to change sign upon crossing filling-factor-specified boundaries of reentrant integer quantum Hall effect (RIQHE) states. This observation violates the known symmetry of electron bubbles thought to be responsible for the RIQHE. We demonstrate theoretically that electron bubbles become elongated in the vicinity of charge defects and form textures of finite size. Calculations confirm that textures lower the energy of excitations. In the two-electron bubble crystal these textures form two-dimensional hedgehogs around defects having one extra electron, and vortices around defects lacking one electron. Strain affects vortices and hedgehogs differently, explaining striking strain-dependent resistivity. The sharp transition from insulating RIQHE state to conducting state is caused by melting of Abrikosov crystal comprised of the defects. The proposed physical mechanism of conductivity due to topological defects is shown to lead to an unusually large magnitude of the strain effect on resistivity in the range of RIQHE filling factors, in agreement with experiment. Research was partially supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Awards DE-SC0010544 (Y.L-G), DE-SC0008630 (L.P.R.), DE-SC0006671 (G.S. and M.M.).
Persistent optical gating of a topological insulator
Yeats, Andrew L.; Pan, Yu; Richardella, Anthony; Mintun, Peter J.; Samarth, Nitin; Awschalom, David D.
2015-01-01
The spin-polarized surface states of topological insulators (TIs) are attractive for applications in spintronics and quantum computing. A central challenge with these materials is to reliably tune the chemical potential of their electrons with respect to the Dirac point and the bulk bands. We demonstrate persistent, bidirectional optical control of the chemical potential of (Bi,Sb)2Te3 thin films grown on SrTiO3. By optically modulating a space-charge layer in the SrTiO3 substrates, we induce a persistent field effect in the TI films comparable to electrostatic gating techniques but without additional materials or processing. This enables us to optically pattern arbitrarily shaped p- and n-type regions in a TI, which we subsequently image with scanning photocurrent microscopy. The ability to optically write and erase mesoscopic electronic structures in a TI may aid in the investigation of the unique properties of the topological insulating phase. The gating effect also generalizes to other thin-film materials, suggesting that these phenomena could provide optical control of chemical potential in a wide range of ultrathin electronic systems. PMID:26601300
Unusual spin dynamics in topological insulators
Dóra, Balázs; Simon, Ferenc
2015-01-01
The dynamic spin susceptibility (DSS) has a ubiquitous Lorentzian form around the Zeeman energy in conventional materials with weak spin orbit coupling, whose spectral width characterizes the spin relaxation rate. We show that DSS has an unusual non-Lorentzian form in topological insulators, which are characterized by strong SOC, and the anisotropy of the DSS reveals the orientation of the underlying spin texture of topological states. At zero temperature, the high frequency part of DSS is universal and increases in certain directions as ωd−1 with d = 2 and 3 for surface states and Weyl semimetals, respectively, while for helical edge states, the interactions renormalize the exponent as d = 2K − 1 with K the Luttinger-liquid parameter. As a result, spin relaxation rate cannot be deduced from the DSS in contrast to the case of usual metals, which follows from the strongly entangled spin and charge degrees of freedom in these systems. PMID:26439629
Topology in QCD and the axion abundance
NASA Astrophysics Data System (ADS)
Kitano, Ryuichiro; Yamada, Norikazu
2015-10-01
The temperature dependence of the topological susceptibility in QCD, χ t , essentially determines the abundance of the QCD axion in the Universe, and is commonly estimated, based on the instanton picture, to be a certain negative power of temperature. While lattice QCD should be able to check this behavior in principle, the temperature range where lattice QCD works is rather limited in practice, because the topological charge is apt to freezes at high temperatures. In this work, two exploratory studies are presented. In the first part, we try to specify the temperature range in the quenched approximation. Since our purpose here is to estimate the range expected in unquenched QCD through quenched simulations, hybrid Monte Carlo (HMC) algorithm is employed instead of heat-bath algorithm. We obtain an indication that unquenched calculations of χ t encounter the serious problem of autocorrelation already at T ˜ 2 T c or even below with the plain HMC. In the second part, we revisit the axion abundance. The absolute value and the temperature dependence of χ t in real QCD can be significantly different from that in the quenched approximation, and is not well established above the critical temperature. Motivated by this fact and precedent arguments which disagree with the conventional instanton picture, we estimate the axion abundance in an extreme case where χ t decreases much faster than the conventional power-like behavior. We find a significant enhancement of the axion abundance in such a case.
Interaction-enabled topological crystalline phases
NASA Astrophysics Data System (ADS)
Lapa, Matthew F.; Teo, Jeffrey C. Y.; Hughes, Taylor L.
2016-03-01
In this article we provide a general mechanism for generating interaction-enabled fermionic topological phases. We illustrate the mechanism with crystalline symmetry-protected topological phases in one, two, and three spatial dimensions. These nontrivial phases require interactions for their existence, and in the cases we consider, the free-fermion classification yields only a trivial phase. For the one- and two-dimensional phases we consider, we provide explicit exactly solvable models which realize the interaction-enabled phases. Similar to the interpretation of the Kitaev Majorana wire as a mean-field p -wave superconductor Hamiltonian arising from an interacting model with quartic interactions, we show that our systems can be interpreted as "mean-field" charge-4 e superconductors arising, e.g., from an interacting model with eight-body interactions or through another physical mechanism. The quartet superconducting nature allows for the teleportation of full Cooper pairs and, in two dimensions, for interesting semiclassical crystalline defects with non-Abelian anyon bound states.
50 CFR 1.5 - Officer in Charge.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 50 Wildlife and Fisheries 1 2010-10-01 2010-10-01 false Officer in Charge. 1.5 Section 1.5 Wildlife and Fisheries UNITED STATES FISH AND WILDLIFE SERVICE, DEPARTMENT OF THE INTERIOR GENERAL PROVISIONS DEFINITIONS § 1.5 Officer in Charge. Officer in Charge means any person in charge of a national fish hatchery, national wildlife refuge,...
Schwerdtfeger, Peter; Wirz, Lukas N; Avery, James
2015-01-01
Fullerenes are carbon molecules that form polyhedral cages. Their bond structures are exactly the planar cubic graphs that have only pentagon and hexagon faces. Strikingly, a number of chemical properties of a fullerene can be derived from its graph structure. A rich mathematics of cubic planar graphs and fullerene graphs has grown since they were studied by Goldberg, Coxeter, and others in the early 20th century, and many mathematical properties of fullerenes have found simple and beautiful solutions. Yet many interesting chemical and mathematical problems in the field remain open. In this paper, we present a general overview of recent topological and graph theoretical developments in fullerene research over the past two decades, describing both solved and open problems. WIREs Comput Mol Sci 2015, 5:96–145. doi: 10.1002/wcms.1207 Conflict of interest: The authors have declared no conflicts of interest for this article. For further resources related to this article, please visit the WIREs website. PMID:25678935
Comprehensible Presentation of Topological Information
Weber, Gunther H.; Beketayev, Kenes; Bremer, Peer-Timo; Hamann, Bernd; Haranczyk, Maciej; Hlawitschka, Mario; Pascucci, Valerio
2012-03-05
Topological information has proven very valuable in the analysis of scientific data. An important challenge that remains is presenting this highly abstract information in a way that it is comprehensible even if one does not have an in-depth background in topology. Furthermore, it is often desirable to combine the structural insight gained by topological analysis with complementary information, such as geometric information. We present an overview over methods that use metaphors to make topological information more accessible to non-expert users, and we demonstrate their applicability to a range of scientific data sets. With the increasingly complex output of exascale simulations, the importance of having effective means of providing a comprehensible, abstract overview over data will grow. The techniques that we present will serve as an important foundation for this purpose.
Nematic colloids, topology and photonics.
Musevic, I
2013-04-13
We review and discuss recent progress in the field of nematic colloids, with an emphasis on possible future applications in photonics. The role of the topology is described, based on experimental manipulations of the topological defects in nematic colloids. The topology of the ordering field in nematics provides the forces between colloidal particles that are unique to these materials. We also discuss recent progress in the new field of active microphotonic devices based on liquid crystals (LCs), where chiral nematic microlasers and tuneable nematic microresonators are just two of the recently discovered examples. We conclude that the combination of topology and microphotonic devices based on LCs provides an interesting platform for future progress in the field of LCs. PMID:23459967
Quantum Chemical Topology: Knowledgeable atoms in peptides
NASA Astrophysics Data System (ADS)
Popelier, Paul L. A.
2012-06-01
The need to improve atomistic biomolecular force fields remains acute. Fortunately, the abundance of contemporary computing power enables an overhaul of the architecture of current force fields, which typically base their electrostatics on fixed atomic partial charges. We discuss the principles behind the electrostatics of a more realistic force field under construction, called QCTFF. At the heart of QCTFF lies the so-called topological atom, which is a malleable box, whose shape and electrostatics changes in response to a changing environment. This response is captured by a machine learning method called Kriging. Kriging directly predicts each multipole moment of a given atom (i.e. the output) from the coordinates of the nuclei surrounding this atom (i.e. the input). This procedure yields accurate interatomic electrostatic energies, which form the basis for future-proof progress in force field design.
Topological defect dynamics in operando battery nanoparticles
NASA Astrophysics Data System (ADS)
Ulvestad, A.; Singer, A.; Clark, J. N.; Cho, H. M.; Kim, J. W.; Harder, R.; Maser, J.; Meng, Y. S.; Shpyrko, O. G.
2015-06-01
Topological defects can markedly alter nanomaterial properties. This presents opportunities for “defect engineering,” where desired functionalities are generated through defect manipulation. However, imaging defects in working devices with nanoscale resolution remains elusive. We report three-dimensional imaging of dislocation dynamics in individual battery cathode nanoparticles under operando conditions using Bragg coherent diffractive imaging. Dislocations are static at room temperature and mobile during charge transport. During the structural phase transformation, the lithium-rich phase nucleates near the dislocation and spreads inhomogeneously. The dislocation field is a local probe of elastic properties, and we find that a region of the material exhibits a negative Poisson’s ratio at high voltage. Operando dislocation imaging thus opens a powerful avenue for facilitating improvement and rational design of nanostructured materials.
Surface conduction in encapsulated topological gated structures
NASA Astrophysics Data System (ADS)
Deshko, Yury; Korzhovska, Inna; Zhao, Lukas; Arefe, Ghidewon; Konczykowski, Marcin; Krusin-Elbaum, Lia
2015-03-01
In three-dimensional (3D) topological insulators (TIs), the surface Dirac fermions intermix with the conducting bulk, thereby complicating access to the low-energy surface charge transport or magnetic response. The subsurface 2D states of bulk origin are vulnerable to bandbending due to surface adatoms, a band modification thought to be responsible for the `ageing' effect. To minimize this effect, we have developed an inert environment mechanical exfoliation technique to fabricate transistor-like gated structures in which prototypical binary TIs as well as ultra-low bulk carrier density ternaries (such as Bi2Te2Se) were encapsulated by thin h-BN layers, with electrical contacts made using exfoliated graphene. The effects of electrostatic tuning by the gate bias voltage on surface conductivity as a function of thickness of the TI layers and the variation with disorder will be presented. Supported by NSF-DMR-1312483, and DOD-W911NF-13-1-0159.
NASA Astrophysics Data System (ADS)
Qu, Dong-Xia; Kou, Xufeng; Lang, Murong; Crowhurst, Jonathan; Armstrong, Michael; Zaug, Joseph; Wang, Kang L.; Chapline, George
2015-03-01
The remarkable nature of surface states in topological insulators is expected to have a unique photocurrent response to electromagnetic radiation. However, the surface and bulk photo-excited charge transport mechanisms, in relation to the band bending at the electrode-topological insulator interface, have not been well understood. Here, we present scanning photocurrent microscopy measurements on a gated topological insulator microdevice and show that the spin-polarized photocurrent displays direction reversal near the electrical contact interfaces. We discuss two possible mechanisms, which alternatively play dominant roles in the helicity-dependent photocurrent map. Our analysis determines the magnitude of each contribution, and reveals the governing process under different gate conditions.
Topological aspects of band theory
NASA Astrophysics Data System (ADS)
Soluyanov, Alexey A.
Band theory has proven to be one of the most successful developments in condensed matter theory. It is the basis of our current understanding of crystalline solids, describing complex electronic behavior in terms of a single quasi-particle that moves in some effective field of the crystal lattice environment and other particles. In recent years topological and geometrical considerations opened a fundamentally new branch of research in band theory. One of the major advances in this field came with the realization that insulating band structures can be classified according to the values of some topological invariants associated with the occupied single-particle states. Insulators that correspond to non-trivial values of these topological invariants realize new states of matter with properties drastically different from those attributed to an ordinary insulator. In this work we address questions that arise in the context of band theory in the presence of topologically non-trivial bands. Part of the thesis is aimed at the actual determination of the presence of non-trivial band topology. We develop a method to distinguish an ordinary insulator from a topological one in the presence of time-reversal symmetry. The method is implemented within the density functional theory framework and is illustrated with applications to real materials in ab initio calculations. Another question considered in this work is that of a real-space representation of topological insulators, and in particular, the construction of Wannier functions - localized real-space wavefunctions. Wannier functions form one of the most powerful tools in band theory, and it is very important to understand how to implement Wannier function techniques in the presence of topological bands. In some cases bands with non-trivial topology do not allow for the construction of exponentially localized Wannier functions. While previous work has shown that in the presence of time-reversal symmetry such a construction should be possible in principle, it has remained unclear how to do it in practice. We present an explicit construction of a Wannier representation for a particular model of a time-reversal invariant topological insulator. This construction is very different from the one used for ordinary band insulators. We then proceed to develop a procedure that allows for such a construction in the general case, without any reference to a particular model. Our work provides a basis for extending Wannier function techniques to topologically non-trivial band structures.
Experimental Realizations of Magnetic Topological Insulator and Topological Crystalline Insulator
NASA Astrophysics Data System (ADS)
Xu, Suyang
2013-03-01
Over the past few years the experimental research on three-dimensional topological insulators have emerged as one of the most rapidly developing fields in condensed matter physics. In this talk, we report on two new developments in the field: The first part is on the dynamic interplay between ferromagnetism and the Z2 topological insulator state (leading to a magnetic topological insulator). We present our spin-resolved photoemission and magnetic dichroic experiments on MBE grown films where a hedgehog-like spin texture is revealed on the magnetically ordered surface of Mn-Bi2Se3 revealing a Berry's phase gradient in energy-momentum space of the crystal. A chemically/electrically tunable Berry's phase switch is further demonstrated via the tuning of the spin groundstate in Mn-Bi2Se3 revealed in our data (Nature Physics 8, 616 (2012)). The second part of this talk describes our experimental observation of a new topological phase of matter, namely a topological crystalline insulator where space group symmetries replace the role of time-reversal symmetry in an otherwise Z2 topological insulator predicted in theory. We experimentally investigate the possibility of a mirror symmetry protected topological phase transition in the Pb1-xSnxTe alloy system, which has long been known to contain an even number of band inversions based on band theory. Our experimental results show that at a composition below the theoretically predicted band inversion, the system is fully gapped, whereas in the band-inverted regime, the surface exhibits even number of spin-polarized Dirac cone states revealing mirror-protected topological order (Nature Communications 3, 1192 (2012)) distinct from that observed in Z2 topological insulators. We discuss future experimental possibilities opened up by these new developments in topological insulators research. This work is in collaboration with M. Neupane, C. Liu, N. Alidoust, I. Belopolski, D. Qian, D.M. Zhang, A. Richardella, A. Marcinkova, Q. Gibson, R. Sankar, Y.J. Wang, T. Chang, H. Jeng, H. Lin, L.A. Wray, J.D. Denlinger, M. Leandersson, T. Balasubramanian, J. Snchez-Barriga, O. Rader, G. Landolt, B. Slomski, J.H. Dil, F.C. Chou, E. Morosan, N. Samarth, R.J. Cava and M.Z. Hasan. This work is primarily supported by U.S. DOE grant DE-FG-02-05ER46200.
Z2 Topological Anderson Insulator
NASA Astrophysics Data System (ADS)
Yamakage, Ai; Nomura, Kentaro; Imura, Ken-Ichiro; Kuramoto, Yoshio
2012-12-01
Effects of disorder on a two-dimensional Z2 topological insulator are studied numerically. We propose and study the phase diagram of a variant of Bernevig-Hughes-Zhang model, which takes account of the sz non-conserving spin-orbit coupling. Using scaling analyses, we determine the phase boundary and the critical exponent characterizing the transition between metallic and the topologically insulating phases.
Refining the shifted topological vertex
Drissi, L. B.; Jehjouh, H.; Saidi, E. H.
2009-01-15
We study aspects of the refining and shifting properties of the 3d MacMahon function C{sub 3}(q) used in topological string theory and BKP hierarchy. We derive the explicit expressions of the shifted topological vertex S{sub {lambda}}{sub {mu}}{sub {nu}}(q) and its refined version T{sub {lambda}}{sub {mu}}{sub {nu}}(q,t). These vertices complete results in literature.
