Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle
NASA Astrophysics Data System (ADS)
Durdevich, Micho; Sontz, Stephen Bruce
2013-05-01
A quantum principal bundle is constructed for every Coxeter group acting on a finite-dimensional Euclidean space E, and then a connection is also defined on this bundle. The covariant derivatives associated to this connection are the Dunkl operators, originally introduced as part of a program to generalize harmonic analysis in Euclidean spaces. This gives us a new, geometric way of viewing the Dunkl operators. In particular, we present a new proof of the commutativity of these operators among themselves as a consequence of a geometric property, namely, that the connection has curvature zero.
On modified Dunkl generalization of Szász operators via q-calculus.
Mursaleen, M; Nasiruzzaman, Md; Alotaibi, Abdullah
2017-01-01
The purpose of this paper is to introduce a modification of q-Dunkl generalization of exponential functions. These types of operators enable better error estimation on the interval [Formula: see text] than the classical ones. We obtain some approximation results via a well-known Korovkin-type theorem and a weighted Korovkin-type theorem. Further, we obtain the rate of convergence of the operators for functions belonging to the Lipschitz class.
Thermodynamics of boson systems related to Dunkl differential-difference operators
NASA Astrophysics Data System (ADS)
Ubriaco, Marcelo R.
2014-11-01
We study the thermodynamics of systems based on a Fock space representation inspired by the differential-difference operators proposed in Dunkl (1989). We calculate thermodynamic functions as the entropy and heat capacity and compare them with the standard boson case. A calculation of the second virial coefficient and the scalar curvature in two and three dimensions show that these systems become repulsive within an interval of negative values of the reflection operator parameter θ. In addition, the stability of this system is examined as a function of θ.
NASA Astrophysics Data System (ADS)
Andraus, Sergio; Katori, Makoto; Miyashita, Seiji
2012-10-01
We consider a one-dimensional system of Brownian particles that repel each other through a logarithmic potential. We study two formulations for the system and the relation between them. The first, Dyson’s Brownian motion model, has an interaction coupling constant determined by the parameter β > 0. When β = 1, 2 and 4, this model can be regarded as a stochastic realization of the eigenvalue statistics of Gaussian random matrices. The second system comes from Dunkl processes, which are defined using differential-difference operators (Dunkl operators) associated with finite abstract vector sets called root systems. When the type-A root system is specified, Dunkl processes constitute a one-parameter system similar to Dyson’s model, with the difference that its particles interchange positions spontaneously. We prove that the type-A Dunkl processes with parameter k > 0 starting from any symmetric initial configuration are equivalent to Dyson’s model with the parameter β = 2k. We focus on the intertwining operators, since they play a central role in the mathematical theory of Dunkl operators, but their general closed form is not yet known. Using the equivalence between symmetric Dunkl processes and Dyson’s model, we extract the effect of the intertwining operator of type A on symmetric polynomials from these processes’ transition probability densities. In the strong coupling limit, the intertwining operator maps all symmetric polynomials onto a function of the sum of their variables. In this limit, Dyson’s model freezes, and it becomes a deterministic process with a final configuration proportional to the roots of the Hermite polynomials multiplied by the square root of the process time, while being independent of the initial configuration.
On Harmonic Analysis Operators in Laguerre-Dunkl and Laguerre-Symmetrized Settings
NASA Astrophysics Data System (ADS)
Nowak, Adam; Stempak, Krzysztof; Szarek, Tomasz Z.
2016-09-01
We study several fundamental harmonic analysis operators in the multi-dimensional context of the Dunkl harmonic oscillator and the underlying group of reflections isomorphic to Z_2^d. Noteworthy, we admit negative values of the multiplicity functions. Our investigations include maximal operators, g-functions, Lusin area integrals, Riesz transforms and multipliers of Laplace and Laplace-Stieltjes type. By means of the general Calderón-Zygmund theory we prove that these operators are bounded on weighted L^p spaces, 1 < p < ∞, and from weighted L^1 to weighted weak L^1. We also obtain similar results for analogous set of operators in the closely related multi-dimensional Laguerre-symmetrized framework. The latter emerges from a symmetrization procedure proposed recently by the first two authors. As a by-product of the main developments we get some new results in the multi-dimensional Laguerre function setting of convolution type.
NASA Astrophysics Data System (ADS)
Mejjaoli, Hatem
2008-12-01
We introduce and study the Dunkl symmetric systems. We prove the well-posedness results for the Cauchy problem for these systems. Eventually we describe the finite speed of it. Next the semi-linear Dunkl-wave equations are also studied.
Noncommutative Circle Bundles and New Dirac Operators
NASA Astrophysics Data System (ADS)
Dąbrowski, Ludwik; Sitarz, Andrzej
2013-02-01
We study spectral triples over noncommutative principal U(1) bundles. Basing on the classical situation and the abstract algebraic approach, we propose an operatorial definition for a connection and compatibility between the connection and the Dirac operator on the total space and on the base space of the bundle. We analyze in details the example of the noncommutative three-torus viewed as a U(1) bundle over the noncommutative two-torus and find all connections compatible with an admissible Dirac operator. Conversely, we find a family of new Dirac operators on the noncommutative tori, which arise from the base-space Dirac operator and a suitable connection.
On Dunkl angular momenta algebra
NASA Astrophysics Data System (ADS)
Feigin, Misha; Hakobyan, Tigran
2015-11-01
We consider the quantum angular momentum generators, deformed by means of the Dunkl operators. Together with the reflection operators they generate a subalgebra in the rational Cherednik algebra associated with a finite real reflection group. We find all the defining relations of the algebra, which appear to be quadratic, and we show that the algebra is of Poincaré-Birkhoff-Witt (PBW) type. We show that this algebra contains the angular part of the Calogero-Moser Hamiltonian and that together with constants it generates the centre of the algebra. We also consider the gl( N ) version of the subalge-bra of the rational Cherednik algebra and show that it is a non-homogeneous quadratic algebra of PBW type as well. In this case the central generator can be identified with the usual Calogero-Moser Hamiltonian associated with the Coxeter group in the harmonic confinement.
Dynamical Localization for Discrete Anderson Dirac Operators
NASA Astrophysics Data System (ADS)
Prado, Roberto A.; de Oliveira, César R.; Carvalho, Silas L.
2017-04-01
We establish dynamical localization for random Dirac operators on the d-dimensional lattice, with d\\in { 1, 2, 3} , in the three usual regimes: large disorder, band edge and 1D. These operators are discrete versions of the continuous Dirac operators and consist in the sum of a discrete free Dirac operator with a random potential. The potential is a diagonal matrix formed by different scalar potentials, which are sequences of independent and identically distributed random variables according to an absolutely continuous probability measure with bounded density and of compact support. We prove the exponential decay of fractional moments of the Green function for such models in each of the above regimes, i.e., (j) throughout the spectrum at larger disorder, (jj) for energies near the band edges at arbitrary disorder and (jjj) in dimension one, for all energies in the spectrum and arbitrary disorder. Dynamical localization in theses regimes follows from the fractional moments method. The result in the one-dimensional regime contrast with one that was previously obtained for 1D Dirac model with Bernoulli potential.
Spherical Dirac GJMS operator determinants
NASA Astrophysics Data System (ADS)
Dowker, J. S.
2015-01-01
Motivated by AdS/CFT, the extension is made to spin-half of a scalar calculation of the conformal anomalies and functional determinants of GJMS operators on spheres. The formal aspects are heuristic but sufficient. A Barnes zeta-function representation again proves effective. The determinants are calculated for the two factorizations of the general Γ-function (intertwiner) form of the GJMS operator, and shown to be equal, even including any multiplicative anomaly. A comment is made on the general eigenvalue problem and a few numerical results are presented. An alternative approach is detailed for odd dimensions and it is shown that the scalar determinants are expressed in terms of the spinor ones, and vice versa. An explicit, general form is given.
Locality properties of Neuberger's lattice Dirac operator
NASA Astrophysics Data System (ADS)
Hernández, Pilar; Jansen, Karl; Lüscher, Martin
1999-07-01
The gauge covariant lattice Dirac operator D which has recently been proposed by Neuberger satisfies the Ginsparg-Wilson relation and thus preserves chiral symmetry. The operator also avoids a doubling of fermion species, but its locality properties are not obvious. We now prove that D is local (with exponentially decaying tails) if the gauge field is sufficiently smooth at the scale of the cutoff. Further analytic and numerical studies moreover suggest that the locality of the operator is in fact guaranteed under far more general conditions.