Topics in topological band systems
NASA Astrophysics Data System (ADS)
Huang, Zhoushen
The discovery of integer quantum Hall effect and its subsequent theoretical formulation heralded a new paradigm of thinking in condensed matter physics, which has by now blossomed into the rapidly growing field of topological phases. In this work we investigate several mutually related topics in the framework of topological band theory. In Chapter 2, we study solutions to boundary states on a lattice and see how they are related to the bulk topology. To elicit a real space manifestation of the non-trivial topology, the presence of a physical edge is not strictly necessary. We study two other possibilities, namely the entanglement spectrum associated with an imaginary spatial boundary, and the localization centers of Wannier functions, in Chapters 3,4, and 5. Topological classification through discrete indices is so far possible only for systems described by pure quantum states---in the existing scheme, quantization is lost for systems in mixed states. In Chapter 6, we present a program through which discrete topological indices can be defined for topological band systems at finite temperature, based on Uhlmann's parallel transport of density matrices. The potential of topologocal insulators in realistic applications lies in the existence of Dirac nodes on its surface spectrum. Dirac physics, however, is not exclusive to TI surfaces. In a recently discovered class of materials known as Weyl semimetals, energy nodes which emit linear dispersions also occur in the bulk material. In Chapter 7, we study the possibility of resonance states induced by localized impurities near the nodal energy in Weyl semimetals, which will help us in understanding the stability of density-of-state suppression at the energy nodes. Finally, in Chapter 8, we apply the topological characterization developed for noninteracting particles to a class of interacting spin models in 3D, which are generalizations of Kitaev's honeycomb model, and identify several exotic quantum phases such as spin metals and spin semimetals.
Clarke, John
1980-09-01
The purpose of this article is to review the theory of charge imbalance, and to discuss its relevance to a number of experimental situations. We introduce the concepts of quasiparticle charge and charge imbalance, and discuss the generation and detection of charge imbalance by tunneling. We describe the relaxation of the injected charge imbalance by inelastic scattering processes, and show how the Boltzmann equation can be solved to obtain the steady state quasiparticle distribution and the charge relaxation rate. Details are given of experiments to measure charge imbalance and the charge relaxation rate when inelastic scattering is the predominant relaxation mechanism. Experiments on and theories of other charge relaxation mechanisms are discussed, namely relaxation via elastic scattering in the presence of energy gap anisotropy, or in the presence of a pair breaking mechanism such as magnetic impurities or an applied supercurrent or magnetic field. We describe three other situations in which charge imbalance occurs, namely the resistance of the NS interface, phase slip centers, and the flow of a supercurrent in the presence of a temperature gradient.
Topological Insulators from Group Cohomology
NASA Astrophysics Data System (ADS)
Alexandradinata, A.; Wang, Zhijun; Bernevig, B. Andrei
2016-04-01
We classify insulators by generalized symmetries that combine space-time transformations with quasimomentum translations. Our group-cohomological classification generalizes the nonsymmorphic space groups, which extend point groups by real-space translations; i.e., nonsymmorphic symmetries unavoidably translate the spatial origin by a fraction of the lattice period. Here, we further extend nonsymmorphic groups by reciprocal translations, thus placing real and quasimomentum space on equal footing. We propose that group cohomology provides a symmetry-based classification of quasimomentum manifolds, which in turn determines the band topology. In this sense, cohomology underlies band topology. Our claim is exemplified by the first theory of time-reversal-invariant insulators with nonsymmorphic spatial symmetries. These insulators may be described as "piecewise topological," in the sense that subtopologies describe the different high-symmetry submanifolds of the Brillouin zone, and the various subtopologies must be pieced together to form a globally consistent topology. The subtopologies that we discover include a glide-symmetric analog of the quantum spin Hall effect, an hourglass-flow topology (exemplified by our recently proposed KHgSb material class), and quantized non-Abelian polarizations. Our cohomological classification results in an atypical bulk-boundary correspondence for our topological insulators.
Topological Photonics for Continuous Media
NASA Astrophysics Data System (ADS)
Silveirinha, Mario
Photonic crystals have revolutionized light-based technologies during the last three decades. Notably, it was recently discovered that the light propagation in photonic crystals may depend on some topological characteristics determined by the manner how the light states are mutually entangled. The usual topological classification of photonic crystals explores the fact that these structures are periodic. The periodicity is essential to ensure that the underlying wave vector space is a closed surface with no boundary. In this talk, we prove that it is possible calculate Chern invariants for a wide class of continuous bianisotropic electromagnetic media with no intrinsic periodicity. The nontrivial topology of the relevant continuous materials is linked with the emergence of edge states. Moreover, we will demonstrate that continuous photonic media with the time-reversal symmetry can be topologically characterized by a Z2 integer. This novel classification extends for the first time the theory of electronic topological insulators to a wide range of photonic platforms, and is expected to have an impact in the design of novel photonic systems that enable a topologically protected transport of optical energy. This work is supported in part by Fundacao para a Ciencia e a Tecnologia Grant Number PTDC/EEI-TEL/4543/2014.
Topological gray-scale watershed transformation
NASA Astrophysics Data System (ADS)
Couprie, Michel; Bertrand, Gilles
1997-10-01
We propose an original approach to the watershed problem, based on topology. We introduce a 1D topology for grayscale images, and more generally for weighted graphs. This topology allows us to precisely define a topological grayscale transformation that generalizes the action of a watershed transformation. Furthermore, we propose an efficient algorithm to compute this topological grayscale transformation,a nd we give an example of application to image segmentation.
Spin-transfer torque generated by a topological insulator.
Mellnik, A R; Lee, J S; Richardella, A; Grab, J L; Mintun, P J; Fischer, M H; Vaezi, A; Manchon, A; Kim, E-A; Samarth, N; Ralph, D C
2014-07-24
Magnetic devices are a leading contender for the implementation of memory and logic technologies that are non-volatile, that can scale to high density and high speed, and that do not wear out. However, widespread application of magnetic memory and logic devices will require the development of efficient mechanisms for reorienting their magnetization using the least possible current and power. There has been considerable recent progress in this effort; in particular, it has been discovered that spin-orbit interactions in heavy-metal/ferromagnet bilayers can produce strong current-driven torques on the magnetic layer, via the spin Hall effect in the heavy metal or the Rashba-Edelstein effect in the ferromagnet. In the search for materials to provide even more efficient spin-orbit-induced torques, some proposals have suggested topological insulators, which possess a surface state in which the effects of spin-orbit coupling are maximal in the sense that an electron's spin orientation is fixed relative to its propagation direction. Here we report experiments showing that charge current flowing in-plane in a thin film of the topological insulator bismuth selenide (Bi2Se3) at room temperature can indeed exert a strong spin-transfer torque on an adjacent ferromagnetic permalloy (Ni81Fe19) thin film, with a direction consistent with that expected from the topological surface state. We find that the strength of the torque per unit charge current density in Bi2Se3 is greater than for any source of spin-transfer torque measured so far, even for non-ideal topological insulator films in which the surface states coexist with bulk conduction. Our data suggest that topological insulators could enable very efficient electrical manipulation of magnetic materials at room temperature, for memory and logic applications. PMID:25056062
NASA Technical Reports Server (NTRS)
Minow, Joseph I.
2014-01-01
(1) High energy (>100keV) electrons penetrate spacecraft walls and accumulate in dielectrics or isolated conductors; (2) Threat environment is energetic electrons with sufficient flux to charge circuit boards, cable insulation, and ungrounded metal faster than charge can dissipate; (3) Accumulating charge density generates electric fields in excess of material breakdown strenght resulting in electrostatic discharge; and (4) System impact is material damage, discharge currents inside of spacecraft Faraday cage on or near critical circuitry, and RF noise.
Bringing Definitions into High Definition
ERIC Educational Resources Information Center
Mason, John
2010-01-01
Why do definitions play such a central role in mathematics? It may seem obvious that precision about the terms one uses is necessary in order to use those terms reasonably (while reasoning). Definitions are chosen so as to be definite about the terms one uses, but also to make both the statement of, and the reasoning to justify, theorems as…
Topological magnetoelectric effects in thin films of topological insulators
NASA Astrophysics Data System (ADS)
Morimoto, Takahiro; Furusaki, Akira; Nagaosa, Naoto
2015-08-01
We propose that the topological magnetoelectric (ME) effect, a hallmark of topological insulators (TIs), can be realized in thin films of TIs in the ν =0 quantum Hall state under magnetic field or by doping two magnetic ions with opposite signs of exchange coupling. These setups have the advantage compared to previously proposed setups that a uniform configuration of magnetic field or magnetization is sufficient for the realization of the topological ME effect. To verify our proposal, we numerically calculate ME response of TI thin films in the cylinder geometry and that of effective 2D models of surface Dirac fermions. The ME response is shown to converge to the quantized value corresponding to the axion angle θ =±π in the limit of the large top and bottom surface area of TI films, where nontopological contributions from the bulk and the side surface are negligible.
Monolayer Topological Insulators: Silicene, Germanene, and Stanene
NASA Astrophysics Data System (ADS)
Ezawa, Motohiko
2015-12-01
We report the recent progress on the theoretical aspects of monolayer topological insulators including silicene, germanene and stanene, which are monolayer honeycomb structures of silicon, germanium and tin, respectively. They show quantum spin Hall effects in nature due to the spin-orbit interaction. The band gap can be tuned by applying perpendicular electric field, which induces a topological phase transition. We also analyze the topological properties of generic honeycomb systems together with the classification of topological insulators. Phase diagrams of topological insulators and superconductors in honeycomb systems are explicitly determined. We also investigate topological electronics including a topological field-effect transistor, the topological Kirchhoff’s law and the topological spin-valleytronics.
Second topological conjugate transformation in symbolic dynamics
NASA Astrophysics Data System (ADS)
Peng, Shou-Li; Zhang, Xu-Sheng
1998-05-01
A topological conjugate transformation defined as the joint actions of both the Derrida-Gervois-Pomeau (DGP) * product operation QC * in the symbolic space (or its corresponding parameter space) and the mapping f\\|QC\\| in the symbolic dynamics of the interval, which with respect to the first topological conjugate transformation (the merely action of QC * ) is called the second topological conjugate transformation, is found. It reveals conspicuously clustering of the orbital points and preserves the topological entropy of the dynamical systems. In analogy to the first topological conjugate transformation, there exist also infinitely many second topological conjugate maps. The second topological conjugate transformation provides a topological foundation for Feigenbaum's [J. Stat. Phys. 19, 25 (1978); 21, 669 (1979)] universalities and a basic topological method for discriminating the compound words in the sense of the DGP * product in the symbolic space Σ2 of two letters. Therefore it opens up a way to seek the generalized * product for the more complex dynamical systems.
Carbon Tetragons as Definitive Spin Switches in Narrow Zigzag Graphene Nanoribbons
NASA Astrophysics Data System (ADS)
Cui, Ping; Zhang, Qiang; Zhu, Hongbin; Li, Xiaoxia; Wang, Weiyi; Li, Qunxiang; Zeng, Changgan; Zhang, Zhenyu
2016-01-01
Precise spatial control of the spin propagation channels is of fundamental and practical importance in future graphene-based spintronic devices. Here we use first-principles calculations to show that when narrow zigzag graphene nanoribbons are connected to form junctions or superlattices, properly placed square-shaped carbon tetragons not only serve as effective bundles of the two incoming spin edge channels, but also act as definitive topological spin switches for the two outgoing channels. The nanoribbon segments are largely drawn from different acene molecules. We further show that such spin switches can lift the degeneracy between the two spin propagation channels, which enables tunability of different magnetic states upon charge doping. Preliminary experimental supports for the realization of such tetragons connecting nanoribbon segments are also presented.
Carbon Tetragons as Definitive Spin Switches in Narrow Zigzag Graphene Nanoribbons.
Cui, Ping; Zhang, Qiang; Zhu, Hongbin; Li, Xiaoxia; Wang, Weiyi; Li, Qunxiang; Zeng, Changgan; Zhang, Zhenyu
2016-01-15
Precise spatial control of the spin propagation channels is of fundamental and practical importance in future graphene-based spintronic devices. Here we use first-principles calculations to show that when narrow zigzag graphene nanoribbons are connected to form junctions or superlattices, properly placed square-shaped carbon tetragons not only serve as effective bundles of the two incoming spin edge channels, but also act as definitive topological spin switches for the two outgoing channels. The nanoribbon segments are largely drawn from different acene molecules. We further show that such spin switches can lift the degeneracy between the two spin propagation channels, which enables tunability of different magnetic states upon charge doping. Preliminary experimental supports for the realization of such tetragons connecting nanoribbon segments are also presented. PMID:26824558
Medlin, John B.
1976-05-25
A charging machine for loading fuel slugs into the process tubes of a nuclear reactor includes a tubular housing connected to the process tube, a charging trough connected to the other end of the tubular housing, a device for loading the charging trough with a group of fuel slugs, means for equalizing the coolant pressure in the charging trough with the pressure in the process tubes, means for pushing the group of fuel slugs into the process tube and a latch and a seal engaging the last object in the group of fuel slugs to prevent the fuel slugs from being ejected from the process tube when the pusher is removed and to prevent pressure liquid from entering the charging machine.
Topological Insulators at Room Temperature
Zhang, Haijun; Liu, Chao-Xing; Qi, Xiao-Liang; Dai, Xi; Fang, Zhong; Zhang, Shou-Cheng; /Stanford U., Phys. Dept.
2010-03-25
Topological insulators are new states of quantum matter with surface states protected by the time-reversal symmetry. In this work, we perform first-principle electronic structure calculations for Sb{sub 2}Te{sub 3}, Sb{sub 2}Se{sub 3}, Bi{sub 2}Te{sub 3} and Bi{sub 2}Se{sub 3} crystals. Our calculations predict that Sb{sub 2}Te{sub 3}, Bi{sub 2}T e{sub 3} and Bi{sub 2}Se{sub 3} are topological insulators, while Sb{sub 2}Se{sub 3} is not. In particular, Bi{sub 2}Se{sub 3} has a topologically non-trivial energy gap of 0.3eV , suitable for room temperature applications. We present a simple and unified continuum model which captures the salient topological features of this class of materials. These topological insulators have robust surface states consisting of a single Dirac cone at the {Lambda} point.
Characterization of heterocyclic rings through quantum chemical topology.
Griffiths, Mark Z; Popelier, Paul L A
2013-07-22
Five-membered rings are found in a myriad of molecules important in a wide range of areas such as catalysis, nutrition, and drug and agrochemical design. Systematic insight into their largely unexplored chemical space benefits from first principle calculations presented here. This study comprehensively investigates a grand total of 764 different rings, all geometry optimized at the B3LYP/6-311+G(2d,p) level, from the perspective of Quantum Chemical Topology (QCT). For the first time, a 3D space of local topological properties was introduced, in order to characterize rings compactly. This space is called RCP space, after the so-called ring critical point. This space is analogous to BCP space, named after the bond critical point, which compactly and successfully characterizes a chemical bond. The relative positions of the rings in RCP space are determined by the nature of the ring scaffold, such as the heteroatoms within the ring or the number of π-bonds. The summed atomic QCT charges of the five ring atoms revealed five features (number and type of heteroatom, number of π-bonds, substituent and substitution site) that dictate a ring's net charge. Each feature independently contributes toward a ring's net charge. Each substituent has its own distinct and systematic effect on the ring's net charge, irrespective of the ring scaffold. Therefore, this work proves the possibility of designing a ring with specific properties by fine-tuning it through manipulation of these five features. PMID:23795608
5 CFR 630.206 - Minimum charge.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 5 Administrative Personnel 1 2010-01-01 2010-01-01 false Minimum charge. 630.206 Section 630.206 Administrative Personnel OFFICE OF PERSONNEL MANAGEMENT CIVIL SERVICE REGULATIONS ABSENCE AND LEAVE Definitions and General Provisions for Annual and Sick Leave § 630.206 Minimum charge. (a) Unless an...
5 CFR 630.206 - Minimum charge.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 5 Administrative Personnel 1 2014-01-01 2014-01-01 false Minimum charge. 630.206 Section 630.206 Administrative Personnel OFFICE OF PERSONNEL MANAGEMENT CIVIL SERVICE REGULATIONS ABSENCE AND LEAVE Definitions and General Provisions for Annual and Sick Leave § 630.206 Minimum charge. (a) Unless an...
5 CFR 630.206 - Minimum charge.
Code of Federal Regulations, 2011 CFR
2011-01-01
... 5 Administrative Personnel 1 2011-01-01 2011-01-01 false Minimum charge. 630.206 Section 630.206 Administrative Personnel OFFICE OF PERSONNEL MANAGEMENT CIVIL SERVICE REGULATIONS ABSENCE AND LEAVE Definitions and General Provisions for Annual and Sick Leave § 630.206 Minimum charge. (a) Unless an...
5 CFR 630.206 - Minimum charge.
Code of Federal Regulations, 2012 CFR
2012-01-01
... 5 Administrative Personnel 1 2012-01-01 2012-01-01 false Minimum charge. 630.206 Section 630.206 Administrative Personnel OFFICE OF PERSONNEL MANAGEMENT CIVIL SERVICE REGULATIONS ABSENCE AND LEAVE Definitions and General Provisions for Annual and Sick Leave § 630.206 Minimum charge. (a) Unless an...
5 CFR 630.206 - Minimum charge.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 5 Administrative Personnel 1 2013-01-01 2013-01-01 false Minimum charge. 630.206 Section 630.206 Administrative Personnel OFFICE OF PERSONNEL MANAGEMENT CIVIL SERVICE REGULATIONS ABSENCE AND LEAVE Definitions and General Provisions for Annual and Sick Leave § 630.206 Minimum charge. (a) Unless an...
Code of Federal Regulations, 2010 CFR
2010-07-01
... CFR PART 191 DISPOSAL REGULATIONS General Provisions § 194.2 Definitions. Unless otherwise indicated... Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) RADIATION PROTECTION PROGRAMS CRITERIA...). Administrator's authorized representative means the director in charge of radiation programs at the...
Code of Federal Regulations, 2011 CFR
2011-07-01
... CFR PART 191 DISPOSAL REGULATIONS General Provisions § 194.2 Definitions. Unless otherwise indicated... Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) RADIATION PROTECTION PROGRAMS CRITERIA...). Administrator's authorized representative means the director in charge of radiation programs at the...
Landau theory of topological defects in multiferroic hexagonal manganites.
Artyukhin, Sergey; Delaney, Kris T; Spaldin, Nicola A; Mostovoy, Maxim
2014-01-01
Topological defects in ordered states with spontaneously broken symmetry often have unusual physical properties, such as fractional electric charge or a quantized magnetic field flux, originating from their non-trivial topology. Coupled topological defects in systems with several coexisting orders give rise to unconventional functionalities, such as the electric-field control of magnetization in multiferroics resulting from the coupling between the ferroelectric and ferromagnetic domain walls. Hexagonal manganites provide an extra degree of freedom: in these materials, both ferroelectricity and magnetism are coupled to an additional, non-ferroelectric structural order parameter. Here we present a theoretical study of topological defects in hexagonal manganites based on Landau theory with parameters determined from first-principles calculations. We explain the observed flip of electric polarization at the boundaries of structural domains, the origin of the observed discrete vortices, and the clamping between ferroelectric and antiferromagnetic domain walls. We show that structural vortices induce magnetic ones and that, consistent with a recent experimental report, ferroelectric domain walls can carry a magnetic moment. PMID:24162883
Haldane phase in one-dimensional topological Kondo insulators
NASA Astrophysics Data System (ADS)
Mezio, Alejandro; Lobos, Alejandro M.; Dobry, Ariel O.; Gazza, Claudio J.
2015-11-01
We investigate the ground-state properties of a recently proposed model for a topological Kondo insulator in one dimension (i.e., the p -wave Kondo-Heisenberg lattice model) by means of the density-matrix renormalization-group method. The nonstandard Kondo interaction in this model is different from the usual (i.e., local) Kondo interaction in that the localized spins couple to the "p -wave" spin density of conduction electrons, inducing a topologically nontrivial insulating ground state. Based on the analysis of the charge- and spin-excitation gaps, the string order parameter, and the spin profile in the ground state, we show that, at half filling and low energies, the system is in the Haldane phase and hosts topologically protected spin-1/2 end states. Beyond its intrinsic interest as a useful "toy model" to understand the effects of strong correlations on topological insulators, we show that the p -wave Kondo-Heisenberg model could be experimentally implemented in p -band optical lattices loaded with ultracold Fermi gases.
Definitely Life but not Definitively
NASA Astrophysics Data System (ADS)
Oliver, Joan D.; Perry, Randall S.
2006-12-01
Although there have been attempts at a definition of life from many disciplines, none is accepted by all as definitive. Some people believe that it is impossible to define life adequately at the moment. We agree with this point of view on linguistic grounds, examining the different types of definition, the contexts in which they are used and their relative usefulness as aids to arriving at a scientific definition of life. We look at some of the more recent definitions and analyse them in the light of our criteria for a good definition. We argue that since there are so many linguistic and philosophical difficulties with such a definition of life, what is needed is a series of working descriptions, which are suited to the audience and context in which they are used and useful for the intended purpose. We provide some ideas and examples of the forms these may take.
Definitely life but not definitively.
Oliver, Joan D; Perry, Randall S
2006-12-01
Although there have been attempts at a definition of life from many disciplines, none is accepted by all as definitive. Some people believe that it is impossible to define 'life' adequately at the moment. We agree with this point of view on linguistic grounds, examining the different types of definition, the contexts in which they are used and their relative usefulness as aids to arriving at a scientific definition of life. We look at some of the more recent definitions and analyse them in the light of our criteria for a good definition. We argue that since there are so many linguistic and philosophical difficulties with such a definition of life, what is needed is a series of working descriptions, which are suited to the audience and context in which they are used and useful for the intended purpose. We provide some ideas and examples of the forms these may take. PMID:17120126
Borohydrides: from sheet to framework topologies.
Schouwink, P; Ley, M B; Jensen, T R; Smrčok, L'; Černý, R
2014-06-01
The five novel compounds ALiM(BH4)4 (A = K or Rb; M = Mg or Mn) and K3Li2Mg2(BH4)9 crystallizing in the space groups Aba2 and P2/c, respectively, represent the first two-dimensional topologies amongst homoleptic borohydrides. The crystal structures have been solved, refined and characterized by synchrotron X-ray powder diffraction, neutron powder diffraction and solid-state DFT calculations. Minimal energies of ordered models corroborate crystal symmetries retrieved from diffraction data. The layered Li-Mg substructure forms negatively charged uninodal 4-connected networks. It is shown that this connectivity cannot generate the long sought-after, bimetallic Li-Mg borohydrides without countercations when assuming preferred coordination polyhedra as found in Mg(BH4)2 and LiBH4. The general properties of the trimetallic compound series are analogous with the anhydrous aluminosilicates. Additionally, a relationship with zeolites is suggested, which are built from three-dimensional Al-Si-O networks with a negative charge on them. The ternary metal borohydride systems are of interest due to their potential as novel hydridic frameworks and will allow exploration of the structural chemistry of light-metal systems otherwise subject to eutectic melting. PMID:24699844
Theory and applications of fluctuating-charge models
NASA Astrophysics Data System (ADS)
Chen, Jiahao
Fluctuating-charge models are computationally efficient methods of treating polarization and charge-transfer phenomena in molecular mechanics and classical molecular dynamics simulations. They are also theoretically appealing as they are minimally parameterized, with parameters corresponding to the chemically important concepts of electronegativities and chemical hardness. However, they are known to overestimate charge transfer for widely separated atoms, leading to qualitative errors in the predicted charge distribution and exaggerated electrostatic properties. We present the charge transfer with polarization current equilibration (QTPIE) model, which solves this problem by introducing distance-dependent electronegativities. A graph-theoretic analysis of the topology of charge transfer allows us to relate the fundamental quantities of charge transfer back to the more familiar variables that represent atomic partial charges. This allows us to formulate a unified theoretical framework for fluctuating-charge models and topological charge descriptors. We also demonstrate the important role of charge screening effects in obtaining correct size extensivity in electrostatic properties. Analyzing the spatial symmetries of these properties allows us to shed light on the role of charge conservation in the electronegativity equalization process. Finally, we develop a water model for use in classical molecular dynamics simulations that is capable of treating both polarization and charge transfer phenomena.
Fidelity approach in topological superconductors
NASA Astrophysics Data System (ADS)
Yao, Dao-Xin; Tian, Wen-Chuan; Huang, Guang-Yao; Wang, Zhi
We study topological superconductivity in the spin-orbit coupling nanowire system by using the fidelity approach. The wire is modeled as a one layer lattice chain with Zeeman energy and spin-orbital coupling, which is in proximity to a multi-layer superconductor. In particular, we study the effects of disorders and find that the fidelity susceptibility has multiple peaks. It is revealed that one peak indicates the topological quantum phase transition, while other peaks are signaling the pinning of the Majorana bound states by disorders. Our study shows that fidelity and fidelity susceptibility are very useful to investigate the topological quantum phase transition in superconductors. This work is supported by NSFC-11574404, 11275279, and NBRPC-2012CB821400.
Topological exploration of subterranean environments
Silver, D.; Ferguson, D.; Morris, A.; Thayer, S.
2006-06-15
The need for reliable maps of subterranean spaces too hazardous for humans to occupy has motivated the development of robotic mapping tools suited to these domains. As such, this work describes a system developed for autonomous topological exploration of mine environments to facilitate the process of mapping. The exploration framework is based upon the interaction of three main components: Node detection, node matching, and edge exploration. Node detection robustly identifies mine corridor intersections from sensor data and uses these features as the building blocks of a topological map. Node matching compares newly observed intersections to those stored in the map, providing global localization during exploration. Edge exploration translates topological exploration objectives into locomotion along mine corridors. This article describes both the robotic platform and the algorithms developed for exploration, and presents results from experiments conducted at a research coal mine near Pittsburgh, PA.
Quantum Capacitance in Topological Insulators
Xiu, Faxian; Meyer, Nicholas; Kou, Xufeng; He, Liang; Lang, Murong; Wang, Yong; Yu, Xinxin; Fedorov, Alexei V.; Zou, Jin; Wang, Kang L.
2012-01-01
Topological insulators show unique properties resulting from massless, Dirac-like surface states that are protected by time-reversal symmetry. Theory predicts that the surface states exhibit a quantum spin Hall effect with counter-propagating electrons carrying opposite spins in the absence of an external magnetic field. However, to date, the revelation of these states through conventional transport measurements remains a significant challenge owing to the predominance of bulk carriers. Here, we report on an experimental observation of Shubnikov-de Haas oscillations in quantum capacitance measurements, which originate from topological helical states. Unlike the traditional transport approach, the quantum capacitance measurements are remarkably alleviated from bulk interference at high excitation frequencies, thus enabling a distinction between the surface and bulk. We also demonstrate easy access to the surface states at relatively high temperatures up to 60 K. Our approach may eventually facilitate an exciting exploration of exotic topological properties at room temperature. PMID:22993694
Emergent surface superconductivity in a 3D topological insulator
NASA Astrophysics Data System (ADS)
Krusin-Elbaum, Lia
Surfaces of three-dimensional topological insulators have emerged as one of the most remarkable states of condensed quantum matter where exotic charge and spin phases of Dirac particles could form. This work reports on novel mesoscopic superconductivity in the topological insulator Sb2Te3 with transition to zero resistance induced through a minor tuning of growth chemistry that depletes bulk conduction channels. The depletion shifts Fermi energy towards the Dirac point as witnessed by a factor of 300 reduction of bulk carrier density and by the largest carrier mobility (>25, 000 cm2V-1s-1) found in any topological material of this class. Direct evidence from transport, the unprecedentedly large diamagnetic screening, and the presence of ~ 25 meV gaps detected by scanning tunneling spectroscopy reveal the superconducting condensate to emerge first in surface puddles at unexpectedly high temperature of ~ 50 K, with the onset of global phase coherence at ~ 9 K. The unconventional spin response of Sb2Te3 and the presence of subsurface 2DEG quantum well states arising from charge transfer to the surface are likely to play a role in the emergent superconducting state. The rich structure of this state lends itself to manipulation via growth conditions and the material parameters such as Fermi velocity and mean free path. This work was supported by NSF DMR-1122594, DMR-1420634, DMR-1322483, and DOD-W911NF-13-1-0159.
Spin-transfer torque generated by a topological insulator
NASA Astrophysics Data System (ADS)
Mellnik, Alex
2015-03-01
Magnetic devices are a leading contender for the implementation of memory and logic technologies that are non-volatile, that can scale to high density and high speed, and that do not wear out. However, widespread application of magnetic memory and logic devices will require the development of efficient mechanisms for reorienting their magnetization using the least possible current and power. We report experiments showing that charge current flowing in-plane in a thin film of the topological insulator Bi2Se3 at room temperature can exert a strong spin-transfer torque on an adjacent metallic ferromagnetic layer, with a direction consistent with that expected from a topological surface state. The spin torque efficiency per unit charge current density in the Bi2Se3 is larger than any previously measured at room temperature. Our data suggest that topological insulators could enable very efficient electrical manipulation of magnetic materials at room temperature, for memory and logic applications. Related publications: A. R. Mellnik, J. S. Lee, A. Richardella, J. L. Grab, P. J. Mintun, M. H. Fischer, A. Vaezi, A. Manchon, E.-A. Kim, N. Samarth, D. C. Ralph, Nature 511, 449-451 (2014).
Coherent single-spin source based on topological insulators
NASA Astrophysics Data System (ADS)
Xing, Yanxia; Yang, Zhong-Liu; Sun, Qing-Feng; Wang, Jian
2015-03-01
We report on the injection of quantized pure spin current into quantum conductors. In particular, we propose an on-demand single-spin source generated by periodically varying the gate voltages of two quantum dots that are connected to a two-dimensional topological insulator via tunneling barriers. Due to the nature of the helical states of the topological insulator, one or several spin pairs can be pumped out per cycle giving rise to a pure quantized alternating spin current. Depending on the phase difference between two gate voltages, this device can serve as an on-demand single-spin emitter or single-charge emitter. Again, due to the helicity of the topological insulator, the single-spin emitter or charge emitter is dissipationless and immune to disorder. The proposed single-spin emitter can be an important building block of future spintronic devices. We gratefully acknowledge the financial support from from NSF-China under Grant (Nos. 11174032 and 11374246), NBRP of China (2012CB921303), and a RGC Grant (HKU 705212P) from the Government of HKSAR.
Topological approximation of the nonlinear Anderson model.
Milovanov, Alexander V; Iomin, Alexander
2014-06-01
We study the phenomena of Anderson localization in the presence of nonlinear interaction on a lattice. A class of nonlinear Schrödinger models with arbitrary power nonlinearity is analyzed. We conceive the various regimes of behavior, depending on the topology of resonance overlap in phase space, ranging from a fully developed chaos involving Lévy flights to pseudochaotic dynamics at the onset of delocalization. It is demonstrated that the quadratic nonlinearity plays a dynamically very distinguished role in that it is the only type of power nonlinearity permitting an abrupt localization-delocalization transition with unlimited spreading already at the delocalization border. We describe this localization-delocalization transition as a percolation transition on the infinite Cayley tree (Bethe lattice). It is found in the vicinity of the criticality that the spreading of the wave field is subdiffusive in the limit t→+∞. The second moment of the associated probability distribution grows with time as a power law ∝ t^{α}, with the exponent α=1/3 exactly. Also we find for superquadratic nonlinearity that the analog pseudochaotic regime at the edge of chaos is self-controlling in that it has feedback on the topology of the structure on which the transport processes concentrate. Then the system automatically (without tuning of parameters) develops its percolation point. We classify this type of behavior in terms of self-organized criticality dynamics in Hilbert space. For subquadratic nonlinearities, the behavior is shown to be sensitive to the details of definition of the nonlinear term. A transport model is proposed based on modified nonlinearity, using the idea of "stripes" propagating the wave process to large distances. Theoretical investigations, presented here, are the basis for consistency analysis of the different localization-delocalization patterns in systems with many coupled degrees of freedom in association with the asymptotic properties of the transport. PMID:25019865
Photoemission spectroscopy studies of new topological insulator materials
NASA Astrophysics Data System (ADS)
Weber, Andrew Patton
As the size of a solid shrinks, the ratio of surface area to bulk volume grows and surface effects become more important. In a world where technologies advance with the shrinking size of electronic devices, one phase of matter has emerged which is fit for the near future of surface-dominated performance. Moreover, it has brought a new set of ideas to solid-state physics and chemistry, especially the understanding that the discipline of topology can be applied to classify the electron band structures. The topological insulator phase yields an exotic metal surface state in which the orientation of the electron's spin is locked perpendicular to its momentum. This property suppresses backscattering (making it possible to pass spin-polarized currents through the material without loss), offers a crucial ingredient for innovative approaches to quantum computation, and provides the basis for observing unique magnetoelectric effects. However, the surface states of materials in the topological insulator phase can wildly differ, so it is of interest to systematically characterize new materials to understand how the structure in position-space is related to the spin-resolved structure of electrons in energy- and momentum-space. We will discuss this relationship as it is probed through spin- and angle-resolved photoemission spectroscopy experiments on three topological (Bi2)m(Bi2Se3)n superlattices: (a) Bi2Se3 (m = 0, n = 1), (b) Bi4Se3 (m = 1, n = 1), and (c) BiSe (m = 1, n = 2). Our studies have not only proven the topological nature of these materials, but also demonstrate how bulk band structure and polar chemical bonding control the surface metal's concentration, dispersion, and spin-orbital character. Case (a) is considered to provide an ideal model of the topological surface metal. Case (b) provides the three important findings: (1) the chemical identity of the surface-termination controls the orbital composition and energy distribution of the surface states, (2) there are two topological states in sequential bulk band gaps, (3) of these, one of topological state undergoes a hybridization effect that yields a momentum-dependent gap in the band structure as large as 85 meV. Case (c) has a practical significance in that the surface metal has a potentially record-breaking carrier density of ~1013cm?2 (estimated from the Fermi surface area), more than an order of magnitude higher than in Bi2Se3. This occurs as a result of charge transfer from the Bi2 layers to the Bi2Se3 layers.