Dirac operator normality and chiral properties
NASA Astrophysics Data System (ADS)
Kerler, W.
Normality and γ5-hermiticity are what gives rise to chiral properties and rules. The Ginsparg-Wilson (GW) relation is only one of the possible spectral constraints. The sum rule for chiral differences of real modes has important consequences. The alternative transformation of Lüscher gives the same Ward identity as the usual chiral one (if zero modes are properly treated). Imposing normality on a general function of the hermitean Wilson-Dirac operator H leads at same time to the GW relation and to the Neuberger operator.
Microscopic Spectrum of the Wilson Dirac Operator
Damgaard, P. H.; Splittorff, K.; Verbaarschot, J. J. M.
2010-10-15
We calculate the leading contribution to the spectral density of the Wilson Dirac operator using chiral perturbation theory where volume and lattice spacing corrections are given by universal scaling functions. We find analytical expressions for the spectral density on the scale of the average level spacing, and introduce a chiral random matrix theory that reproduces these results. Our work opens up a novel approach to the infinite-volume limit of lattice gauge theory at finite lattice spacing and new ways to extract coefficients of Wilson chiral perturbation theory.
Spectrum of the Wilson Dirac operator at finite lattice spacings
Akemann, G.; Damgaard, P. H.; Splittorff, K.; Verbaarschot, J. J. M.
2011-04-15
We consider the effect of discretization errors on the microscopic spectrum of the Wilson Dirac operator using both chiral perturbation theory and chiral random matrix theory. A graded chiral Lagrangian is used to evaluate the microscopic spectral density of the Hermitian Wilson Dirac operator as well as the distribution of the chirality over the real eigenvalues of the Wilson Dirac operator. It is shown that a chiral random matrix theory for the Wilson Dirac operator reproduces the leading zero-momentum terms of Wilson chiral perturbation theory. All results are obtained for a fixed index of the Wilson Dirac operator. The low-energy constants of Wilson chiral perturbation theory are shown to be constrained by the Hermiticity properties of the Wilson Dirac operator.
The squares of the dirac and spin-dirac operators on a riemann-cartan space(time)
NASA Astrophysics Data System (ADS)
Notte-Cuello, E. A.; Rodrigues, W. A.; Souza, Q. A. G.
2007-08-01
In this paper we introduce the Dirac and spin-Dirac operators associated to a connection on Riemann-Cartan space(time) and standard Dirac and spin-Dirac operators associated with a Levi-Civita connection on a Riemannian (Lorentzian) space(time) and calculate the squares of these operators, which play an important role in several topics of modern mathematics, in particular in the study of the geometry of moduli spaces of a class of black holes, the geometry of NS-5 brane solutions of type II supergravity theories and BPS solitons in some string theories. We obtain a generalized Lichnerowicz formula, decompositions of the Dirac and spin-Dirac operators and their squares in terms of the standard Dirac and spin-Dirac operators and using the fact that spinor fields (sections of a spin-Clifford bundle) have representatives in the Clifford bundle we present also a noticeable relation involving the spin-Dirac and the Dirac operators.
Dirac operator on spinors and diffeomorphisms
NASA Astrophysics Data System (ADS)
Dąbrowski, Ludwik; Dossena, Giacomo
2013-01-01
The issue of general covariance of spinors and related objects is reconsidered. Given an oriented manifold M, to each spin structure σ and Riemannian metric g there is associated a space Sσ, g of spinor fields on M and a Hilbert space {H}_{σ, g}= L^2(S_{σ, g}, vol_{g}(M)) of L2-spinors of Sσ, g. The group Diff+(M) of orientation-preserving diffeomorphisms of M acts both on g (by pullback) and on [σ] (by a suitably defined pullback f*σ). Any f ∈ Diff+(M) lifts in exactly two ways to a unitary operator U from {H}_{σ, g} to {H}_{f^*σ ,f^*g}. The canonically defined Dirac operator is shown to be equivariant with respect to the action of U, so in particular its spectrum is invariant under the diffeomorphisms.
Zero-modes of the QED Neuberger Dirac operator
NASA Astrophysics Data System (ADS)
Berg, Bernd A.; Heller, Urs M.; Markum, Harald; Pullirsch, Rainer; Sakuler, Wolfgang
2002-03-01
We consider 4 d compact lattice QED in the quenched approximation. First, we briefly summarize the spectrum of the staggered Dirac operator and its connection with random matrix theory. Afterwards we present results for the low-lying eigenmodes of the Neuberger overlap-Dirac operator. In the strong coupling phase we find exact zero-modes. Subsequently we discuss possibly related topological excitations of the U(1) lattice gauge theory.
Zero-modes of the QED Neuberger Dirac operator
NASA Astrophysics Data System (ADS)
Berg, Bernd A.; Heller, Urs M.; Markum, Harald; Pullirsch, Rainer; Sakuler, Wolfgang
We consider 4d compact lattice QED in the quenched approximation. First, we briefly summarize the spectrum of the staggered Dirac operator and its connection with random matrix theory. Afterwards we present results for the low-lying eigenmodes of the Neuberger overlap-Dirac operator. In the strong coupling phase we find exact zero-modes. Subsequently we discuss possibly related topological excitations of the U(1) lattice gauge theory.
The right inverse of Dirac operator in octonionic space
NASA Astrophysics Data System (ADS)
Wang, Haiyan; Bian, Xiaoli
2017-09-01
The octonion Dirac equation also called wave equation is an important equation which formulates the localization spaces for subluminal and superluminal particles. The purpose of this paper is to look for the right inverse operator of octonion Dirac operator in Hölder space. However, some difficulties will arise in noncommutative and nonassociative setting. We note that the associator is available to overcome the difficulties.
Spectral Gaps of Dirac Operators Describing Graphene Quantum Dots
NASA Astrophysics Data System (ADS)
Benguria, Rafael D.; Fournais, Søren; Stockmeyer, Edgardo; Van Den Bosch, Hanne
2017-06-01
The two-dimensional Dirac operator describes low-energy excitations in graphene. Different choices for the boundary conditions give rise to qualitative differences in the spectrum of the resulting operator. For a family of boundary conditions, we find a lower bound to the spectral gap around zero, proportional to |Ω|-1/2, where {Ω } \\subset R2 is the bounded region where the Dirac operator acts. This family contains the so-called infinite mass and armchair cases used in the physics literature for the description of graphene quantum dots.
Zeta functions of the Dirac operator on quantum graphs
NASA Astrophysics Data System (ADS)
Harrison, J. M.; Weyand, T.; Kirsten, K.
2016-10-01
We construct spectral zeta functions for the Dirac operator on metric graphs. We start with the case of a rose graph, a graph with a single vertex where every edge is a loop. The technique is then developed to cover any finite graph with general energy independent matching conditions at the vertices. The regularized spectral determinant of the Dirac operator is also obtained as the derivative of the zeta function at a special value. In each case the zeta function is formulated using a contour integral method, which extends results obtained for Laplace and Schrödinger operators on graphs.
Eigenvalue estimates for the Dirac-Schrödinger operators
NASA Astrophysics Data System (ADS)
Morel, Bertrand
2001-04-01
We give new estimates for the eigenvalues of the hypersurface Dirac operator in terms of the intrinsic energy-momentum tensor, the mean curvature and the scalar curvature. We also discuss their limiting cases as well as the limiting cases of the estimates obtained by Zhang and Hijazi [Math. Res. Lett. 5 (1998) 199; 6 (1999) 465; Ann. Glob. Anal. Geom., in press]. We compare these limiting cases with those corresponding to the Friedrich and Hijazi inequalities. We conclude by comparing these results to intrinsic estimates for the Dirac-Schrödinger operator D f=D- {1}/{2}f .
A toy model for higher spin Dirac operators
Eelbode, D. Van de Voorde, L.
2010-02-15
This paper deals with the higher spin Dirac operator Q{sub 2,1} acting on functions taking values in an irreducible representation space for so(m) with highest weight (5/2, 3/2, 1/2,..., 1/2). . This operator acts as a toy model for generalizations of the classical Rarita-Schwinger equations in Clifford analysis. Polynomial null solutions for this operator are studied in particular.