Tunable multifunctional topological insulators in ternary Heusler and related compounds
NASA Astrophysics Data System (ADS)
Felser, Claudia
2011-03-01
Recently the quantum spin Hall effect was theoretically predicted and experimentally realized in quantum wells based on the binary semiconductor HgTe. The quantum spin Hall state and topological insulators are new states of quantum matter interesting for both fundamental condensed-matter physics and material science. Many Heusler compounds with C1b structure are ternary semiconductors that are structurally and electronically related to the binary semiconductors. The diversity of Heusler materials opens wide possibilities for tuning the bandgap and setting the desired band inversion by choosing compounds with appropriate hybridization strength (by the lattice parameter) and magnitude of spin--orbit coupling (by the atomic charge). Based on first-principle calculations we demonstrate that around 50 Heusler compounds show band inversion similar to that of HgTe. The topological state in these zero-gap semiconductors can be created by applying strain or by designing an appropriate quantumwell structure, similar to the case of HgTe. Many of these ternary zero-gap semiconductors (LnAuPb, LnPdBi, LnPtSb and LnPtBi) contain the rare-earth element Ln, which can realize additional properties ranging from superconductivity (for example LaPtBi) to magnetism (for example GdPtBi) and heavy fermion behaviour (for example YbPtBi). These properties can open new research directions in realizing the quantized anomalous Hall effect and topological superconductors. Heusler compounds are similar to a stuffed diamond, correspondingly, it should be possible to find the ``high Z'' equivalent of graphene in a graphite-like structure with 18 valence electrons and with inverted bands. Indeed the ternary compounds, such as LiAuSe and KHgSb with a honeycomb structure of their Au-Se and Hg-Sb layers feature band inversion very similar to HgTe which is a strong precondition for existence of the topological surface states. These materials have a gap at the Fermi energy and are therefore candidates for 3D-topological insulators. Additionally they are centro-symmetric, therefore, it is possible to determine the parity of their wave functions, and hence, their topological character. Surprisingly, the compound KHgSb with the strong SOC is topologically trivial, whereas LiAuSe is found to be a topological non-trivial insulator.
NASA Astrophysics Data System (ADS)
Wang, Jing; Chen, Xi; Zhu, Bang-Fen; Zhang, Shou-Cheng
2013-12-01
We propose to form a junction between p- and n-type on the surface of an ideal topological insulator (Bi1-xSbx)2Te3, in which carrier type and density are locally controlled by composition graded doping or electrical gating. Such topological p-n junction are promising for possible device application. A single gapless chiral edge state localized along the junction interface appears in the presence of an external magnetic field, and it can be probed by scanning tunneling microscopy and transport measurements.
Quantum cosmology with nontrivial topologies
Vargas, T.
2008-10-10
Quantum creation of a universe with a nontrivial spatial topology is considered. Using the Euclidean functional integral prescription, we calculate the wave function of such a universe with cosmological constant and without matter. The minisuperspace path integral is calculated in the semiclassical approximation, and it is shown that in order to include the nontrivial topologies in the path integral approach to quantum cosmology, it is necessary to generalize the sum over compact and smooth 4-manifolds to sum over finite-volume compact 4-orbifolds.
Topological Superconductivity in Dirac Semimetals.
Kobayashi, Shingo; Sato, Masatoshi
2015-10-30
Dirac semimetals host bulk band-touching Dirac points and a surface Fermi loop. We develop a theory of superconducting Dirac semimetals. Establishing a relation between the Dirac points and the surface Fermi loop, we clarify how the nontrivial topology of Dirac semimetals affects their superconducting state. We note that the unique orbital texture of Dirac points and a structural phase transition of the crystal favor symmetry-protected topological superconductivity with a quartet of surface Majorana fermions. We suggest the possible application of our theory to recently discovered superconducting states in Cd_{3}As_{2}. PMID:26565490
United States. Bonneville Power Administration.
1993-12-01
The Bonneville Power Administration`s definition of terms are documented here. The terms primarily focus on transmission, generation and distribution, but also cover BPA services and responsibilities.
Amplified topological characteristics of MBE-grown Bi2Se3/II-VI semiconductor superlattices
NASA Astrophysics Data System (ADS)
Chen, Zhiyi; Zhao, Lukas; Korzhovska, Inna; Tamargo, Maria; Krusin, Lia
2015-03-01
Access to charge transport in Dirac surface states of topological insulators (TIs) such as Bi2Se3 is faced with two big challenges: one is significant bulk conduction and another is intermixing of topological states with nontopological 2DEG quantum well states formed by bending of bulk electronic bands near the surface. The latter effect is thought to arise via charge transfer from surface adatoms and, therefore, the choice of layers abutting topological surfaces can be critical. Here we report a successful molecular beam epitaxy growth of Bi2Se3/ZnxCd1-xSe superlattices that improve topological characteristics of individual 8 - 10 nm thick TI layers. We show that in these superlattices the two-dimensional (2D) weak antilocalization quantum correction to classical magnetoresistance, associated with topological Berry phase, scales with the number of TI layers, with one quantum channel per layer. The Berry phase of ? obtained independently from Shubnikov de Haas quantum oscillations demonstrates robust topological interfaces in the multilayer structure. Supported by NSF-DMR-1122594 and DOD-W911NF-13-1-0159.
EDITORIAL: Progress in topological insulators Progress in topological insulators
NASA Astrophysics Data System (ADS)
Morpurgo, Alberto; Trauzettel, Björn
2012-12-01
One of the most remarkable discoveries of the last few years in condensed matter physics is that the established distinction of crystalline solids in metals and insulators—which relies on the material band-structure—is incomplete. During the last several decades, the band structure of an uncountable variety of compounds of increasing complexity have been computed, and yet it has been overlooked that in the presence of sufficiently strong spin-orbit interaction, a new class of materials can be realized, that intrinsically behaves as insulators in their bulk and as metals at their surface. The discovery of this new class of materials was made only recently by Kane and Mele, during their theoretical studies of graphene in the presence of a sufficiently strong intrinsic spin-orbit interaction. Although the strength of the spin-orbit interaction in graphene is not sufficient to make the topological insulating state visible experimentally under currently reachable conditions, the validity and the originality of the concept were fully appreciated. Predictions for the occurrence of a two-dimensional topological insulating state in HgTe/CdTe heterostructures were made by Bernevig, Hughes and Zhang, and were followed by the experimental verification at Würzburg, in the Molenkamp group. Within a couple of years, this work brought the concept of topological insulator from an abstract theoretical discovery to an experimental reality, which stimulated further work. The concept of topological insulators was extended to the case of three-dimensional systems, for which an ideal experimental probe is angle-resolved photo-emission spectroscopy. Using this technique, specific theoretical predictions that had been made regarding the topological insulating character of different materials (e.g., for Bi-based compounds such as BiSb, Bi2Se3 or Bi2Te3), were verified experimentally through the direct observation of the Dirac surface fermions. This research was sufficient to put on solid theoretical and experimental grounds the notion of topological insulators, but, clearly, the excitement associated with this new concept goes well beyond the initial predictions and verifications. Theoretically, it is interesting to extend the concept of topological insulating states to interacting systems, to investigate the interplay of this new state of matter with other phenomena, such as superconductivity or magnetism, and to analyze all possible different experimental manifestations of the topologically insulating state. Furthermore, it is interesting to classify topological insulators and topological superconductors in both the absence and the presence of Coulomb interactions. Experimentally, the angle-resolved experimental measurements are only a first step, and what one would really like to do is, for instance, to realize nano-electronic devices with this new class of materials, much in the same way as is being done for graphene. It is in these new directions that current work is focusing, trying to solve experimental difficulties which are often present due to the limited material control of these systems that we currently have. The articles that are published in this issue provide an excellent demonstration of the spectrum of activities that is being pursued, as well as an introduction to some of the most established achievements in the field. As such, they will serve as a useful guideline for the interested reader to different important aspects in the field, from its start to the present.
Electrical control of spin in topological insulators
NASA Astrophysics Data System (ADS)
Chang, Kai
2012-02-01
All-electrical manipulation of electron spin in solids becomes a central issue of quantum information processing and quantum computing. The many previous proposals are based on spin-orbit interactions in semiconductors. Topological insulator, a strong spin-orbit coupling system, make it possible to control the spin transport electrically. Recent calculations proved that external electric fields can drive a HgTe quantum well from normal band insulator phase to topological insulator phase [1]. Since the topological edge states are robust against local perturbation, the controlling of edge states using local fields is a challenging task. We demonstrate that a p-n junction created electrically in HgTe quantum wells with inverted band structure exhibits interesting intraband and interband tunneling processes. We find a perfect intraband transmission for electrons injected perpendicularly to the interface of the p-n junction. The opacity and transparency of electrons through the p-n junction can be tuned by changing the incidence angle, the Fermi energy and the strength of the Rashba spin-orbit interaction (RSOI). The occurrence of a conductance plateau due to the formation of topological edge states in a quasi-one-dimensional p-n junction can be switched on and off by tuning the gate voltage. The spin orientation can be substantially rotated when the samples exhibit a moderately strong RSOI [2]. An electrical switching of the edge-state transport can also be realized using quantum point contacts in quantum spin Hall bars. The switch-on/off of the edge channel is caused by the finite size effect of the quantum point contact and therefore can be manipulated by tuning the voltage applied on the split gate [3,4]. The magnetic ions doped on the surface of 3D TI can be correlated through the helical electrons. The RKKY interaction mediated by the helical Dirac electrons consists of the Heisenberg-like, Ising-like, and Dzyaloshinskii-Moriya (DM)-like terms, which can be tuned by changing the gate voltage. It provides us a new way to control surface magnetism electrically. The gap opened by doped magnetic ions can lead to a short-range Bloembergen-Rowland interaction. The competition among the Heisenberg, Ising, and DM terms leads to rich spin configurations and an anomalous Hall effect on different lattices [4]. There are many proposals for quantum computation scheme are based on the spin in semiconductor quantum dots. Topological insulator quantum dots display a very different behavior with that of conventional semiconductor quantum dots [5]. In sharp contrast to conventional semiconductor quantum dots, the quantum states in the gap of the HgTe QD are fully spin-polarized and show ring-like density distributions near the boundary of the QD and optically dark. The persistent charge currents and magnetic moments, i.e., the Aharonov-Bohm effect, can be observed in such a QD structure. This feature offers us a practical way to detect these exotic ring-like edge states by using the SQUID technique. [0pt]Refs: [1] W. Yang, Kai Chang, and S. C. Zhang, Phys. Rev. Lett. 100, 056602 (2008); J. Li and Kai Chang, Appl. Phys. Lett. 95, 222110 (2009). [2] L. B. Zhang, Kai Chang, X. C. Xie, H. Buhmann and L. W. Molenkamp, New J. Phys. 12, 083058 (2010). [3] L. B. Zhang, F. Cheng, F. Zhai and Kai Chang, Phys. Rev. B 83 081402(R) (2011); Z. H. Wu, F. Zhai, F. M. Peeters, H. Q. Xu and Kai Chang, Phys, Rev. Lett. 106, 176802 (2011). [4] J. J. Zhu, D. X. Yao, S. C. Zhang, and Kai Chang, Phys. Rev. Lett. 106, 097201 (2011). [5] Kai Chang, and Wen-Kai Lou, Phys. Rev. Lett. 106, 206802 (2011).
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Architectures for Parafermionic Topological Matter in Two Dimensions
NASA Astrophysics Data System (ADS)
Burrello, Michele; van Heck, Bernard; Cobanera, Emilio
2013-03-01
Recent proposals exploit edge modes of fractional topological insulators (FTIs), induced superconducting pairing, and back-scattering to realize one-dimensional systems of parafermions. We extend these proposals to two dimensions and analyze the effect of the superconducting islands' charging energy on the parafermions they host. We focus on two two-dimensional architectures, the tile and stripe configurations, characterized by different distributions of FTIs and derive the associated parafermionic effective Hamiltonians. The tile model realizes the Z2 m toric code in low-order perturbation theory and hence possesses full topological quantum order. By exploiting dualities, we obtain the phase diagram and generalized order parameters for both the tile and stripe models of parafermions. This work was supported by the Dutch Science Foundation NWO/FOM and an ERC Advanced Investigator grant.
Interface currents in topological superconductor-ferromagnet junctions
NASA Astrophysics Data System (ADS)
Brydon, Philip; Timm, Carsten; Schnyder, Andreas
2013-03-01
Both fully gapped and nodal pairing states of noncentrosymmetric superconductors (NCS) display non-trivial topological properties, manifested by topologically protected dispersing and flat-band surface states. Using a 2D model of an NCS, we show that the surface states typically have strong spin-polarization sμ = x , z (ky) , which is odd in the surface-Brillouin-zone momentum ky. Upon placing the NCS in proximity contact with a ferromagnet, the coupling to the exchange field gives a perturbative correction to the energy of these states ~sμ (ky) , thus generating an interface charge current ~∂kysμ (ky) in the NCS. This is most clearly realized in a nodal NCS, where the weak dispersion acquired by the singly degenerate zero-energy flat bands leads to a strong enhancement of the interface current at low temperatures. We argue that this effect is a ``smoking-gun'' signature of the singly degenerate flat bands.
Crystallographic topology and its applications
Johnson, C.K.; Burnett, M.N.; Dunbar, W.D.
1996-10-01
Geometric topology and structural crystallography concepts are combined to define a new area we call Structural Crystallographic Topology, which may be of interest to both crystallographers and mathematicians. In this paper, we represent crystallographic symmetry groups by orbifolds and crystal structures by Morse - functions. The Morse function uses mildly overlapping Gaussian thermal-motion probability density functions centered on atomic sites to form a critical net with peak, pass, pale, and pit critical points joined into a graph by density gradient-flow separatrices. Critical net crystal structure drawings can be made with the ORTEP-III graphics pro- An orbifold consists of an underlying topological space with an embedded singular set that represents the Wyckoff sites of the crystallographic group. An orbifold for a point group, plane group, or space group is derived by gluing together equivalent edges or faces of a crystallographic asymmetric unit. The critical-net-on-orbifold model incorporates the classical invariant lattice complexes of crystallography and allows concise quotient-space topological illustrations to be drawn without the repetition that is characteristic of normal crystal structure drawings.
Topological excitations in magnetic materials
NASA Astrophysics Data System (ADS)
Bazeia, D.; Doria, M. M.; Rodrigues, E. I. B.
2016-05-01
In this work we propose a new route to describe topological excitations in magnetic systems through a single real scalar field. We show here that spherically symmetric structures in two spatial dimensions, which map helical excitations in magnetic materials, admit this formulation and can be used to model skyrmion-like structures in magnetic materials.
Phantom stars and topology change
DeBenedictis, Andrew; Garattini, Remo; Lobo, Francisco S. N.
2008-11-15
In this work, we consider time-dependent dark-energy star models, with an evolving parameter {omega} crossing the phantom divide {omega}=-1. Once in the phantom regime, the null energy condition is violated, which physically implies that the negative radial pressure exceeds the energy density. Therefore, an enormous negative pressure in the center may, in principle, imply a topology change, consequently opening up a tunnel and converting the dark-energy star into a wormhole. The criteria for this topology change are discussed and, in particular, we consider a Casimir energy approach involving quasilocal energy difference calculations that may reflect or measure the occurrence of a topology change. We denote these exotic geometries consisting of dark-energy stars (in the phantom regime) and phantom wormholes as phantom stars. The final product of this topological change, namely, phantom wormholes, have far-reaching physical and cosmological implications, as in addition to being used for interstellar shortcuts, an absurdly advanced civilization may manipulate these geometries to induce closed timelike curves, consequently violating causality.
Rapid membrane protein topology prediction
Hennerdal, Aron; Elofsson, Arne
2011-01-01
Summary: State-of-the-art methods for topology of α-helical membrane proteins are based on the use of time-consuming multiple sequence alignments obtained from PSI-BLAST or other sources. Here, we examine if it is possible to use the consensus of topology prediction methods that are based on single sequences to obtain a similar accuracy as the more accurate multiple sequence-based methods. Here, we show that TOPCONS-single performs better than any of the other topology prediction methods tested here, but ∼6% worse than the best method that is utilizing multiple sequence alignments. Availability and Implementation: TOPCONS-single is available as a web server from http://single.topcons.net/ and is also included for local installation from the web site. In addition, consensus-based topology predictions for the entire international protein index (IPI) is available from the web server and will be updated at regular intervals. Contact: arne@bioinfo.se Supplementary information: Supplementary data are avaliable at Bioinformatics online. PMID:21493661
Topological design of torsional metamaterials
NASA Astrophysics Data System (ADS)
Vitelli, Vincenzo; Paulose, Jayson; Meeussen, Anne; Topological Mechanics Lab Team
Frameworks - stiff elements with freely hinged joints - model the mechanics of a wide range of natural and artificial structures, including mechanical metamaterials with auxetic and topological properties. The unusual properties of the structure depend crucially on the balance between degrees of freedom associated with the nodes, and the constraints imposed upon them by the connecting elements. Whereas networks of featureless nodes connected by central-force springs have been well-studied, many real-world systems such as frictional granular packings, gear assemblies, and flexible beam meshes incorporate torsional degrees of freedom on the nodes, coupled together with transverse shear forces exerted by the connecting elements. We study the consequences of such torsional constraints on the mechanics of periodic isostatic networks as a foundation for mechanical metamaterials. We demonstrate the existence of soft modes of topological origin, that are protected against disorder or small perturbations of the structure analogously to their counterparts in electronic topological insulators. We have built a lattice of gears connected by rigid beams that provides a real-world demonstration of a torsional metamaterial with topological edge modes and mechanical Weyl modes.
NASA Astrophysics Data System (ADS)
Zverev, V. V.; Filippov, B. N.
2016-03-01
A three-dimensional computer simulation of dynamic processes occurring in a domain wall moving in a soft-magnetic uniaxial film with in-plane anisotropy has been performed based on the micromagnetic approach. It has been shown that the domain wall motion is accompanied by topological transformations of the magnetization distribution, or, more specifically, by "fast" processes associated with the creation and annihilation of vortices, antivortices, and singular (Bloch) points. The method used for visualizing the topological structure of magnetization distributions is based on the numerical determination of topological charges of two types by means of the integration over the contours and surfaces with variable geometry. The obtained data indicate that the choice of the initial configuration predetermines the dynamic scenario of topological transformations.
Continuity and Separation in Symmetric Topologies
ERIC Educational Resources Information Center
Harris, J.; Lynch, M.
2007-01-01
In this note, it is shown that in a symmetric topological space, the pairs of sets separated by the topology determine the topology itself. It is then shown that when the codomain is symmetric, functions which separate only those pairs of sets that are already separated are continuous, generalizing a result found by M. Lynch.
Fractionally charged skyrmions in fractional quantum Hall effect
NASA Astrophysics Data System (ADS)
Balram, Ajit C.; Wurstbauer, U.; Wójs, A.; Pinczuk, A.; Jain, J. K.
2015-11-01
The fractional quantum Hall effect has inspired searches for exotic emergent topological particles, such as fractionally charged excitations, composite fermions, abelian and nonabelian anyons and Majorana fermions. Fractionally charged skyrmions, which support both topological charge and topological vortex-like spin structure, have also been predicted to occur in the vicinity of 1/3 filling of the lowest Landau level. The fractional skyrmions, however, are anticipated to be exceedingly fragile, suppressed by very small Zeeman energies. Here we show that, slightly away from 1/3 filling, the smallest manifestations of the fractional skyrmion exist in the excitation spectrum for a broad range of Zeeman energies, and appear in resonant inelastic light scattering experiments as well-defined resonances slightly below the long wavelength spin wave mode. The spectroscopy of these exotic bound states serves as a sensitive tool for investigating the residual interaction between composite fermions, responsible for delicate new fractional quantum Hall states in this filling factor region.
Fractionally charged skyrmions in fractional quantum Hall effect
Balram, Ajit C.; Wurstbauer, U.; Wójs, A.; Pinczuk, A.; Jain, J. K.
2015-01-01
The fractional quantum Hall effect has inspired searches for exotic emergent topological particles, such as fractionally charged excitations, composite fermions, abelian and nonabelian anyons and Majorana fermions. Fractionally charged skyrmions, which support both topological charge and topological vortex-like spin structure, have also been predicted to occur in the vicinity of 1/3 filling of the lowest Landau level. The fractional skyrmions, however, are anticipated to be exceedingly fragile, suppressed by very small Zeeman energies. Here we show that, slightly away from 1/3 filling, the smallest manifestations of the fractional skyrmion exist in the excitation spectrum for a broad range of Zeeman energies, and appear in resonant inelastic light scattering experiments as well-defined resonances slightly below the long wavelength spin wave mode. The spectroscopy of these exotic bound states serves as a sensitive tool for investigating the residual interaction between composite fermions, responsible for delicate new fractional quantum Hall states in this filling factor region. PMID:26608906
Fractionally charged skyrmions in fractional quantum Hall effect.
Balram, Ajit C; Wurstbauer, U; Wójs, A; Pinczuk, A; Jain, J K
2015-01-01
The fractional quantum Hall effect has inspired searches for exotic emergent topological particles, such as fractionally charged excitations, composite fermions, abelian and nonabelian anyons and Majorana fermions. Fractionally charged skyrmions, which support both topological charge and topological vortex-like spin structure, have also been predicted to occur in the vicinity of 1/3 filling of the lowest Landau level. The fractional skyrmions, however, are anticipated to be exceedingly fragile, suppressed by very small Zeeman energies. Here we show that, slightly away from 1/3 filling, the smallest manifestations of the fractional skyrmion exist in the excitation spectrum for a broad range of Zeeman energies, and appear in resonant inelastic light scattering experiments as well-defined resonances slightly below the long wavelength spin wave mode. The spectroscopy of these exotic bound states serves as a sensitive tool for investigating the residual interaction between composite fermions, responsible for delicate new fractional quantum Hall states in this filling factor region. PMID:26608906
Fractionally charged skyrmions in fractional quantum Hall effect
Balram, Ajit C.; Wurstbauer, U.; Wójs, A.; Pinczuk, A.; Jain, J. K.
2015-11-26
The fractional quantum Hall effect has inspired searches for exotic emergent topological particles, such as fractionally charged excitations, composite fermions, abelian and nonabelian anyons and Majorana fermions. Fractionally charged skyrmions, which support both topological charge and topological vortex-like spin structure, have also been predicted to occur in the vicinity of 1/3 filling of the lowest Landau level. The fractional skyrmions, however, are anticipated to be exceedingly fragile, suppressed by very small Zeeman energies. Here we show that, slightly away from 1/3 filling, the smallest manifestations of the fractional skyrmion exist in the excitation spectrum for a broad range of Zeeman energies, and appear in resonant inelastic light scattering experiments as well-defined resonances slightly below the long wavelength spin wave mode. The spectroscopy of these exotic bound states serves as a sensitive tool for investigating the residual interaction between composite fermions, responsible for delicate new fractional quantum Hall states in this filling factor region.
Code of Federal Regulations, 2011 CFR
2011-07-01
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Code of Federal Regulations, 2013 CFR
2013-07-01
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Code of Federal Regulations, 2012 CFR
2012-07-01
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2010-07-01
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Detecting monopole charge in Weyl semimetals via quantum interference transport
NASA Astrophysics Data System (ADS)
Dai, Xin; Lu, Hai-Zhou; Shen, Shun-Qing; Yao, Hong
2016-04-01
Topological Weyl semimetals can host Weyl nodes with monopole charges in momentum space. How to detect the signature of the monopole charges in quantum transport remains a challenging topic. Here, we reveal the connection between the parity of monopole charge in topological semimetals and the quantum interference corrections to the conductivity. We show that the parity of monopole charge determines the sign of the quantum interference correction, with odd and even parity yielding the weak antilocalization and weak localization effects, respectively. This is attributed to the Berry phase difference between time-reversed trajectories circulating the Fermi sphere that encloses the monopole charges. From standard Feynman diagram calculations, we further show that the weak-field magnetoconductivity at low temperatures is proportional to +√{B } in double-Weyl semimetals and -√{B } in single-Weyl semimetals, respectively, which could be verified experimentally.
Electrostatic tuning of the surface states of irradiated topological insulators
NASA Astrophysics Data System (ADS)
Korzhovska, Inna; Zhao, Lukas; Deshko, Yury; Arefe, Ghidewon; Konczykowsky, Marcin; Krusin-Elbaum, Lia; Columbia University Collaboration
2015-03-01
One of the main obstacles to accessing charge transport through Dirac surface states of topological insulators (TIs) is a significant conduction in the bulk. We have developed a new approach of reaching a stable charge neutrality point (CNP) using irradiation with 2.5 MeV energy electrons. By controlling the beam fluence and annealing protocol we can convert bulk conductivity from p- (hole-like) to n-type (electron-like) and back, crossing the Dirac point while preserving the robust topological signatures of surface channels. Electron beams act to compensate charged bulk defects and pull the Fermi level into the bulk gap - a process that decreases bulk conductivity by orders of magnitude to a minimum, ?min, at CNP. We study the origins of minimum conductivity in electron-irradiated TIs in a transistor-like gated structures fabricated in inert environment by mechanical exfoliation with Bi2Te3 as a prototypical TI and h-BN as a gate dielectric. The effects of electrostatic tuning by the gate bias voltage on surface conductivity near CNP will be presented. Supported by NSF-DMR-1312483, and DOD-W911NF-13-1-0159.
Constructing a logical, regular axis topology from an irregular topology
Faraj, Daniel A.
2014-07-01
Constructing a logical regular topology from an irregular topology including, for each axial dimension and recursively, for each compute node in a subcommunicator until returning to a first node: adding to a logical line of the axial dimension a neighbor specified in a nearest neighbor list; calling the added compute node; determining, by the called node, whether any neighbor in the node's nearest neighbor list is available to add to the logical line; if a neighbor in the called compute node's nearest neighbor list is available to add to the logical line, adding, by the called compute node to the logical line, any neighbor in the called compute node's nearest neighbor list for the axial dimension not already added to the logical line; and, if no neighbor in the called compute node's nearest neighbor list is available to add to the logical line, returning to the calling compute node.
Constructing a logical, regular axis topology from an irregular topology
Faraj, Daniel A.
2014-07-22
Constructing a logical regular topology from an irregular topology including, for each axial dimension and recursively, for each compute node in a subcommunicator until returning to a first node: adding to a logical line of the axial dimension a neighbor specified in a nearest neighbor list; calling the added compute node; determining, by the called node, whether any neighbor in the node's nearest neighbor list is available to add to the logical line; if a neighbor in the called compute node's nearest neighbor list is available to add to the logical line, adding, by the called compute node to the logical line, any neighbor in the called compute node's nearest neighbor list for the axial dimension not already added to the logical line; and, if no neighbor in the called compute node's nearest neighbor list is available to add to the logical line, returning to the calling compute node.
Heckeroth, S.; McLees, C.
1996-11-01
Concern about the depletion of non-renewable energy resources and the life threatening pollution and climatic changes caused by their use has led to a renewed interest in passive solar design. However, transportation consumes four times the energy used in housing and causes about 10 times the air pollution because of its total reliance on petroleum. This paper will suggest direct solar charging opportunities that can be integrated into the built environment. Major advances in electric vehicle (EV) and photovoltaic (PV) technologies will soon make solar charging a viable option for transportation. More efficient motors, high-power controllers, quick chargers and new developments in battery technology will soon make electric vehicles have performance comparable to gas vehicles. The rise in efficiency, the decreasing cost and the integration of photovoltaic panels as roofing will make workplace and home solar charging an economic alternative to the gas pump.
Topological aspects of polarization structured beams
NASA Astrophysics Data System (ADS)
Kumar, Vijay; Viswanathan, Nirmal K.
2014-02-01
Polarization structured optical beams have half-integer topological structures: star, lemon, monstar in π-symmetric polarization ellipse orientation tensor field and integer-index topological structures: saddle, spiral, node in 2π-symmetric Poynting vector field. Topological approach to study the polarization structured optical beams is carried out and presented here in some detail. These polarization structured light beams are demonstrated to be the best platform to explore the topological interdependencies. The dependence of one type of topological structure on the other is used to control the Poynting vector density distribution and locally enhance the angular momentum density as compared to its constituent beam fields.
Boson condensation in topologically ordered quantum liquids
NASA Astrophysics Data System (ADS)
Neupert, Titus; He, Huan; von Keyserlingk, Curt; Sierra, Germán; Bernevig, B. Andrei
2016-03-01
Boson condensation in topological quantum field theories (TQFT) has been previously investigated through the formalism of Frobenius algebras and the use of vertex lifting coefficients. While general, this formalism is physically opaque and computationally arduous: analyses of TQFT condensation are practically performed on a case by case basis and for very simple theories only, mostly not using the Frobenius algebra formalism. In this paper, we provide a way of treating boson condensation that is computationally efficient. With a minimal set of physical assumptions, such as commutativity of lifting and the definition of confined particles, we can prove a number of theorems linking Boson condensation in TQFT with chiral algebra extensions, and with the factorization of completely positive matrices over Z+. We present numerically efficient ways of obtaining a condensed theory fusion algebra and S matrices; and we then use our formalism to prove several theorems for the S and T matrices of simple current condensation and of theories which upon condensation result in a low number of confined particles. We also show that our formalism easily reproduces results existent in the mathematical literature such as the noncondensability of five and ten layers of the Fibonacci TQFT.
Synthesis and characterization of 3D topological insulators: a case TlBi(S1-xSex)2
NASA Astrophysics Data System (ADS)
Segawa, Kouji
2015-02-01
In this article, practical methods for synthesizing Tl-based ternary III-V-VI2 chalcogenide TlBi(S1-xSex)2 are described in detail, along with characterization by x-ray diffraction and charge transport properties. The TlBi(S1-xSex)2 system is interesting because it shows a topological phase transition, where a topologically nontrivial phase changes to a trivial phase without changing the crystal structure qualitatively. In addition, Dirac semimetals whose bulk band structure shows a Dirac-like dispersion are considered to exist near the topological phase transition. The technique shown here is also generally applicable for other chalcogenide topological insulators, and will be useful for studying topological insulators and related materials.
Universal Cyclic Topology in Polymer Networks
NASA Astrophysics Data System (ADS)
Wang, Rui; Alexander-Katz, Alfredo; Johnson, Jeremiah A.; Olsen, Bradley D.
2016-05-01
Polymer networks invariably possess topological defects: loops of different orders which have profound effects on network properties. Here, we demonstrate that all cyclic topologies are a universal function of a single dimensionless parameter characterizing the conditions for network formation. The theory is in excellent agreement with both experimental measurements of hydrogel loop fractions and Monte Carlo simulations without any fitting parameters. We demonstrate the superposition of the dilution effect and chain-length effect on loop formation. The one-to-one correspondence between the network topology and primary loop fraction demonstrates that the entire network topology is characterized by measurement of just primary loops, a single chain topological feature. Different cyclic defects cannot vary independently, in contrast to the intuition that the densities of all topological species are freely adjustable. Quantifying these defects facilitates studying the correlations between the topology and properties of polymer networks, providing a key step in overcoming an outstanding challenge in polymer physics.
Quark masses, the Dashen phase, and gauge field topology
Creutz, Michael
2013-12-15
The CP violating Dashen phase in QCD is predicted by chiral perturbation theory to occur when the up–down quark mass difference becomes sufficiently large at fixed down-quark mass. Before reaching this phase, all physical hadronic masses and scattering amplitudes are expected to behave smoothly with the up-quark mass, even as this mass passes through zero. In Euclidean space, the topological susceptibility of the gauge fields is positive at positive quark masses but diverges to negative infinity as the Dashen phase is approached. A zero in this susceptibility provides a tentative signal for the point where the mass of the up quark vanishes. I discuss potential ambiguities with this determination. -- Highlights: •The CP violating Dashen phase in QCD occurs when the up quark mass becomes sufficiently negative. •Before reaching this phase, all physical hadronic masses and scattering amplitudes behave smoothly with the up-quark mass. •The topological susceptibility of the gauge fields diverges to negative infinity as the Dashen phase is approached. •A zero in the topological susceptibility provides a tentative signal for the point where the mass of the up quark vanishes. •The universality of this definition remains unproven. Potential ambiguities are discussed.
High voltage high repetition rate pulse using Marx topology
NASA Astrophysics Data System (ADS)
Hakki, A.; Kashapov, N.
2015-06-01
The paper describes Marx topology using MOSFET transistors. Marx circuit with 10 stages has been done, to obtain pulses about 5.5KV amplitude, and the width of the pulses was about 30μsec with a high repetition rate (PPS > 100), Vdc = 535VDC is the input voltage for supplying the Marx circuit. Two Ferrite ring core transformers were used to control the MOSFET transistors of the Marx circuit (the first transformer to control the charging MOSFET transistors, the second transformer to control the discharging MOSFET transistors).