The Dunkl-Williams constant, convexity, smoothness and normal structure
NASA Astrophysics Data System (ADS)
Jiménez-Melado, A.; Llorens-Fuster, E.; Mazcuñán-Navarro, E. M.
2008-06-01
In this paper we exhibit some connections between the Dunkl-Williams constant and some other well-known constants and notions. We establish bounds for the Dunkl-Williams constant that explain and quantify a characterization of uniformly nonsquare Banach spaces in terms of the Dunkl-Williams constant given by M. Baronti and P.L. Papini. We also study the relationship between Dunkl-Williams constant, the fixed point property for nonexpansive mappings and normal structure.
Topological phases in the Neuberger-Dirac operator
NASA Astrophysics Data System (ADS)
Chiu, Ting-Wai
1999-12-01
The response of the Neuberger-Dirac fermion operator D=1+V in the topologically nontrivial background gauge field depends on the negative mass parameter m0 in the Wilson-Dirac fermion operator Dw, which enters D through the unitary operator V=Dw(D†wDw)-1/2. We classify the topological phases of D by comparing its index to the topological charge of the smooth background gauge field. An exact discrete symmetry in the topological phase diagram is proved for any gauge configurations. A formula for the index of D in each topological phase is derived by obtaining the total chiral charge of the zero modes in the exact solution of the free fermion propagator.
Eigenvalue spectrum of massless Dirac operators on the lattice
NASA Astrophysics Data System (ADS)
Farchioni, F.; Hip, I.; Lang, C. B.; Wohlgenannt, M.
1999-05-01
We present a detailed study of the interplay between chiral symmetry and spectral properties of the Dirac operator in lattice gauge theories. We consider, in the framework of the Schwinger model, the fixed point action and a fermion action recently proposed by Neuberger. Both actions show the remnant of chiral symmetry on the lattice as formulated in the Ginsparg-Wilson relation. We check this issue for practical implementations, also evaluating the fermion condensate in a finite volume by a subtraction procedure. Moreover, we investigate the distribution of the eigenvalues of a properly defined anti-hermitian lattice Dirac operator, studying the statistical properties at the low lying edge of the spectrum. The comparison with the predictions of chiral Random Matrix Theory enables us to obtain an estimate of the infinite volume fermion condensate.
The Index of Dirac Operators on Incomplete Edge Spaces
NASA Astrophysics Data System (ADS)
Albin, Pierre; Gell-Redman, Jesse
2016-09-01
We derive a formula for the index of a Dirac operator on a compact, even-dimensional incomplete edge space satisfying a ''geometric Witt condition''. We accomplish this by cutting off to a smooth manifold with boundary, applying the Atiyah-Patodi-Singer index theorem, and taking a limit. We deduce corollaries related to the existence of positive scalar curvature metrics on incomplete edge spaces.
Spectral functionals, nonholonomic Dirac operators, and noncommutative Ricci flows
Vacaru, Sergiu I.
2009-07-15
We formulate a noncommutative generalization of the Ricci flow theory in the framework of spectral action approach to noncommutative geometry. Grisha Perelman's functionals are generated as commutative versions of certain spectral functionals defined by nonholonomic Dirac operators and corresponding spectral triples. We derive the formulas for spectral averaged energy and entropy functionals and state the conditions when such values describe (non)holonomic Riemannian configurations.
NASA Astrophysics Data System (ADS)
Kragh, Helge
2005-07-01
Preface; 1. Early years; 2. Discovery of quantum mechanics; 3. Relativity and spinning electrons; 4. Travels and thinking; 5. The dream of philosophers; 6. Quanta and fields; 7. Fifty years of a physicist's life; 8. 'The so-called quantum electrodynamics'; 9. Electrons and ether; 10. Just a disappointment; 11. Adventures in cosmology; 12. The purest soul; 13. Philosophy in physics; 14. The principle of mathematical beauty; Appendices; Bibliography of P. A. M. Dirac; Notes and references; General bibliography; Index of names; Index of subjects.
Lattice QCD simulation with the overlap Dirac operator
NASA Astrophysics Data System (ADS)
Howard, Joseph
A complete understanding of the predictions of Quantum Chromodynamics (QCD) will be an important part of moving particle physics beyond the current Standard Model. At the energy scales relevant to bound QCD systems, such as the pion and the proton, non-perturbative techniques must be used to estimate QCD predictions. The non-perturbative method used to investigate QCD is lattice QCD, or QCD on a discrete spacetime lattice. One aspect of continuum QCD that should be preserved in lattice QCD is chiral symmetry. The inability of maintaining such symmetry in the discretization of the Dirac equation has for years been a shortcoming of lattice QCD. Recently, however, Neuberger has introduced the overlap Dirac operator, which preserves exact chiral symmetry, even at finite lattice spacing. This dissertation describes a simulation of lattice QCD using the Wilson gauge action and the overlap Dirac operator, performed on two separate lattices. The first was an 183 x 64 lattice (where the first number represents the spatial extent and the second the extent in time) with coupling beta = 6.0 (lattice spacing a-1 ≃ 2.0 GeV), and the second a 143 x 48 lattice with coupling beta = 5.85 (lattice spacing a-1 ≃ 1.5 GeV). The finer 183 x 64 lattice size was chosen in order to allow a large enough extent in time for prediction of QCD observables that previous investigations using smaller lattices were unable to predict. The coarser 143 x 48 lattice was chosen to have roughly the same physical volume as the finer lattice, allowing for an investigation into scaling effects. The dissertation begins with a review of the basics of QCD and lattice QCD, including descriptions of the overlap Dirac operator and chiral symmetry on the lattice. Next, the results from the two simulations are presented. The chiral nature of the overlap Dirac operator is confirmed. The light hadron spectrum is presented, along with decay constants and other observables. An investigation is described on the use
The singular and the 2:1 anisotropic Dunkl oscillators in the plane
NASA Astrophysics Data System (ADS)
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
2013-08-01
Two Dunkl oscillator models are considered: one singular and the other with a 2:1 frequency ratio. These models are defined by Hamiltonians which include the reflection operators in the two variables x and y. The singular or caged Dunkl oscillator is second-order superintegrable and admits separation of variables in both Cartesian and polar coordinates. The spectrum of the Hamiltonian is obtained algebraically and the separated wavefunctions are given in the terms of Jacobi, Laguerre and generalized Hermite polynomials. The symmetry generators are constructed from the \\mathfrak {su}(1,1) dynamical operators of the one-dimensional model and generate a cubic symmetry algebra. In terms of the symmetries responsible for the separation of variables, the symmetry algebra of the singular Dunkl oscillator is quadratic and can be identified with a special case of the Askey-Wilson AW(3) algebra with central involutions. The 2:1 anisotropic Dunkl oscillator model is also second-order superintegrable. The energies of the system are obtained algebraically, the symmetry generators are constructed using the dynamical operators and the resulting symmetry algebra is quadratic. The general system appears to admit separation of variables only in Cartesian coordinates. Special cases where separation occurs in both Cartesian and parabolic coordinates are considered. In the latter case the wavefunctions satisfy the biconfluent Heun equation and depend on a transcendental separation constant.
Anomalies of Dirac Type Operators on Euclidean Space
NASA Astrophysics Data System (ADS)
Carey, Alan; Grosse, Harald; Kaad, Jens
2015-04-01
We develop by example a type of index theory for non-Fredholm operators. A general framework using cyclic homology for this notion of index was introduced in a separate article (Carev and Kaad, Topological invariance of the homological index. arXiv:1402.0475 [math.KT], 2014) where it may be seen to generalise earlier ideas of Carey-Pincus and Gesztesy-Simon on this problem. Motivated by an example in two dimensions in Bollé et al. (J Math Phys 28:1512-1525, 1987) we introduce in this paper a class of examples of Dirac type operators on that provide non-trivial examples of our homological approach. Our examples may be seen as extending old ideas about the notion of anomaly introduced by physicists to handle topological terms in quantum action principles, with an important difference, namely, we are dealing with purely geometric data that can be seen to arise from the continuous spectrum of our Dirac type operators.