Topological interactions in spacetimes with thick line defects
NASA Astrophysics Data System (ADS)
Moraes, Fernando; Carvalho, A. M.; Costa, Ismael V.; Oliveira, F. A.; Furtado, Claudio
2003-08-01
In this work we study the topologically induced electric self-energy and self-force on a long, straight, wire in two distinct, but similar, spacetimes: (i) the Gott-Hiscock thick cosmic string spacetime, and (ii) the spacetime of a continuous distribution of infinitely thin cosmic strings over a disk of finite radius. In each case we obtain the electric self-energy and self-force both in the internal and external regions of the defect distribution. The self-force is always repulsive, independently of the sign of the charge, and is maximum on the string’s surface, in both cases.
Formation of a topological non-Fermi liquid in MnSi.
Ritz, R; Halder, M; Wagner, M; Franz, C; Bauer, A; Pfleiderer, C
2013-05-01
Fermi liquid theory provides a remarkably powerful framework for the description of the conduction electrons in metals and their ordering phenomena, such as superconductivity, ferromagnetism, and spin- and charge-density-wave order. A different class of ordering phenomena of great interest concerns spin configurations that are topologically protected, that is, their topology can be destroyed only by forcing the average magnetization locally to zero. Examples of such configurations are hedgehogs (points at which all spins are either pointing inwards or outwards) and vortices. A central question concerns the nature of the metallic state in the presence of such topologically distinct spin textures. Here we report a high-pressure study of the metallic state at the border of the skyrmion lattice in MnSi, which represents a new form of magnetic order composed of topologically non-trivial vortices. When long-range magnetic order is suppressed under pressure, the key characteristic of the skyrmion lattice--that is, the topological Hall signal due to the emergent magnetic flux associated with the topological winding--is unaffected in sign or magnitude and becomes an important characteristic of the metallic state. The regime of the topological Hall signal in temperature, pressure and magnetic field coincides thereby with the exceptionally extended regime of a pronounced non-Fermi-liquid resistivity. The observation of this topological Hall signal in the regime of the NFL resistivity suggests empirically that spin correlations with non-trivial topological character may drive a breakdown of Fermi liquid theory in pure metals. PMID:23636328
Topological mechanics of gyroscopic metamaterials.
Nash, Lisa M; Kleckner, Dustin; Read, Alismari; Vitelli, Vincenzo; Turner, Ari M; Irvine, William T M
2015-11-24
Topological mechanical metamaterials are artificial structures whose unusual properties are protected very much like their electronic and optical counterparts. Here, we present an experimental and theoretical study of an active metamaterial--composed of coupled gyroscopes on a lattice--that breaks time-reversal symmetry. The vibrational spectrum displays a sonic gap populated by topologically protected edge modes that propagate in only one direction and are unaffected by disorder. We present a mathematical model that explains how the edge mode chirality can be switched via controlled distortions of the underlying lattice. This effect allows the direction of the edge current to be determined on demand. We demonstrate this functionality in experiment and envision applications of these edge modes to the design of one-way acoustic waveguides. PMID:26561580
Topological mechanics of gyroscopic metamaterials
Nash, Lisa M.; Kleckner, Dustin; Read, Alismari; Vitelli, Vincenzo; Turner, Ari M.; Irvine, William T. M.
2015-01-01
Topological mechanical metamaterials are artificial structures whose unusual properties are protected very much like their electronic and optical counterparts. Here, we present an experimental and theoretical study of an active metamaterial—composed of coupled gyroscopes on a lattice—that breaks time-reversal symmetry. The vibrational spectrum displays a sonic gap populated by topologically protected edge modes that propagate in only one direction and are unaffected by disorder. We present a mathematical model that explains how the edge mode chirality can be switched via controlled distortions of the underlying lattice. This effect allows the direction of the edge current to be determined on demand. We demonstrate this functionality in experiment and envision applications of these edge modes to the design of one-way acoustic waveguides. PMID:26561580
Topological defects in extended inflation
NASA Technical Reports Server (NTRS)
Copeland, Edmund J.; Kolb, Edward W.; Liddle, Andrew R.
1990-01-01
The production of topological defects, especially cosmic strings, in extended inflation models was considered. In extended inflation, the Universe passes through a first-order phase transition via bubble percolation, which naturally allows defects to form at the end of inflation. The correlation length, which determines the number density of the defects, is related to the mean size of bubbles when they collide. This mechanism allows a natural combination of inflation and large scale structure via cosmic strings.
Topological Insulator Nanowires and Nanoribbons
Kong, D.S.
2010-06-02
Recent theoretical calculations and photoemission spectroscopy measurements on the bulk Bi{sub 2}Se{sub 3} material show that it is a three-dimensional topological insulator possessing conductive surface states with nondegenerate spins, attractive for dissipationless electronics and spintronics applications. Nanoscale topological insulator materials have a large surface-to-volume ratio that can manifest the conductive surface states and are promising candidates for devices. Here we report the synthesis and characterization of high quality single crystalline Bi{sub 2}Se{sub 3} nanomaterials with a variety of morphologies. The synthesis of Bi{sub 2}Se{sub 3} nanowires and nanoribbons employs Au-catalyzed vapor-liquid-solid (VLS) mechanism. Nanowires, which exhibit rough surfaces, are formed by stacking nanoplatelets along the axial direction of the wires. Nanoribbons are grown along [11-20] direction with a rectangular crosssection and have diverse morphologies, including quasi-one-dimensional, sheetlike, zigzag and sawtooth shapes. Scanning tunneling microscopy (STM) studies on nanoribbons show atomically smooth surfaces with {approx}1 nm step edges, indicating single Se-Bi-Se-Bi-Se quintuple layers. STM measurements reveal a honeycomb atomic lattice, suggesting that the STM tip couples not only to the top Se atomic layer, but also to the Bi atomic layer underneath, which opens up the possibility to investigate the contribution of different atomic orbitals to the topological surface states. Transport measurements of a single nanoribbon device (four terminal resistance and Hall resistance) show great promise for nanoribbons as candidates to study topological surface states.
Dynamics, Spectral Geometry and Topology
Burghelea, Dan
2011-02-10
The paper is an informal report on joint work with Stefan Haller on Dynamics in relation with Topology and Spectral Geometry. By dynamics one means a smooth vector field on a closed smooth manifold; the elements of dynamics of concern are the rest points, instantons and closed trajectories. One discusses their counting in the case of a generic vector field which has some additional properties satisfied by a still very large class of vector fields.
Hopf algebras and topological recursion
NASA Astrophysics Data System (ADS)
Esteves, João N.
2015-11-01
We consider a model for topological recursion based on the Hopf algebra of planar binary trees defined by Loday and Ronco (1998 Adv. Math. 139 293-309 We show that extending this Hopf algebra by identifying pairs of nearest neighbor leaves, and thus producing graphs with loops, we obtain the full recursion formula discovered by Eynard and Orantin (2007 Commun. Number Theory Phys. 1 347-452).
Inconsistency of topologically massive hypergravity
NASA Technical Reports Server (NTRS)
Aragone, C.; Deser, S.
1985-01-01
The coupled topologically massive spin-5/2 gravity system in D = 3 dimensions whose kinematics represents dynamical propagating gauge invariant massive spin-5/2 and spin-2 excitations, is shown to be inconsistent, or equivalently, not locally hypersymmetric. In contrast to D = 4, the local constraints on the system arising from failure of the fermionic Bianchi identities do not involve the 'highest spin' components of the field, but rather the auxiliary spinor required to construct a consistent massive model.
Interfacing Topological Insulators with Ferromagnetism
NASA Astrophysics Data System (ADS)
Richardella, Anthony
In topological insulators, the surface states arise from strong spin-orbit coupling while the degeneracy of the Dirac point is protected by time reversal symmetry. Introducing magnetism in proximity to the surface states breaks this symmetry, destroying the non-trivial Berry phase at the Dirac point and leads to a hedgehog spin texture near the newly opened magnetic gap. This symmetry broken phase leads to a host of unusual physics, such as the quantum anomalous Hall (QAH) effect. In this talk, we discuss the growth by molecular beam epitaxy and characterization of such magnetically interfaced and magnetically doped topological insulators. Such materials often suffer from structural defects and interfacial layers, as well as from degradation during device fabrication. In particular, it is shown that Cr doped (Bi1-x,Sbx)2Te3 can exhibit perfect Hall quantization at low temperatures despite these defects. However, the magnetic ordering of this material was found to be quite unusual, displaying a super-paramagnetic like character, perhaps reflecting this disorder. Such observations highlight the surprising behavior of such broken symmetry phases in topological materials. This work was performed in collaboration with A. Kandala, M. Liu, W. Wang, N.P. Ong, C.-X. Liu, and N. Samarth, in addition to the authors of the references cited. This work was supported by funding from ARO/MURI, DARPA and ONR.
Charge density distribution in aminomethylphosphonic acid.
Janicki, Rafał; Starynowicz, Przemysław
2010-10-01
The experimental charge density distribution in aminomethylphosphonic acid has been determined from X-ray diffraction and its topological features have been analyzed. The results have shown that the P-O bonds are highly polarized, moreover the P-OH bond is weaker than the bonds to unprotonated O atoms. These facts have been confirmed by theoretical density functional theory (DFT) calculations, which have shown that the single, strongly polarized bonds within the phosphonate group are modified by hyperconjugation effects. PMID:20841922
Polymer Amide as an Early Topology
McGeoch, Julie E. M.; McGeoch, Malcolm W.
2014-01-01
Hydrophobic polymer amide (HPA) could have been one of the first normal density materials to accrete in space. We present ab initio calculations of the energetics of amino acid polymerization via gas phase collisions. The initial hydrogen-bonded di-peptide is sufficiently stable to proceed in many cases via a transition state into a di-peptide with an associated bound water molecule of condensation. The energetics of polymerization are only favorable when the water remains bound. Further polymerization leads to a hydrophobic surface that is phase-separated from, but hydrogen bonded to, a small bulk water complex. The kinetics of the collision and subsequent polymerization are discussed for the low-density conditions of a molecular cloud. This polymer in the gas phase has the properties to make a topology, viz. hydrophobicity allowing phase separation from bulk water, capability to withstand large temperature ranges, versatility of form and charge separation. Its flexible tetrahedral carbon atoms that alternate with more rigid amide groups allow it to deform and reform in hazardous conditions and its density of hydrogen bonds provides adhesion that would support accretion to it of silicon and metal elements to form a stellar dust material. PMID:25048204
Semiclassical geometry of charged black holes
Frolov, Andrei V.; Kristjansson, Kristjan R.; Thorlacius, Larus
2005-07-15
At the classical level, two-dimensional dilaton gravity coupled to an abelian gauge field has charged black hole solutions, which have much in common with four-dimensional Reissner-Nordstroem black holes, including multiple asymptotic regions, timelike curvature singularities, and Cauchy horizons. The black hole spacetime is, however, significantly modified by quantum effects, which can be systematically studied in this two-dimensional context. In particular, the back-reaction on the geometry due to pair-creation of charged fermions destabilizes the inner horizon and replaces it with a spacelike curvature singularity. The semiclassical geometry has the same global topology as an electrically neutral black hole.
Charged balanced black rings in five dimensions
NASA Astrophysics Data System (ADS)
Kleihaus, Burkhard; Kunz, Jutta; Schnülle, Kirsten
2011-05-01
We present balanced black ring solutions of pure Einstein-Maxwell theory in five dimensions. The solutions are asymptotically flat, and their tension and gravitational self-attraction are balanced by the repulsion due to rotation and electrical charge. Hence the solutions are free of conical singularities and possess a regular horizon which exhibits the ring topology S×S. We discuss the global charges and the horizon properties of the solutions and show that they satisfy a Smarr relation. We construct these black rings numerically, restricting to the case of black rings with a rotation in the direction of the S and large black rings. We compare these to the blackfold results.
Non-topological nature of the edge current in a chiral p-wave superconductor
NASA Astrophysics Data System (ADS)
Taylor, Edward; Huang, Wen; Lederer, Samuel; Kallin, Catherine
2015-03-01
The edges of time reversal symmetry breaking topological superconductors support chiral Majorana bound states as well as spontaneous charge currents. The Majorana modes are a robust, topological property, but the charge currents are non-topological-and therefore sensitive to microscopic details-even if we neglect Meissner screening. We give insight into the non-topological nature of edge currents in chiral p-wave superconductors using a variety of theoretical techniques, including lattice Bogoliubov-de Gennes equations, the quasiclassical approximation, and the gradient expansion, and describe those special cases where edge currents do have a topological character. While edge currents are not quantized, they are generically large, but can be substantially reduced for a sufficiently anisotropic gap function, a scenario of possible relevance for the putative chiral p-wave superconductor Sr2RuO4 . Supported by NSERC and CIFAR at McMaster and by the Canada Research Chair and Canada Council Killam programs and NSF Grant No. NSF PHY11-25915 (CK). SL is supported by the DOE Office of Basic Energy Sciences, contract DEAC02-76SF00515
Magnetic End States in a Strongly Interacting One-Dimensional Topological Kondo Insulator
NASA Astrophysics Data System (ADS)
Lobos, Alejandro M.; Dobry, Ariel O.; Galitski, Victor
2015-04-01
Topological Kondo insulators are strongly correlated materials where itinerant electrons hybridize with localized spins, giving rise to a topologically nontrivial band structure. Here, we use nonperturbative bosonization and renormalization-group techniques to study theoretically a one-dimensional topological Kondo insulator, described as a Kondo-Heisenberg model, where the Heisenberg spin-1 /2 chain is coupled to a Hubbard chain through a Kondo exchange interaction in the p -wave channel (i.e., a strongly correlated version of the prototypical Tamm-Schockley model). We derive and solve renormalization-group equations at two-loop order in the Kondo parameter, and find that, at half filling, the charge degrees of freedom in the Hubbard chain acquire a Mott gap, even in the case of a noninteracting conduction band (Hubbard parameter U =0 ). Furthermore, at low enough temperatures, the system maps onto a spin-1 /2 ladder with local ferromagnetic interactions along the rungs, effectively locking the spin degrees of freedom into a spin-1 chain with frozen charge degrees of freedom. This structure behaves as a spin-1 Haldane chain, a prototypical interacting topological spin model, and features two magnetic spin-1 /2 end states for chains with open boundary conditions. Our analysis allows us to derive an insightful connection between topological Kondo insulators in one spatial dimension and the well-known physics of the Haldane chain, showing that the ground state of the former is qualitatively different from the predictions of the naive mean-field theory.
Physical meaning of the QTAIM topological parameters in hydrogen bonding.
Duarte, Darío J R; Angelina, Emilio L; Peruchena, Nélida M
2014-11-01
This work examined the local topological parameters of charge density at the hydrogen bond (H-bond) critical points of a set of substituted formamide cyclic dimers and enolic tautomers. The analysis was performed not only on the total electron density of the hydrogen bonded complexes but also on the intermediate electron density differences derived from the Morokuma energy decomposition scheme. Through the connection between these intermediate electron density differences and the corresponding differences in topological parameters, the meaning of topological parameters variation due to hydrogen bonding (H-bonding) becomes evident. Thus, for example, we show in a plausible way that the potential energy density differences at the H-bond critical point properly describe the electrostatics of H-bonding, and local kinetic energy density differences account for the localization/delocalization degree of the electrons at that point. The results also support the idea that the total electronic energy density differences at the H-bond critical point describe the strength of the interaction rather than its covalent character as is commonly considered. PMID:25367044
A Bosonic Analogue of a Topological Dirac Semi-Metal
NASA Astrophysics Data System (ADS)
Lapa, Matthew; Cho, Gil Young; Hughes, Taylor
We construct a bosonic analogue of a two-dimensional topological Dirac Semi-Metal (DSM). The low-energy description of the most basic 2D DSM model consists of two Dirac cones at positions +/-k0 in momentum space. The local stability of the Dirac cones is guaranteed by a composite symmetry Z2, where is time-reversal and is inversion. This model also exhibits interesting time-reversal and inversion symmetry breaking electromagnetic responses. In this work we construct a bosonic analogue of a DSM by replacing each Dirac cone with a copy of the O (4) Nonlinear Sigma Model (NLSM) with topological theta term and theta angle θ = +/- π . One copy of this NLSM also describes the gapless surface termination of the 3D Bosonic Topological Insulator (BTI). We compute the time-reversal and inversion symmetry breaking electromagnetic responses for our model and show that they are twice the value one gets in the DSM case. We also investigate the local stability of the individual O (4) NLSM's in the BSM model. Along the way we clarify many aspects of the surface theory of the BTI including the electromagnetic response, the charges of vortex excitations, and the stability to symmetry-allowed perturbations. Nsf CAREER DMR-1351895.
Raman Studies of Vibrational Properties of Doped Topological Insulators
NASA Astrophysics Data System (ADS)
Means-Shively, Casie; Ji, Chao; Andersen, Heidi; Ye, Zhipeng; He, Rui; Purdue University Collaboration
2015-03-01
The main objective of our research was to use Raman spectroscopy to probe the phonon properties of doped and undoped topological insulators. Topological insulators are unique in that they are conductive on the surface yet insulating in the bulk. Our main focus was on doped and undoped Bi2Te3, a representative topological insulator material. The phonon properties and the coupling between phonons and charge carriers in these materials have not been well studied. We were able to probe variably doped Bi2Te3 with a spectrometer to observe and compare the spectra of each material. We were also able to use a variable temperature cryostat to observe and compare spectra of these materials at temperatures ranging from ~ 7K to ~ 294K. Our conclusion is that the frequency, linewidth, and intensity of the vibrational modes of Bi2Te3 are dependent on temperature as well as doping. This research is supported by the American Chemical Society Petroleum Research Fund (Grant 53401-UNI10) and National Science Foundation MRI Grant (No. DMR-1337207).
Glueballs, strings and topology in SU(N) gauge theory
NASA Astrophysics Data System (ADS)
Teper, M.
2002-05-01
I show how one can use lattice methods to calculate various continuum properties of SU( N) gauge theories; in part to explore old ideas that N = 3 might be close to N = ∞. I describe calculations of the low-lying 'glueball' mass spectrum, of the string tensions of k-strings and of topological fluctuations for 2 ≤ N ≤ 5. We find that mass ratios appear to show a rapid approach to the large— N limit, and, indeed, can be described all the way down to SU(2) using just a leading O(1/ N2) correction. We confirm that the smooth large— N limit we find is confining and is obtained by keeping a constant 't Hooft coupling. We find that the ratio of the k = 2 string tension to the k = 1 fundamental string tension is much less than the naive (unbound) value of 2 and is considerably greater than the naive bag model prediction; in fact it is consistent, within quite small errors, with either the M(-theory)QCD-inspired conjecture that σ k ∝ sin(π k/N) or with 'Casimir scaling'. Finally I describe calculations of the topological charge of the gauge fields. We observe that, as expected, the density of small-size instantons vanishes rapidly as N increases, while the topological susceptibility appears to have a non-zero N = ∞ limit.
A new class of (2 + 1)-dimensional topological superconductors with {Z}_8 topological classification
NASA Astrophysics Data System (ADS)
Qi, Xiao-Liang
2013-06-01
The classification of topological states of matter depends on spatial dimension and symmetry class. For non-interacting topological insulators and superconductors, the topological classification is obtained systematically and non-trivial topological insulators are classified by either integer or Z2. The classification of interacting topological states of matter is much more complicated and only special cases are understood. In this paper we study a new class of topological superconductors in (2 + 1) dimensions which has time-reversal symmetry and a {Z}_2 spin conservation symmetry. We demonstrate that the superconductors in this class are classified by {Z}_8 when electron interaction is considered, while the classification is {Z} without interaction.
NASA Astrophysics Data System (ADS)
Zeng, Bei; Wen, Xiao-Gang
2015-03-01
In this work, we present some new understanding of topological order, including three main aspects. (1) It was believed that classifying topological orders corresponds to classifying gapped quantum states. We show that such a statement is not precise. We introduce the concept of gapped quantum liquid as a special kind of gapped quantum states that can "dissolve" any product states on additional sites. Topologically ordered states actually correspond to gapped quantum liquids with stable ground-state degeneracy. Symmetry-breaking states for on-site symmetry are also gapped quantum liquids, but with unstable ground-state degeneracy. (2) We point out that the universality classes of generalized local unitary (gLU) transformations (without any symmetry) contain both topologically ordered states and symmetry-breaking states. This allows us to use a gLU invariant—topological entanglement entropy—to probe the symmetry-breaking properties hidden in the exact ground state of a finite system, which does not break any symmetry. This method can probe symmetry- breaking orders even without knowing the symmetry and the associated order parameters. (3) The universality classes of topological orders and symmetry-breaking orders can be distinguished by stochastic local (SL) transformations (i.e., local invertible transformations): small SL transformations can convert the symmetry-breaking classes to the trivial class of product states with finite probability of success, while the topological-order classes are stable against any small SL transformations, demonstrating a phenomenon of emergence of unitarity. This allows us to give a definition of long-range entanglement based on SL transformations, under which only topologically ordered states are long-range entangled.
NASA Astrophysics Data System (ADS)
Campbell, Michael G.; Tasinkevych, Mykola; Smalyukh, Ivan I.
2014-05-01
Polymer dispersed liquid crystals are a useful model system for studying the relationship between surface topology and defect structures. They are comprised of a polymer matrix with suspended spherical nematic drops and are topologically constrained to host defects of an elementary hedgehog charge per droplet, such as bulk or surface point defects or closed disclination loops. We control the genus of the closed surfaces confining such micrometer-sized nematic drops with tangential boundary conditions for molecular alignment imposed by the polymer matrix, allowing us to avoid defects or, on the contrary, to generate them in a controlled way. We show, both experimentally and through numerical modeling, that topological constraints in nematic microdrops can be satisfied by hosting topologically stable half-integer bulk defect lines anchored to opposite sides of handlebody surfaces. This enriches the interplay of topologies of closed surfaces and fields with nonpolar symmetry, yielding new unexpected configurations that cannot be realized in vector fields, having potential implications for topologically similar defects in cosmology and other fields.
From an array of quantum wires to three-dimensional fractional topological insulators
NASA Astrophysics Data System (ADS)
Sagi, Eran; Oreg, Yuval
2015-11-01
The coupled-wires approach has been shown to be useful in describing two-dimensional strongly interacting topological phases. In this manuscript, we extend this approach to three-dimensions, and construct a model for a fractional strong topological insulator. This topologically ordered phase has an exotic gapless state on the surface, called a fractional Dirac liquid, which cannot be described by the Dirac theory of free fermions. Like in noninteracting strong topological insulators, the surface is protected by the presence of time-reversal symmetry and charge conservation. We show that upon breaking these symmetries, the gapped fractional Dirac liquid presents unique features. In particular, the gapped phase that results from breaking time-reversal symmetry has a halved fractional Hall conductance of the form σx y=1/2 e/2m h if the filling is ν =1 /m . On the other hand, if the surface is gapped by proximity coupling to an s -wave superconductor, we end up with an exotic topological superconductor. To reveal the topological nature of this superconducting phase, we partition the surface into two regions: one with broken time-reversal symmetry and another coupled to a superconductor. We find a fractional Majorana mode, which cannot be described by a free Majorana theory, on the boundary between the two regions. The density of states associated with tunneling into this one-dimensional channel is proportional to ωm -1, in analogy to the edge of the corresponding Laughlin state.
Quantum Anomalous Hall effect in a Topological Insulator coupled to a Skyrmion Lattice
NASA Astrophysics Data System (ADS)
Bhowmick, Tonmoy; Barlas, Yafis; Yin, Gen; Lake, Roger
A Skyrmion is a topologically protected spin texture characterized by a topological charge that has been experimentally observed in both bulk B20 compounds and thin films. In a quantum anomalous Hall phase, a material develops a topologically nontrivial electronic structure giving rise to quantized hall conductivity without any external magnetic field. We predict that a conventional bulk topological insulating material (e.g. Bi2 Se3, Bi2 Te3 Sb2 Te3) in proximity with a Skyrmion crystal, with a weak exchange coupling, will be driven into an anomalous Hall insulating phase characterized by a nonzero integer chern number in the gap. We have calculated band structure, identified the gaps, and calculated the chern number at those gaps. The calculations show that the non trivial topological properties of the Skyrmion spin texture can be imprinted on the Dirac electrons of the topological insulator. Electronic structure calculations were supported by the NSF (ECCS-1408168). Micromagnetic simulations were supported by SHINES Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award #DE-SC0012670.
Scanning tunneling microscopy studies of topological insulators.
Zhao, Kun; Lv, Yan-Feng; Ji, Shuai-Hua; Ma, Xucun; Chen, Xi; Xue, Qi-Kun
2014-10-01
Scanning tunneling microscopy (STM), with surface sensitivity, is an ideal tool to probe the intriguing properties of the surface state of topological insulators (TIs) and topological crystalline insulators (TCIs). We summarize the recent progress on those topological phases revealed by STM studies. STM observations have directly confirmed the existence of the topological surface states and clearly revealed their novel properties. We also discuss STM work on magnetic doped TIs, topological superconductors and crystalline symmetry-protected surface states in TCIs. The studies have greatly promoted our understanding of the exotic properties of the new topological phases, as well as put forward new challenges. STM will continue to play an important role in this rapidly growing field from the point view of both fundamental physics and applications. PMID:25214502
Photonic simulation of topological excitations in metamaterials
Tan, Wei; Sun, Yong; Chen, Hong; Shen, Shun-Qing
2014-01-01
Condensed matter systems with topological order and metamaterials with left-handed chirality have attracted recently extensive interests in the fields of physics and optics. So far the topological order and chirality of electromagnetic wave are two independent concepts, and there is no work to address their connection. Here we propose to establish the relation between the topological order in condensed matter systems and the chirality in metamaterials, by mapping explicitly Maxwell's equations to the Dirac equation in one dimension. We report an experimental implement of the band inversion in the Dirac equation, which accompanies change of chirality of electromagnetic wave in metamaterials, and the first microwave measurement of topological excitations and topological phases in one dimension. Our finding provides a proof-of-principle example that electromagnetic wave in the metamaterials can be used to simulate the topological order in condensed matter systems and quantum phenomena in relativistic quantum mechanics in a controlled laboratory environment. PMID:24452532
Topological characterization of periodically driven quantum systems
NASA Astrophysics Data System (ADS)
Kitagawa, Takuya; Berg, Erez; Rudner, Mark; Demler, Eugene
2010-12-01
Topological properties of physical systems can lead to robust behaviors that are insensitive to microscopic details. Such topologically robust phenomena are not limited to static systems but can also appear in driven quantum systems. In this paper, we show that the Floquet operators of periodically driven systems can be divided into topologically distinct (homotopy) classes and give a simple physical interpretation of this classification in terms of the spectra of Floquet operators. Using this picture, we provide an intuitive understanding of the well-known phenomenon of quantized adiabatic pumping. Systems whose Floquet operators belong to the trivial class simulate the dynamics generated by time-independent Hamiltonians, which can be topologically classified according to the schemes developed for static systems. We demonstrate these principles through an example of a periodically driven two-dimensional hexagonal lattice tight-binding model which exhibits several topological phases. Remarkably, one of these phases supports chiral edge modes even though the bulk is topologically trivial.
A tunable topological insulator in the spin helical Dirac transport regime.
Hsieh, D; Xia, Y; Qian, D; Wray, L; Dil, J H; Meier, F; Osterwalder, J; Patthey, L; Checkelsky, J G; Ong, N P; Fedorov, A V; Lin, H; Bansil, A; Grauer, D; Hor, Y S; Cava, R J; Hasan, M Z
2009-08-27
Helical Dirac fermions-charge carriers that behave as massless relativistic particles with an intrinsic angular momentum (spin) locked to its translational momentum-are proposed to be the key to realizing fundamentally new phenomena in condensed matter physics. Prominent examples include the anomalous quantization of magneto-electric coupling, half-fermion states that are their own antiparticle, and charge fractionalization in a Bose-Einstein condensate, all of which are not possible with conventional Dirac fermions of the graphene variety. Helical Dirac fermions have so far remained elusive owing to the lack of necessary spin-sensitive measurements and because such fermions are forbidden to exist in conventional materials harbouring relativistic electrons, such as graphene or bismuth. It has recently been proposed that helical Dirac fermions may exist at the edges of certain types of topologically ordered insulators-materials with a bulk insulating gap of spin-orbit origin and surface states protected against scattering by time-reversal symmetry-and that their peculiar properties may be accessed provided the insulator is tuned into the so-called topological transport regime. However, helical Dirac fermions have not been observed in existing topological insulators. Here we report the realization and characterization of a tunable topological insulator in a bismuth-based class of material by combining spin-imaging and momentum-resolved spectroscopies, bulk charge compensation, Hall transport measurements and surface quantum control. Our results reveal a spin-momentum locked Dirac cone carrying a non-trivial Berry's phase that is nearly 100 per cent spin-polarized, which exhibits a tunable topological fermion density in the vicinity of the Kramers point and can be driven to the long-sought topological spin transport regime. The observed topological nodal state is shown to be protected even up to 300 K. Our demonstration of room-temperature topological order and non-trivial spin-texture in stoichiometric Bi(2)Se(3).M(x) (M(x) indicates surface doping or gating control) paves the way for future graphene-like studies of topological insulators, and applications of the observed spin-polarized edge channels in spintronic and computing technologies possibly at room temperature. PMID:19620959
Dirac single particle and plasmon excitations in topological insulators
NASA Astrophysics Data System (ADS)
Lupi, Stefano
Topological Insulators (TIs), like Bi2Se3 and Bi2Te3, are one of the most intriguing issues at focus in Condensed Matter Physics. TIs exhibit a band gap in the bulk like ordinary insulators, but have intrinsic 2D conducting states on their edge and surface. This means that the topology, associated with the electronic wavefunctions of the system, changes discontinuously when passing from the bulk to the surface. The edge states arise from a strong spin-orbit coupling, and they are backscattering protected, i.e. not sensitive to disorder (except that coming from magnetic impurities). Such as graphene, TIs surface charge transport is carried out by Dirac fermions, with a very high surface carrier density (n >= 1013 cm-2) , compared to typical values on metal surfaces. Apart single particle excitations, Dirac fermions in TIs sustain exotic plasmonic (collective) modes whose properties of tunability and temperature dependence can be used for photonics applications at the nanoscale. Moreover, unlike plasmons in metals, Dirac plasmons in TIs are expected to be strongly affected by an external magnetic field B due to fact that the cyclotron frequency is comparable to the the plasmon frequency, in particular when plasmons are engineered in the terahertz region of the electromagnetic spectrum. In this talk, after a general review on the properties of Topological Insulators, I will discuss the terahertz linear response of Dirac plasmons in TIs and their behavior under a strong magnetic field up to 30 T. The appearance of strong non-linear optical effects, when the THz electric field reaches values on the order of 1 MV/cm, will be also discussed. In the second part of the talk, I will discuss the sub-ps dynamics of Dirac single-particle and collective excitations as measured by optical-pump THz-probe experiments. Both the steady state and time-resolved experiments provide a unifying picture of single particle and collective electronic excitations in Topological Insulators.
Quantum mechanical probability current as electromagnetic 4-current from topological EM fields
NASA Astrophysics Data System (ADS)
van der Mark, Martin B.
2015-09-01
Starting from a complex 4-potential A = αdβ we show that the 4-current density in electromagnetism and the probability current density in relativistic quantum mechanics are of identical form. With the Dirac-Clifford algebra Cl1,3 as mathematical basis, the given 4-potential allows topological solutions of the fields, quite similar to Bateman's construction, but with a double field solution that was overlooked previously. A more general nullvector condition is found and wave-functions of charged and neutral particles appear as topological configurations of the electromagnetic fields.
Spin-electricity conversion induced by spin injection into topological insulators.
Shiomi, Y; Nomura, K; Kajiwara, Y; Eto, K; Novak, M; Segawa, Kouji; Ando, Yoichi; Saitoh, E
2014-11-01
We report successful spin injection into the surface states of topological insulators by using a spin pumping technique. By measuring the voltage that shows up across the samples as a result of spin pumping, we demonstrate that a spin-electricity conversion effect takes place in the surface states of bulk-insulating topological insulators Bi(1.5)Sb(0.5)Te(1.7)Se(1.3) and Sn-doped Bi(2)Te(2)Se. In this process, the injected spins are converted into a charge current along the Hall direction due to the spin-momentum locking on the surface state. PMID:25415913
Kong, Desheng; Cui, Yi
2011-11-01
Electrical charges on the boundaries of topological insulators favour forward motion over back-scattering at impurities, producing low-dissipation, metallic states that exist up to room temperature in ambient conditions. These states have the promise to impact a broad range of applications from electronics to the production of energy, which is one reason why topological insulators have become the rising star in condensed-matter physics. There are many challenges in the processing of these exotic materials to use the metallic states in functional devices, and they present great opportunities for the chemistry and materials science research communities. PMID:22024879
Algebra and topology for applications to physics
NASA Technical Reports Server (NTRS)
Rozhkov, S. S.
1987-01-01
The principal concepts of algebra and topology are examined with emphasis on applications to physics. In particular, attention is given to sets and mapping; topological spaces and continuous mapping; manifolds; and topological groups and Lie groups. The discussion also covers the tangential spaces of the differential manifolds, including Lie algebras, vector fields, and differential forms, properties of differential forms, mapping of tangential spaces, and integration of differential forms.