Dirac operator on the sphere with attached wires
NASA Astrophysics Data System (ADS)
E, N. Grishanov; D, A. Eremin; D, A. Ivanov; I, Yu Popov
2016-04-01
An explicitly solvable model for tunnelling of relativistic spinless particles through a sphere is suggested. The model operator is constructed by an operator extensions theory method from the orthogonal sum of the Dirac operators on a semi-axis and on the sphere. The transmission coefficient is obtained. The dependence of the transmission coefficient on the particle energy has a resonant character. One observes pairs of the Breit-Wigner and the Fano resonances. It correlates with the corresponding results for a non-relativistic particle. Project partially financially supported by the Funds from the Government of the Russian Federation (Grant No. 074-U01), the Funds from the Ministry of Education and Science of the Russian Federation (GOSZADANIE 2014/190) (Grant Nos. 14.Z50.31.0031 and 1.754.2014/K), and the President Foundation of the Russian Federation (Grant No. MK-5001.2015.1).
Symmetry operators for Dirac's equation on two-dimensional spin manifolds
Fatibene, Lorenzo; McLenaghan, Raymond G.; Smith, Shane N.; Rastelli, Giovanni
2009-05-15
It is shown that the second order symmetry operators for the Dirac equation on a general two-dimensional spin manifold may be expressed in terms of Killing vectors and valence 2 Killing tensors. The role of these operators in the theory of separation of variables for the Dirac equation is studied.
Simple Evaluation of the Chiral Jacobian with the Overlap Dirac Operator
NASA Astrophysics Data System (ADS)
Suzuki, H.
1999-07-01
The chiral Jacobian, which is defined with Neuberger's overlap Dirac operator of the lattice fermion, is explicitly evaluated in the continuum limit without expanding it in the gauge coupling constant. Our calculational scheme is simple and straightforward. We determine a coefficient of the chiral anomaly for general values of the mass parameter and the Wilson parameter of the overlap Dirac operator.
Dirac operator zero-modes on a torus
Tenjinbayashi, Yasushi; Igarashi, Hiroshi; Fujiwara, Takanori . E-mail: fujiwara@mx.ibaraki.ac.jp
2007-02-15
We study Dirac operator zero-modes on a torus for gauge background with uniform field strengths. Under the basic translations of the torus coordinates the wave functions are subject to twisted periodic conditions. In suitable torus coordinates the zero-mode wave functions can be related to holomorphic functions of the complex torus coordinates. Half of the twisted boundary conditions for the holomorphic part of the zero-mode wave function can be made periodic or anti-periodic. The remaining half is until coordinate dependent but diagonal. We completely solve the twisted boundary conditions and construct the zero-mode wave functions. The chirality and the degeneracy of the zero-modes are uniquely determined by the gauge background and are consistent with the index theorem.
A Perturbation of the Dunkl Harmonic Oscillator on the Line
NASA Astrophysics Data System (ADS)
Álvarez López, Jesús A.; Calaza, Manuel
2015-07-01
Let J_σ be the Dunkl harmonic oscillator on R (σ>-1/2). For 00, it is proved that, if σ>u-1/2, then the operator U=J_σ+ξ|x|^{-2u}, with appropriate domain, is essentially self-adjoint in L^2({R},|x|^{2σ} dx), the Schwartz space S is a core of overline U^{1/2}, and overline U has a discrete spectrum, which is estimated in terms of the spectrum of overline{J_σ}. A generalization J_{σ,τ} of J_σ is also considered by taking different parameters σ and τ on even and odd functions. Then extensions of the above result are proved for J_{σ,τ}, where the perturbation has an additional term involving, either the factor x^{-1} on odd functions, or the factor x on even functions. Versions of these results on R_+ are derived.
Wilson, fixed point and Neuberger's lattice Dirac operator for the Schwinger model
NASA Astrophysics Data System (ADS)
Farchioni, F.; Hip, I.; Lang, C. B.
1998-12-01
We perform a comparison between different lattice regularizations of the Dirac operator for massless fermions in the framework of the single and two flavor Schwinger model. We consider a) the Wilson-Dirac operator at the critical value of the hopping parameter; b) Neuberger's overlap operator; c) the fixed point operator. We test chiral properties of the spectrum, dispersion relations and rotational invariance of the mesonic bound state propagators.
Decomposition of the polynomial kernel of arbitrary higher spin Dirac operators
Eelbode, D.; Raeymaekers, T.; Van der Jeugt, J.
2015-10-15
In a series of recent papers, we have introduced higher spin Dirac operators, which are generalisations of the classical Dirac operator. Whereas the latter acts on spinor-valued functions, the former acts on functions taking values in arbitrary irreducible half-integer highest weight representations for the spin group. In this paper, we describe how the polynomial kernel spaces of such operators decompose in irreducible representations of the spin group. We will hereby make use of results from representation theory.
Lower bounds for the eigenvalues of the Dirac operator on Spinc manifolds
NASA Astrophysics Data System (ADS)
Nakad, Roger
2010-10-01
In this paper, we extend the Hijazi inequality, involving the energy-momentum tensor, to the eigenvalues of the Dirac operator on Spin manifolds without boundary. The limiting case is then studied and an example is given.
A Possible Generalization of Dirac's Phase Operator and its Relation to Paul's Phase Operator
NASA Astrophysics Data System (ADS)
Zhou, Jun; Fan, Hong-yi
2017-02-01
In this paper we generalize Dirac's phase operator {1}/{√ {N}}a by defining a new phase operator √ {{a+tilde {a}^{dagger }}/{a^{dagger }+tilde {a}}} in doubled Fock space, where tilde {a} is a fictitious mode which annihilates the fictitious vacuum state \\vert tilde {0} rangle . It turns out that √ {a+tilde {a}^{dagger }/{a^{dagger }+tilde {a}}} corresponds to a classical phase in the entangled state representation and is unitary. Remarkably, < tilde {0} \\vert √ {a+tilde {a}^{dagger }/{a^{dagger }+tilde {a}}} \\vert tilde {0} rangle is just the Paul's phase operator whose antinormally ordered form is {ďots } {1}/{√ {N}}aďots . We also employ the method of integration within ordered product of operators to obtain the Fock representation of Paul's phase operator, from which one can see how it deffers from Susskind-Glogower's phase operator.
Normal forms of an abstract Dirac operator and applications to scattering theory
NASA Astrophysics Data System (ADS)
Thaller, Bernd
1988-01-01
The unitary transformations which convert an abstract Dirac operator into an ``even'' (resp. ``odd'') operator are determined. The problem is formulated and solved completely within the general setup of supersymmetric quantum mechanics. This leads to some apparently new applications in relativistic quantum mechanics, where the transformations are known as the Foldy-Wouthuysen (resp. Cini-Touschek) transformations. The scattering theory for abstract Dirac operators is discussed and the utility of the general theory is illustrated by proving existence of relativistic Mo/ller operators for scattering from long-range magnetic fields.
The local counting function of operators of Dirac and Laplace type
NASA Astrophysics Data System (ADS)
Li, Liangpan; Strohmaier, Alexander
2016-06-01
Let P be a non-negative self-adjoint Laplace type operator acting on sections of a hermitian vector bundle over a closed Riemannian manifold. In this paper we review the close relations between various P-related coefficients such as the mollified spectral counting coefficients, the heat trace coefficients, the resolvent trace coefficients, the residues of the spectral zeta function as well as certain Wodzicki residues. We then use the Wodzicki residue to obtain results about the local counting function of operators of Dirac and Laplace type. In particular, we express the second term of the mollified spectral counting function of Dirac type operators in terms of geometric quantities and characterize those Dirac type operators for which this coefficient vanishes.
Perturbative analysis of the Neuberger Dirac operator in the Schrödinger functional
NASA Astrophysics Data System (ADS)
Takeda, Shinji
2008-06-01
We investigate the spectrum of the free Neuberger-Dirac operator D on the Schrödinger functional (SF). We check that the lowest few eigen-values of the Hermitian operator DN†D in unit of L converge to the continuum limit properly. We also perform a one-loop calculation of the SF coupling, and then check the universality and investigate lattice artifacts of the step scaling function. It turns out that the lattice artifacts for the Neuberger-Dirac operator are comparable to those of the clover action.