Lectures on black holes, topological strings and quantum attractors
NASA Astrophysics Data System (ADS)
Pioline, Boris
2006-11-01
In these lecture notes, we review some recent developments on the relation between the macroscopic entropy of four-dimensional BPS black holes and the microscopic counting of states, beyond the thermodynamical, large charge limit. After a brief overview of charged black holes in supergravity and string theory, we give an extensive introduction to special and very special geometry, attractor flows and topological string theory, including holomorphic anomalies. We then expose the Ooguri Strominger Vafa (OSV) conjecture which relates microscopic degeneracies to the topological string amplitude and review precision tests of this formula on 'small' black holes. Finally, motivated by a holographic interpretation of the OSV conjecture, we discuss the radial quantization of BPS black holes (i.e. quantum attractors) and present a recent conjecture relating exact black hole degeneracies to Fourier coefficients of certain automorphic forms. Lectures delivered at the RTN Winter School on Strings, Supergravity and Gauge theories, (CERN, January 16 20, 2006), the 11th APCTP/KIAS String Winter School (Pohang, Feb 8 15 2005) and the Winter School on the Attractor Mechanism (Frascati, March 20 24, 2006).
Topological crystalline Bose insulator in two dimensions via entanglement spectrum
NASA Astrophysics Data System (ADS)
Ware, Brayden; Kimchi, Itamar; Parameswaran, S. A.; Bauer, Bela
2015-11-01
Strongly correlated analogs of topological insulators have been explored in systems with purely on-site symmetries, such as time-reversal or charge conservation. Here, we use recently developed tensor network tools to study a quantum state of interacting bosons which is featureless in the bulk, but distinguished from an atomic insulator in that it exhibits entanglement which is protected by its spatial symmetries. These properties are encoded in a model many-body wave function that describes a fully symmetric insulator of bosons on the honeycomb lattice at half filling per site. While the resulting integer unit cell filling allows the state to bypass "no-go" theorems that trigger fractionalization at fractional filling, it nevertheless has nontrivial entanglement, protected by symmetry. We demonstrate this by computing the boundary entanglement spectra, finding a gapless entanglement edge described by a conformal field theory as well as degeneracies protected by the nontrivial action of combined charge conservation and spatial symmetries on the edge. Here, the tight-binding representation of the space group symmetries plays a particular role in allowing certain entanglement cuts that are not allowed on other lattices of the same symmetry, suggesting that the lattice representation can serve as an additional symmetry ingredient in protecting an interacting topological phase. Our results extend to a related insulating state of electrons, with short-ranged entanglement and no band insulator analog.
NASA Astrophysics Data System (ADS)
Blanco-Redondo, Andrea; Andonegui, Imanol; Collins, Matthew J.; Harari, Gal; Lumer, Yaakov; Rechtsman, Mikael C.; Eggleton, Benjamin J.; Segev, Mordechai
2016-04-01
One-dimensional models with topological band structures represent a simple and versatile platform to demonstrate novel topological concepts. Here we experimentally study topologically protected states in silicon at the interface between two dimer chains with different Zak phases. Furthermore, we propose and demonstrate that, in a system where topological and trivial defect modes coexist, we can probe them independently. Tuning the configuration of the interface, we observe the transition between a single topological defect and a compound trivial defect state. These results provide a new paradigm for topologically protected waveguiding in a complementary metal-oxide-semiconductor compatible platform and highlight the novel concept of isolating topological and trivial defect modes in the same system that can have important implications in topological physics.
Park, Byung Cheol; Kim, Tae-Hyeon; Sim, Kyung Ik; Kang, Boyoun; Kim, Jeong Won; Cho, Beongki; Jeong, Kwang-Ho; Cho, Mann-Ho; Kim, Jae Hoon
2015-01-01
Strong spin-orbit interaction and time-reversal symmetry in topological insulators generate novel quantum states called topological surface states. Their study provides unique opportunities to explore exotic phenomena such as spin Hall effects and topological phase transitions, relevant to the development of quantum devices for spintronics and quantum computation. Although ultrahigh-vacuum surface probes can identify individual topological surface states, standard electrical and optical experiments have so far been hampered by the interference of bulk and quantum well states. Here, with terahertz time-domain spectroscopy of ultrathin Bi₂Se₃ films, we give evidence for topological phase transitions, a single conductance quantum per topological surface state, and a quantized terahertz absorbance of 2.9% (four times the fine structure constant). Our experiment demonstrates the feasibility to isolate, detect and manipulate topological surface states in the ambient at room temperature for future fundamental research on the novel physics of topological insulators and their practical applications. PMID:25775141
Emergence of magnetic topological states in topological insulators doped with magnetic impurities
NASA Astrophysics Data System (ADS)
Tran, Minh-Tien; Nguyen, Hong-Son; Le, Duc-Anh
2016-04-01
Emergence of the topological invariant and the magnetic moment in topological insulators doped with magnetic impurities is studied based on a mutual cooperation between the spin-orbit coupling of electrons and the spin exchange of these electrons with magnetic impurity moments. The mutual cooperation is realized based on the Kane-Mele model in the presence of magnetic impurities. The topological invariants and the spontaneous magnetization are self-consistently determined within the dynamical mean-field theory. We find different magnetic topological phase transitions, depending on the electron filling. At half filling an antiferromagnetic topological insulator, which exhibits the quantum spin Hall effect, exists in the phase region between the paramagnetic topological insulator and the trivially topological antiferromagnetic insulator. At quarter and three-quarter fillings, a ferromagnetic topological insulator, which exhibits the quantum anomalous Hall effect, occurs in the strong spin-exchange regime.
Blanco-Redondo, Andrea; Andonegui, Imanol; Collins, Matthew J; Harari, Gal; Lumer, Yaakov; Rechtsman, Mikael C; Eggleton, Benjamin J; Segev, Mordechai
2016-04-22
One-dimensional models with topological band structures represent a simple and versatile platform to demonstrate novel topological concepts. Here we experimentally study topologically protected states in silicon at the interface between two dimer chains with different Zak phases. Furthermore, we propose and demonstrate that, in a system where topological and trivial defect modes coexist, we can probe them independently. Tuning the configuration of the interface, we observe the transition between a single topological defect and a compound trivial defect state. These results provide a new paradigm for topologically protected waveguiding in a complementary metal-oxide-semiconductor compatible platform and highlight the novel concept of isolating topological and trivial defect modes in the same system that can have important implications in topological physics. PMID:27152805
NASA Astrophysics Data System (ADS)
Xiong, Yuting; Gu, Zhaojun; Jin, Wei
In this paper, a novel practical algorithmic solution for automatic discovering the physical topology of switched Ethernet was proposed. Our algorithm collects standard SNMP MIB information that is widely supported in modern IP networks and then builds the physical topology of the active network. We described the relative definitions, system model and proved the correctness of the algorithm. Practically, the algorithm was implemented in our visualization network monitoring system. We also presented the main steps of the algorithm, core codes and running results on the lab network. The experimental results clearly validate our approach, demonstrating that our algorithm is simple and effective which can discover the accurate up-to-date physical network topology.
Topological deformation of isolated horizons
Liko, Tomas
2008-03-15
We show that the Gauss-Bonnet term can have physical effects in four dimensions. Specifically, the entropy of a black hole acquires a correction term that is proportional to the Euler characteristic of the cross sections of the horizon. While this term is constant for a single black hole, it will be a nontrivial function for a system with dynamical topologies such as black-hole mergers: it is shown that for certain values of the Gauss-Bonnet parameter, the second law of black-hole mechanics can be violated.
Topological description of mirage effects
NASA Astrophysics Data System (ADS)
Doss-Hammel, Stephen M.; Platt, Nathan
1995-08-01
Infrared search and track systems are important to the Navy as early warning devices to detect fast moving sea-skimming threats. Sensors must be able to analyze severely distorted images since the propagation medium consists of long horizontal paths that are near the ocean surface. The thermodynamics of this configuration foster the formation of gradients in the refractivity, which in turn can create striking and puzzling anomalies in the perceived image. An accurate simulation of the propagation characteristics of signals is crucial to help elucidate possible errors. We describe work to develop simple topological methods to understand propagation distortions in the marine and coastal environment.
Geometry, topology, and string theory
Varadarajan, Uday
2003-07-10
A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated.
Solar flares and magnetic topology
NASA Technical Reports Server (NTRS)
Sturrock, P. A.
1987-01-01
This article is a very brief review and comparison of the observational properties of flares and theoretical concepts of models of flares, especially the concepts of magnetic topology and its evolution. We examine the environmental aspects of flare behavior. Some of these aspects must be consequences of unknown processes occurring below the photosphere. Other aspects involve structures - such as filaments - that are closely related to flares. We then examine properties of flares to try to distinguish the different phases of energy release that can occur in the course of a flare. Finally a schematic scenario is offered to interpret these phases in terms of this scenario.
Topological deformation of isolated horizons
NASA Astrophysics Data System (ADS)
Liko, Tom
2008-03-01
We show that the Gauss-Bonnet term can have physical effects in four dimensions. Specifically, the entropy of a black hole acquires a correction term that is proportional to the Euler characteristic of the cross sections of the horizon. While this term is constant for a single black hole, it will be a nontrivial function for a system with dynamical topologies such as black-hole mergers: it is shown that for certain values of the Gauss-Bonnet parameter, the second law of black-hole mechanics can be violated.
Peptides that influence membrane topology
NASA Astrophysics Data System (ADS)
Wong, Gerard C. L.
2014-03-01
We examine the mechanism of a range of polypeptides that influence membrane topology, including antimicrobial peptides, cell penetrating peptides, viral fusion peptides, and apoptosis proteins, and show how a combination of geometry, coordination chemistry, and soft matter physics can be used to approach a unified understanding. We will also show how such peptides can impact biomedical problems such as auto-immune diseases (psoriasis, lupus), infectious diseases (viral and bacterial infections), and mitochondrial pathologies (under-regulated apoptosis leads to neurodegenerative diseases whereas over-regulated apoptosis leads to cancer.)
Topological Bloch bands in graphene superlattices
Song, Justin C. W.; Samutpraphoot, Polnop; Levitov, Leonid S.
2015-01-01
We outline a designer approach to endow widely available plain materials with topological properties by stacking them atop other nontopological materials. The approach is illustrated with a model system comprising graphene stacked atop hexagonal boron nitride. In this case, the Berry curvature of the electron Bloch bands is highly sensitive to the stacking configuration. As a result, electron topology can be controlled by crystal axes alignment, granting a practical route to designer topological materials. Berry curvature manifests itself in transport via the valley Hall effect and long-range chargeless valley currents. The nonlocal electrical response mediated by such currents provides diagnostics for band topology. PMID:26286992
Copying and Evolution of Neuronal Topology
Fernando, Chrisantha; Karishma, K. K.; Szathmáry, Eörs
2008-01-01
We propose a mechanism for copying of neuronal networks that is of considerable interest for neuroscience for it suggests a neuronal basis for causal inference, function copying, and natural selection within the human brain. To date, no model of neuronal topology copying exists. We present three increasingly sophisticated mechanisms to demonstrate how topographic map formation coupled with Spike-Time Dependent Plasticity (STDP) can copy neuronal topology motifs. Fidelity is improved by error correction and activity-reverberation limitation. The high-fidelity topology-copying operator is used to evolve neuronal topologies. Possible roles for neuronal natural selection are discussed. PMID:19020662
Magnetic topology of emerging flux regions
NASA Astrophysics Data System (ADS)
Pariat, Etienne
Coronal magnetic fields structure and governs the dynamics of the solar atmosphere. These magnetic fields are often complex, composed of multiples domains of magnetic-field-lines connectivity. The topology of the magnetic field allows a synthetic description of these complex magnetic field by highlighting the structural elements that are important for the dynamic and the activity of the corona. Topology identifies the key elements where magnetic reconnection will preferentially occurs, and allows to explain and predict the evolution of the coronal plasma. However the topological elements - such as null points, separatrices, separators - do not appear out of thin air. Along with energy, and helicity, the magnetic topology of an active region is build up as the consequence of flux emergence. Some topological elements, such as bald-patches, are even fully part of the mechanism of flux emergence mechanism and drive the evolution and the structuration of the coronal magnetic field as it crosses the lower layer of the solar atmosphere. In the present talk I will therefore review our current understanding of the formation of active region in terms of magnetic topology. I will speak on how the topological structures which are key to solar activity are formed. Meanwhile I'll also discus the topological properties of emerging active region and how topology influences the very process of flux emergence.
Uranyl peroxide closed clusters containing topological squares
Unruh, Daniel K.; Burtner, Alicia; Pressprich, Laura; Sigmon, Ginger E.; Burns, Peter C
2010-01-01
Four self-assembling clusters of uranyl peroxide polyhedra have been formed in alkaline aqueous solutions and structurally characterized. These clusters consist of 28, 30, 36 and 44 uranyl polyhedra and exhibit complex new topologies. Each has a structure that contains topological squares, pentagons and hexagons. Analysis of possible topologies within boundary constraints indicates a tendency for adoption of higher symmetry topologies in these cases. Small angle X-ray scattering data demonstrated that crystals of one of these clusters can be dissolved in ultrapure water and that the clusters remain intact for at least several days.
Topology of nonsymmorphic crystalline insulators and superconductors
NASA Astrophysics Data System (ADS)
Shiozaki, Ken; Sato, Masatoshi; Gomi, Kiyonori
2016-05-01
Topological classification in our previous paper [K. Shiozaki and M. Sato, Phys. Rev. B 90, 165114 (2014), 10.1103/PhysRevB.90.165114] is extended to nonsymmorphic crystalline insulators and superconductors. Using the twisted equivariant K theory, we complete the classification of topological crystalline insulators and superconductors in the presence of additional order-two nonsymmorphic space-group symmetries. The order-two nonsymmorphic space groups include half-lattice translation with Z2 flip, glide, twofold screw, and their magnetic space groups. We find that the topological periodic table shows modulo-2 periodicity in the number of flipped coordinates under the order-two nonsymmorphic space group. It is pointed out that the nonsymmorphic space groups allow Z2 topological phases even in the absence of time-reversal and/or particle-hole symmetries. Furthermore, the coexistence of the nonsymmorphic space group with time-reversal and/or particle-hole symmetries provides novel Z4 topological phases, which have not been realized in ordinary topological insulators and superconductors. We present model Hamiltonians of these new topological phases and analytic expressions of the Z2 and Z4 topological invariants. The half-lattice translation with Z2 spin flip and glide symmetry are compatible with the existence of boundaries, leading to topological surface gapless modes protected by the order-two nonsymmorphic symmetries. We also discuss unique features of these gapless surface modes.
NASA Astrophysics Data System (ADS)
Zhang, Dan-Wei; Zhao, Y. X.; Liu, Rui-Bin; Xue, Zheng-Yuan; Zhu, Shi-Liang; Wang, Z. D.
2016-04-01
Since the well-known PT symmetry has its fundamental significance and implication in physics, where PT denotes a joint operation of space inversion P and time reversal T , it is important and intriguing to explore exotic PT -invariant topological metals and to physically realize them. Here we develop a theory for a different type of topological metals that are described by a two-band model of PT -invariant topological nodal loop states in a three-dimensional Brillouin zone, with the topological stability being revealed through the PT -symmetry-protected nontrivial Z2 topological charge even in the absence of both P and T symmetries. Moreover, the gapless boundary modes are demonstrated to originate from the nontrivial topological charge of the bulk nodal loop. Based on these exact results, we propose an experimental scheme to realize and to detect tunable PT -invariant topological nodal loop states with ultracold atoms in an optical lattice, in which atoms with two hyperfine spin states are loaded in a spin-dependent three-dimensional optical lattice and two pairs of Raman lasers are used to create out-of-plane spin-flip hopping with site-dependent phase. It is shown that such a realistic cold-atom setup can yield topological nodal loop states, having a tunable band-touching ring with the twofold degeneracy in the bulk spectrum and nontrivial surface states. The nodal loop states are actually protected by the combined PT symmetry and are characterized by a Z2-type invariant (or topological charge), i.e., a quantized Berry phase. Remarkably, we demonstrate with numerical simulations that (i) the characteristic nodal ring can be detected by measuring the atomic transfer fractions in a Bloch-Zener oscillation; (ii) the topological invariant may be measured based on the time-of-flight imaging; and (iii) the surface states may be probed through Bragg spectroscopy. The present proposal for realizing topological nodal loop states in cold-atom systems may provide a unique experimental platform for exploring exotic PT -invariant topological physics.
Spin Charge Separation in the Quantum Spin Hall State
Qi, Xiao-Liang; Zhang, Shou-Cheng; /Stanford U., Phys. Dept.
2010-03-19
The quantum spin Hall state is a topologically non-trivial insulator state protected by the time reversal symmetry. We show that such a state always leads to spin-charge separation in the presence of a {pi} flux. Our result is generally valid for any interacting system. We present a proposal to experimentally observe the phenomenon of spin-charge separation in the recently discovered quantum spin Hall system.