The Dunkl Oscillator in the Plane II: Representations of the Symmetry Algebra
NASA Astrophysics Data System (ADS)
Genest, Vincent X.; Ismail, Mourad E. H.; Vinet, Luc; Zhedanov, Alexei
2014-08-01
The superintegrability, wavefunctions and overlap coefficients of the Dunkl oscillator model in the plane were considered in the first part. Here finite-dimensional representations of the symmetry algebra of the system, called the Schwinger-Dunkl algebra sd(2), are investigated. The algebra sd(2) has six generators, including two involutions and a central element, and can be seen as a deformation of the Lie algebra . Two of the symmetry generators, J 3 and J 2, are respectively associated to the separation of variables in Cartesian and polar coordinates. Using the parabosonic creation/annihilation operators, two bases for the representations of sd(2), the Cartesian and circular bases, are constructed. In the Cartesian basis, the operator J 3 is diagonal and the operator J 2 acts in a tridiagonal fashion. In the circular basis, the operator J 2 is block upper-triangular with all blocks 2 × 2 and the operator J 3 acts in a tridiagonal fashion. The expansion coefficients between the two bases are given by the Krawtchouk polynomials. In the general case, the eigenvectors of J 2 in the circular basis are generated by the Heun polynomials, and their components are expressed in terms of the para-Krawtchouk polynomials. In the fully isotropic case, the eigenvectors of J 2 are generated by little -1 Jacobi or ordinary Jacobi polynomials. The basis in which the operator J 2 is diagonal is considered. In this basis, the defining relations of the Schwinger-Dunkl algebra imply that J 3 acts in a block tridiagonal fashion with all blocks 2 × 2. The matrix elements of J 3 in this basis are given explicitly.
NASA Astrophysics Data System (ADS)
Katsnelson, M. I.; Nazaikinskii, V. E.
2012-09-01
In topological terms, we compute the spectral flow of an arbitrary family of self-adjoint Dirac-type operators with classical (local) boundary conditions on a compact Riemannian manifold with boundary under the assumption that the initial and terminal operators of the family are conjugate by an automorphism of the bundle in which the operators act. We use this result to study conditions for the existence of a nonzero spectral flow of a family of self-adjoint Dirac-type operators with local boundary conditions in a two-dimensional domain with a nontrivial topology and discuss possible physical realizations of a nonzero spectral flow.
On Painleve VI transcendents related to the Dirac operator on the hyperbolic disk
Lisovyy, O.
2008-09-15
Dirac Hamiltonian on the Poincare disk in the presence of an Aharonov-Bohm flux and a uniform magnetic field admits a one-parameter family of self-adjoint extensions. We determine the spectrum and calculate the resolvent for each element of this family. Explicit expressions for Green's functions are then used to find Fredholm determinant representations for the tau function of the Dirac operator with two branch points on the Poincare disk. Isomonodromic deformation theory for the Dirac equation relates this tau function to a one-parameter class of solutions of the Painleve VI equation with {gamma}=0. We analyze long-distance behavior of the tau function, as well as the asymptotics of the corresponding Painleve VI transcendents as s{yields}1. Considering the limit of flat space, we also obtain a class of solutions of the Painleve V equation with {beta}=0.
Spectral asymmetry of the massless Dirac operator on a 3-torus
Downes, Robert J. Vassiliev, Dmitri; Levitin, Michael
2013-11-15
Consider the massless Dirac operator on a 3-torus equipped with Euclidean metric and standard spin structure. It is known that the eigenvalues can be calculated explicitly: the spectrum is symmetric about zero and zero itself is a double eigenvalue. The aim of the paper is to develop a perturbation theory for the eigenvalue with smallest modulus with respect to perturbations of the metric. Here the application of perturbation techniques is hindered by the fact that eigenvalues of the massless Dirac operator have even multiplicity, which is a consequence of this operator commuting with the antilinear operator of charge conjugation (a peculiar feature of dimension 3). We derive an asymptotic formula for the eigenvalue with smallest modulus for arbitrary perturbations of the metric and present two particular families of Riemannian metrics for which the eigenvalue with smallest modulus can be evaluated explicitly. We also establish a relation between our asymptotic formula and the eta invariant.
A comparative study of numerical methods for the overlap Dirac operator-a status report
NASA Astrophysics Data System (ADS)
van den Eshof, J.; Frommer, A.; Lippert, Th.; Schilling, K.; van der Vorst, H.
Improvements of various methods to compute the sign function of the hermitian Wilson-Dirac matrix within the overlap operator are presented. An optimal partial fraction expansion (PFE) based on a theorem of Zolotarev is given. Benchmarks show that this PFE together with removal of converged systems within a multi-shift CG appears to approximate the sign function times a vector most efficiently. A posteriori error bounds are given.
Spectrum of the QCD Dirac operator and chiral random matrix theory
Verbaarschot, J. )
1994-04-18
We argue that the spectrum of the QCD Dirac operator near zero virtuality can be described by random matrix theory. As in the case of the classical random matrix ensembles of Dyson we have three different cases: the chiral orthogonal ensemble, the chiral unitary ensemble, and the chiral symplectic ensemble. They correspond to gauge groups SU(2) in the fundamental representation, SU([ital N][sub [ital c
On Generalised Dolbeault Sequence for Four Dirac Operators in Dimension 6
NASA Astrophysics Data System (ADS)
Krump, Lukáš
2010-09-01
The Hartog's type phenomena in several complex variables are best understood in term of the Dolbeault sequence. A lot of attention was paid in the last decades to its analogue in the function theory of several Clifford variables. The first operator in this resolution is the Dirac operator in several variables. The complete description is known in the stable case in dimension 4. In the nonstable case, other tools like the Penrose transform must be used, which gives an algebraic description of the resolution. The next step is an explicite analytic construction of the operators in the resolution, which is to some extent shown here.
Overlap Dirac operator at nonzero chemical potential and random matrix theory.
Bloch, Jacques; Wettig, Tilo
2006-07-07
We show how to introduce a quark chemical potential in the overlap Dirac operator. The resulting operator satisfies a Ginsparg-Wilson relation and has exact zero modes. It is no longer gamma5 Hermitian, but its nonreal eigenvalues still occur in pairs. We compute the spectral density of the operator on the lattice and show that, for small eigenvalues, the data agree with analytical predictions of non-Hermitian chiral random matrix theory for both trivial and nontrivial topology. We also explain an observed change in the number of zero modes as a function of chemical potential.
Overlap Dirac Operator at Nonzero Chemical Potential and Random Matrix Theory
Bloch, Jacques; Wettig, Tilo
2006-07-07
We show how to introduce a quark chemical potential in the overlap Dirac operator. The resulting operator satisfies a Ginsparg-Wilson relation and has exact zero modes. It is no longer {gamma}{sub 5} Hermitian, but its nonreal eigenvalues still occur in pairs. We compute the spectral density of the operator on the lattice and show that, for small eigenvalues, the data agree with analytical predictions of non-Hermitian chiral random matrix theory for both trivial and nontrivial topology. We also explain an observed change in the number of zero modes as a function of chemical potential.
On Some Algebraic and Combinatorial Properties of Dunkl Elements
NASA Astrophysics Data System (ADS)
Kirillov, Anatol N.
2013-06-01
We introduce and study a certain class of nonhomogeneous quadratic algebras together with the special set of mutually commuting elements inside of each, the so-called Dunkl elements. We describe relations among the Dunkl elements. This result is a further generalization of similar results obtained in [S. Fomin and A. N. Kirillov, Quadratic algebras, Dunkl elements and Schubert calculus, in Advances in Geometry (eds. J.-S. Brylinski, V. Nistor, B. Tsygan and P. Xu), Progress in Math. Vol. 172 (Birkhäuser Boston, Boston, 1995), pp. 147-182, A. Postnikov, On a quantum version of Pieri's formula, in Advances in Geometry (eds. J.-S. Brylinski, R. Brylinski, V. Nistor, B. Tsygan and P. Xu), Progress in Math. Vol. 172 (Birkhäuser Boston, 1995), pp. 371-383 and A. N. Kirillov and T. Maenor, A Note on Quantum K-Theory of Flag Varieties, preprint]. As an application we describe explicitly the set of relations among the Gaudin elements in the group ring of the symmetric group, cf. [E. Mukhin, V. Tarasov and A. Varchenko, Bethe Subalgebras of the Group Algebra of the Symmetric Group, preprint arXiv:1004.4248]. Also we describe a few combinatorial properties of some special elements in the associative quasi-classical Yang-Baxter algebra in a connection with the values of the β-Grothendieck polynomials for some special permutations, and on the other hand, with the Ehrhart polynomial of the Chan-Robbins polytope.
On Some Algebraic and Combinatorial Properties of Dunkl Elements
NASA Astrophysics Data System (ADS)
Kirillov, Anatol N.
2012-11-01
We introduce and study a certain class of nonhomogeneous quadratic algebras together with the special set of mutually commuting elements inside of each, the so-called Dunkl elements. We describe relations among the Dunkl elements. This result is a further generalization of similar results obtained in [S. Fomin and A. N. Kirillov, Quadratic algebras, Dunkl elements and Schubert calculus, in Advances in Geometry (eds. J.-S. Brylinski, V. Nistor, B. Tsygan and P. Xu), Progress in Math. Vol. 172 (Birkhäuser Boston, Boston, 1995), pp. 147-182, A. Postnikov, On a quantum version of Pieri's formula, in Advances in Geometry (eds. J.-S. Brylinski, R. Brylinski, V. Nistor, B. Tsygan and P. Xu), Progress in Math. Vol. 172 (Birkhäuser Boston, 1995), pp. 371-383 and A. N. Kirillov and T. Maenor, A Note on Quantum K-Theory of Flag Varieties, preprint]. As an application we describe explicitly the set of relations among the Gaudin elements in the group ring of the symmetric group, cf. [E. Mukhin, V. Tarasov and A. Varchenko, Bethe Subalgebras of the Group Algebra of the Symmetric Group, preprint arXiv:1004.4248]. Also we describe a few combinatorial properties of some special elements in the associative quasi-classical Yang-Baxter algebra in a connection with the values of the β-Grothendieck polynomials for some special permutations, and on the other hand, with the Ehrhart polynomial of the Chan-Robbins polytope.
Edwards, R.G.; Heller, U.M.; Narayanan, R.
1999-10-01
The low-lying spectrum of the Dirac operator is predicted to be universal, within three classes, depending on symmetry properties specified according to random matrix theory. The three universal classes are the orthogonal, unitary and symplectic ensembles. Lattice gauge theory with staggered fermions has verified two of the cases so far, unitary and symplectic, with staggered fermions in the fundamental representation of SU(3) and SU(2). We verify the missing case here, namely orthogonal, with staggered fermions in the adjoint representation of SU(N{sub c}), N{sub c}=2,3. {copyright} {ital 1999} {ital The American Physical Society}
Zeta functions of Dirac and Laplace-type operators over finite cylinders
NASA Astrophysics Data System (ADS)
Kirsten, Klaus; Loya, Paul; Park, Jinsung
2006-08-01
In this paper, a complete description of the zeta functions and corresponding zeta determinants for Dirac and Laplace-type operators over finite cylinders using the contour integration method, for example described in [K. Kirsten, Spectral Functions in Mathematics and Physics, Chapman & Hall/CRC Press, Boca Raton, 2001] is given. Different boundary conditions, local and non-local ones, are considered. The method is shown to be very powerful in that it is easily adapted to each situation and in that answers are very elegantly obtained.
The Spectral Flow for Dirac Operators on Compact Planar Domains with Local Boundary Conditions
NASA Astrophysics Data System (ADS)
Prokhorova, Marina
2013-09-01
Let Dt, {0≤slantt≤slant1} be a 1-parameter family of Dirac type operators on a two-dimensional disk with m - 1 holes. Suppose that all operators Dt have the same symbol, and that D1 is conjugate to D0 by a scalar gauge transformation. Suppose that all operators Dt are considered with the same elliptic local boundary condition. Our main result is a computation of the spectral flow for such a family of operators. The answer is obtained up to multiplication by an integer constant depending only on the number of holes in the disk. This constant is calculated explicitly for the case of the annulus (m = 2).
Lorentz-violating modification of Dirac theory based on spin-nondegenerate operators
NASA Astrophysics Data System (ADS)
Reis, J. A. A. S.; Schreck, M.
2017-04-01
The Standard Model extension (SME) parametrizes all possible Lorentz-violating contributions to the Standard Model and general relativity. It can be considered as an effective framework to describe possible quantum-gravity effects for energies much below the Planck energy. In the current paper, the spin-nondegenerate operators of the SME fermion sector are the focus. The propagators, energies, and solutions to the modified Dirac equation are obtained for several families of coefficients including nonminimal ones. The particle energies and spinors are computed at first order in Lorentz violation and, with the optical theorem, they are shown to be consistent with the propagators. The optical theorem is then also used to derive the matrices formed from a spinor and its Dirac conjugate at all orders in Lorentz violation. The results are the first explicit ones derived for the spin-nondegenerate operators. They will prove helpful for future phenomenological calculations in the SME that rely on the footing of quantum field theory.
Spectral properties of the Wilson-Dirac operator and random matrix theory
NASA Astrophysics Data System (ADS)
Kieburg, Mario; Verbaarschot, Jacobus J. M.; Zafeiropoulos, Savvas
2013-11-01
Random matrix theory has been successfully applied to lattice quantum chromodynamics. In particular, a great deal of progress has been made on the understanding, numerically as well as analytically, of the spectral properties of the Wilson-Dirac operator. In this paper, we study the infrared spectrum of the Wilson-Dirac operator via random matrix theory including the three leading order a2 correction terms that appear in the corresponding chiral Lagrangian. A derivation of the joint probability density of the eigenvalues is presented. This result is used to calculate the density of the complex eigenvalues, the density of the real eigenvalues, and the distribution of the chiralities over the real eigenvalues. A detailed discussion of these quantities shows how each low-energy constant affects the spectrum. Especially we consider the limit of small and large (which is almost the mean field limit) lattice spacing. Comparisons with Monte Carlo simulations of the random matrix theory show a perfect agreement with the analytical predictions. Furthermore we present some quantities which can be easily used for comparison of lattice data and the analytical results.
The Generalised Dolbeault Complex for Four Dirac Operators in the Stable Rank
NASA Astrophysics Data System (ADS)
Krump, Lukáš
2008-09-01
The Hartog's type phenomena in several complex variables are best understood in term of the Dolbeault sequence. A lot of attention was paid in the last decades to its analogue in the function theory of several Clifford variables. The first operator in this resolution is the Dirac operator in several variables. The complete description is known in dimension 4. Much less is known in higher dimensions. The case of three variables was described completely by F. Colombo, I. Sabadini, F. Sommen, D. C. Struppa. The full description of the complex for all dimensions is not known at present. Even the case of the stable range (i.e., when the number of variables is less or equal to the half of dimension) is still not fully understood. In the paper, we construct the resolution for the case of four variables in the stable range. The main tool used in the construction is the Penrose transform.
Ginsparg-Wilson Dirac operator in monopole backgrounds on the fuzzy 2-sphere
Aoki, Hajime; Maeda, Toshiharu; Iso, Satoshi
2007-04-15
In previous papers, we studied 't Hooft-Polyakov (TP) monopole configurations in U(2) gauge theory on the fuzzy 2-sphere, and showed that they have nonzero topological charges in the formalism based on the Ginsparg-Wilson (GW) relation. In this paper, we will show an index theorem in the TP monopole background, which is defined in the projected space, and provides meaning of the projection operator. We also extend the index theorem to general configurations which do not satisfy the equation of motion, and show that configuration space can be classified into topological sectors. We further calculate the spectrum of the GW Dirac operator in TP monopole backgrounds, and consider the index theorem in these cases.
FFT-split-operator code for solving the Dirac equation in 2+1 dimensions
NASA Astrophysics Data System (ADS)
Mocken, Guido R.; Keitel, Christoph H.
2008-06-01
The main part of the code presented in this work represents an implementation of the split-operator method [J.A. Fleck, J.R. Morris, M.D. Feit, Appl. Phys. 10 (1976) 129-160; R. Heather, Comput. Phys. Comm. 63 (1991) 446] for calculating the time-evolution of Dirac wave functions. It allows to study the dynamics of electronic Dirac wave packets under the influence of any number of laser pulses and its interaction with any number of charged ion potentials. The initial wave function can be either a free Gaussian wave packet or an arbitrary discretized spinor function that is loaded from a file provided by the user. The latter option includes Dirac bound state wave functions. The code itself contains the necessary tools for constructing such wave functions for a single-electron ion. With the help of self-adaptive numerical grids, we are able to study the electron dynamics for various problems in 2+1 dimensions at high spatial and temporal resolutions that are otherwise unachievable. Along with the position and momentum space probability density distributions, various physical observables, such as the expectation values of position and momentum, can be recorded in a time-dependent way. The electromagnetic spectrum that is emitted by the evolving particle can also be calculated with this code. Finally, for planning and comparison purposes, both the time-evolution and the emission spectrum can also be treated in an entirely classical relativistic way. Besides the implementation of the above-mentioned algorithms, the program also contains a large C++ class library to model the geometric algebra representation of spinors that we use for representing the Dirac wave function. This is why the code is called "Dirac++". Program summaryProgram title: Dirac++ or (abbreviated) d++ Catalogue identifier: AEAS_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAS_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing
Spectrum of the Dirac operator and multigrid algorithm with dynamical staggered fermions
Kalkreuter, T. Fachbereich Physik , Humboldt-Universitaet, Invalidenstrasse 110, D-10099 Berlin )
1995-02-01
Complete spectra of the staggered Dirac operator [ital ];sD are determined in quenched four-dimensional SU(2) gauge fields, and also in the presence of dynamical fermions. Periodic as well as antiperiodic boundary conditions are used. An attempt is made to relate the performance of multigrid (MG) and conjugate gradient (CG) algorithms for propagators with the distribution of the eigenvalues of [ital ];sD. The convergence of the CG algorithm is determined only by the condition number [kappa] and by the lattice size. Since [kappa]'s do not vary significantly when quarks become dynamic, CG convergence in unquenched fields can be predicted from quenched simulations. On the other hand, MG convergence is not affected by [kappa] but depends on the spectrum in a more subtle way.
Dirac operators, shell interactions, and discontinuous gauge functions across the boundary
NASA Astrophysics Data System (ADS)
Mas, Albert
2017-02-01
Given a bounded smooth domain Ω ⊂ ℝ3, we explore the relation between couplings of the free Dirac operator -iα ṡ ∇ + mβ with pure electrostatic shell potentials λδ∂Ω (λ ∈ ℝ) and some perturbations of those potentials given by the normal vector field N on the shell ∂Ω, namely, {λe + λn(α ṡ N)}δ∂Ω (λe, λn ∈ ℝ). Under the appropriate change of parameters, the couplings with perturbed and unperturbed electrostatic shell potentials yield unitarily equivalent self-adjoint operators. The proof relies on the construction of an explicit family of unitary operators that is well adapted to the study of shell interactions and fits within the framework of gauge theory. A generalization of such unitary operators also allows us to deal with the self-adjointness of couplings of -iα ṡ ∇ + mβ with some shell potentials of magnetic type, namely, λ(α ṡ N) δ∂Ω with λ ∈ C 1 ( ∂ Ω ) .
Superspace unitary operator in QED with Dirac and complex scalar fields: Superfield approach
NASA Astrophysics Data System (ADS)
Shukla, D.; Bhanja, T.; Malik, R. P.
2015-10-01
We exploit the strength of the superspace (SUSP) unitary operator to obtain the results of the application of the horizontality condition (HC) within the framework of the augmented version of the superfield formalism that is applied to the interacting systems of Abelian 1-form gauge theories where the U(1) Abelian 1-form gauge field couples to the Dirac and complex scalar fields in the physical four (3 + 1)-dimensions of spacetime. These interacting theories are generalized onto a (4, 2)-dimensional supermanifold that is parametrized by the four (3 + 1) -dimensional (4D) spacetime variables and a pair of Grassmannian variables. To derive the (anti-)BRST symmetries for the matter fields, we impose the gauge-invariant restrictions (GIRs) on the superfields defined on the (4, 2)-dimensional supermanifold. We discuss various outcomes that emerge out from our knowledge of the SUSP unitary operator and its Hermitian conjugate. The latter operator is derived without imposing any operation of Hermitian conjugation on the parameters and fields of our theory from outside. This is an interesting observation in our present investigation.
NASA Astrophysics Data System (ADS)
Pais, Abraham; Jacob, Maurice; Olive, David I.; Atiyah, Michael F.
1998-02-01
Preface Peter Goddard; Dirac memorial address Stephen Hawking; 1. Paul Dirac: aspects of his life and work Abraham Pais; 2. Antimatter Maurice Jacob; 3. The monopole David Olive; 4. The Dirac equation and geometry Michael F. Atiyah.
NASA Astrophysics Data System (ADS)
Pais, Abraham; Jacob, Maurice; Olive, David I.; Atiyah, Michael F.
2005-09-01
Preface Peter Goddard; Dirac memorial address Stephen Hawking; 1. Paul Dirac: aspects of his life and work Abraham Pais; 2. Antimatter Maurice Jacob; 3. The monopole David Olive; 4. The Dirac equation and geometry Michael F. Atiyah.
Exactness of the generalized Dolbeault complex for k Dirac operators in the stable rank
NASA Astrophysics Data System (ADS)
Krump, Lukáš; Salač, Tomáš
2012-09-01
The Hartog's type phenomena in several complex variables are best understood in terms of the Dolbeault sequence. A lot of attention was paid in the last decades to its analogue in the function theory of several Clifford variables, i.e. the Dirac operator in several variables. A so-called BGG resolution of this operator is then an analogue to the Dolbeault sequence. The complete description is known in dimension 4. Much less is known in higher dimensions. The case of three variables was described completely by F. Colombo, I. Sabadini, F. Sommen, D. C. Struppa. The full description of the complex for all dimensions is not known at present. In the case of the stable rank (i.e., when the number of variables is less or equal to the half of the even dimension), certain progress has been done. In the paper, we construct the resolution for the case of k variables in the stable range, we show the case of k = 4 in details, and we show the exactness of this sequence. The tools used in the construction are the Penrose transform, Čech cohomology and Leray theorem.
Spectral properties of a Dirac operator in the chiral quark soliton model
Arai, Asao; Hayashi, Kunimitsu; Sasaki, Itaru
2005-05-01
We consider a Dirac operator H acting in the Hilbert space L{sup 2}(R{sup 3};C{sup 4})xC{sup 2}, which describes a Hamiltonian of the chiral quark soliton model in nuclear physics. The mass term of H is a matrix-valued function formed out of a function F:R{sup 3}{yields}R, called a profile function, and a vector field n on R{sup 3}, which fixes pointwise a direction in the isospin space of the pion. We first show that, under suitable conditions, H may be regarded as a generator of a supersymmetry. In this case, the spectra of H are symmetric with respect to the origin of R. We then identify the essential spectrum of H under some condition for F. For a class of profile functions F, we derive an upper bound for the number of discrete eigenvalues of H. Under suitable conditions, we show the existence of a positive energy ground state or a negative energy ground state for a family of scaled deformations of H. A symmetry reduction of H is also discussed. Finally a unitary transformation of H is given, which may have a physical interpretation.
Dirac operators on the fuzzy AdS2 with the spins 1/2 and 1
NASA Astrophysics Data System (ADS)
Fakhri, H.; Lotfizadeh, M.
2011-10-01
It is shown here how the pseudo chirality and Dirac operators with the spins 1/2 and 1 on the commutative and fuzzy AdS2 should be constructed. The finite-dimensional and nonunitary representations of SU(1, 1) carrying the spin degrees of freedom 1/2 and 1 are used for the Dirac fields on commutative and fuzzy AdS2. In the fuzzy case, an explicit description of pseudo generalization of the Ginsparg-Wilson algebra is used to construct projective modules. The projector couplings left angular momentum and spin on the fuzzy AdS2 are used to produce minimum total angular momenta. They are realized by the first two and three representations of the total angular momentum for the spins 1/2 and 1, respectively. The pseudo projectors, the pseudo chirality, and Dirac operators with the spins 1/2 and 1 on the fuzzy AdS2 tend to their corresponding operators in the commutative limit.
Supersymmetric analysis of the Dirac-Weyl operator within PT symmetry
Yeşiltaş, Özlem
2014-08-15
Two-dimensional effective Hamiltonian for a massless Dirac electron interacting with a hyperbolic magnetic field is discussed within PT symmetry. Factorization method and polynomial procedures are used to solve Dirac equation for the constant Fermi velocity and the effective potential which is complex Scarf II potential. The more general effective Scarf II potential models are also obtained within pseudo-supersymmetry. Finally, an extension of Panella and Roy's work [Phys. Lett. A 376, 2580–2583 (2012)] to the both PT symmetric and real Scarf II partner potentials is given using the position dependent Fermi velocity.
Trace formulas and Borg-type theorems for matrix-valued Jacobi and Dirac finite difference operators
NASA Astrophysics Data System (ADS)
Clark, Steve; Gesztesy, Fritz; Renger, Walter
Borg-type uniqueness theorems for matrix-valued Jacobi operators H and supersymmetric Dirac difference operators D are proved. More precisely, assuming reflectionless matrix coefficients A,B in the self-adjoint Jacobi operator H=AS++A-S-+B (with S± the right/left shift operators on the lattice Z) and the spectrum of H to be a compact interval [E-,E+], E-
A Limit Relation for Dunkl-Bessel Functions of Type A and B
NASA Astrophysics Data System (ADS)
Rösler, Margit; Voit, Michael
2008-12-01
We prove a limit relation for the Dunkl-Bessel function of type BN with multiplicity parameters k1 on the roots ±ei and k2 on ±ei±ej where k1 tends to infinity and the arguments are suitably scaled. It gives a good approximation in terms of the Dunkl-type Bessel function of type AN-1 with multiplicity k2. For certain values of k2 an improved estimate is obtained from a corresponding limit relation for Bessel functions on matrix cones.
SU(1,1) solution for the Dunkl oscillator in two dimensions and its coherent states
NASA Astrophysics Data System (ADS)
Salazar-Ramırez, M.; Ojeda-Guillén, D.; Mota, R. D.; Granados, V. D.
2017-01-01
We study the Dunkl oscillator in two dimensions by the su(1,1) algebraic method. We apply the Schrödinger factorization to the radial Hamiltonian of the Dunkl oscillator to find the su(1,1) Lie algebra generators. The energy spectrum is found by using the theory of unitary irreducible representations. By solving analytically the Schrödinger equation, we construct the Sturmian basis for the unitary irreducible representations of the su(1,1) Lie algebra. We construct the SU(1,1) Perelomov radial coherent states for this problem and compute their time evolution.
Spectral and localization properties for the one-dimensional Bernoulli discrete Dirac operator
NASA Astrophysics Data System (ADS)
de Oliveira, César R.; Prado, Roberto A.
2005-07-01
An one-dimensional (1D) Dirac tight-binding model is considered and it is shown that its nonrelativistic limit is the 1D discrete Schrödinger model. For random Bernoulli potentials taking two values (without correlations), for typical realizations and for all values of the mass, it is shown that its spectrum is pure point, whereas the zero mass case presents dynamical delocalization for specific values of the energy. The massive case presents dynamical localization (excluding some particular values of the energy). Finally, for general potentials the dynamical moments for distinct masses are compared, especially the massless and massive Bernoulli cases.
NASA Astrophysics Data System (ADS)
Fujiwara, T.
2002-01-01
We investigate numerically the spectrum of the hermitian Wilson-Dirac operator in abelian gauge theories on finite lattices. The spectral flows for a continuous family of abelian gauge fields connecting different topological sectors are shown to have a characteristic structure leading to the lattice index theorem. We find that the index of Neuberger's Dirac operator coincides with the topological charge for a wide class of gauge field configurations. In two dimensions the eigenvalue spectra for some special but nontrivial configurations can be described by a set of characteristic polynomials and the index can be found exactly.
Three dimensional Dirac semimetals
NASA Astrophysics Data System (ADS)
Zaheer, Saad
We extend the physics of graphene to three dimensional systems by showing that Dirac points can exist on the Fermi surface of realistic materials in three dimensions. Many of the exotic electronic properties of graphene can be ascribed to the pseudorelativistic behavior of its charge carriers due to two dimensional Dirac points on the Fermi surface. We show that certain nonsymmorphic spacegroups exhibit Dirac points among the irreducible representations of the appropriate little group at high symmetry points on the surface of the Brillouin zone. We provide a list of all Brillouin zone momenta in the 230 spacegroups that can host Dirac points. We describe microscopic considerations necessary to design materials in one of the candidate spacegroups such that the Dirac point appears at the Fermi energy without any additional non-Dirac-like Fermi pockets. We use density functional theory based methods to propose six new Dirac semimetals: BiO 2 and SbO2 in the beta-cristobalite lattice (spacegroup 227), and BiCaSiO4, BiMgSiO4, BiAlInO 4, and BiZnSiO4 in the distorted spinels lattice (spacegroup 74). Additionally we derive effective Dirac Hamiltonians given group representative operators as well as tight binding models incorporating spin-orbit coupling. Finally we study the Fermi surface of zincblende (spacegroup 216) HgTe which is effectively point-like at Gamma in the Brillouin zone and exhibits accidental degeneracies along a threefold rotation axis. Whereas compressive strain gaps the band structure into a topological insulator, tensile strain shifts the accidental degeneracies away from Gamma and enlarges the Fermi surface. States on the Fermi surface exhibit nontrivial spin texture marked by winding of spins around the threefold rotation axis and by spin vortices indicating a change in the winding number. This is confirmed by microscopic calculations performed in tensile strained HgTe and Hg0.5Zn 0.5 Te as well as k.p theory. We conclude with a summary of recent
NASA Astrophysics Data System (ADS)
Brown, Laurie M.
Paul Dirac was a brilliant and original thinker. He used his physical intuition and his ideal of mathematical beauty to construct bridges between major areas of physics. This article discusses several such important works, including the bridge between quantum mechanics and relativity that led to his prediction of the existence of antimatter.
NASA Astrophysics Data System (ADS)
Puhr, Matthias; Buividovich, Pavel
2016-11-01
We present a method for the numerical calculation of derivatives of functions of general complex matrices. The method can be used in combination with any algorithm that evaluates or approximates the desired matrix function, in particular with implicit Krylov-Ritz-type approximations. An important use case for the method is the evaluation of the overlap Dirac operator in lattice Quantum Chromodynamics (QCD) at finite chemical potential, which requires the application of the sign function of a non-Hermitian matrix to some source vector. While the sign function of non-Hermitian matrices in practice cannot be efficiently approximated with source-independent polynomials or rational functions, sufficiently good approximating polynomials can still be constructed for each particular source vector. Our method allows for an efficient calculation of the derivatives of such implicit approximations with respect to the gauge field or other external parameters, which is necessary for the calculation of conserved lattice currents or the fermionic force in Hybrid Monte-Carlo or Langevin simulations. We also give an explicit deflation prescription for the case when one knows several eigenvalues and eigenvectors of the matrix being the argument of the differentiated function. We test the method for the two-sided Lanczos approximation of the finite-density overlap Dirac operator on realistic SU(3) gauge field configurations on lattices with sizes as large as 14 ×143 and 6 ×183.
NASA Astrophysics Data System (ADS)
Kursunoglu, Behram N.; Wigner, Eugene Paul
1990-04-01
Portrait R. Feyman; List of contributors; A memorial to P. A. M. Dirac B. N. Kursunoglu; Preface B. N. Kursunoglu and E. P. Wigner; Chronology; Part I. Human Side: 1. Thinking of my darling Paul M. Dirac; 2. Dirac in coral gables S. A. Kursunoglu; 3. Recollections of Paul Dirac at Florida State University J. E. Lannutti; 4. My association with Professor Dirac Harish-Chandra; 5. What Paul Dirac meant in my life N. Kemmer; 6. Dirac's way R. Peierls; 7. An experimenter's view of P. A. M. Dirac A. D. Krisch; 8. Dirac at the University of Miami H. K. Stanford; 9. Remembering Paul Dirac E. P. Wigner; Part II. More Scientific Ideas: 10. Another side to Paul Dirac R. H. Dalitz; 11. Playing with equations, the Dirac way A. Pais; 12. Paul Dirac and Werner Heisenberg - a partnership in science L. M. Brown and H. Rechenberg; 13. Dirac's magnetic monopole and the fine structure constant W. J. Marciano and M. Goldhaber; 14. Magnetic monopoles and the halos of galaxies F. Hoyle; 15. The inadequacies of quantum field theory P. A. M. Dirac; 16. Dirac and the foundation of quantum mechanics P. T. Matthews; Part III. Influenced and Inspired by Association: 17. At the feet of Dirac J. C. Polkinghorne; 18. Reminiscences of Paul Dirac N. Mott; 19. From relativistic quantum theory to the human brain H. J. Lipkin; 20. Dirac in 1962, weak and gravitational radiation interactions J. Weber; 21. Schrödinger's cat W. E. Lamb, Jr.; 22. Dirac and finite field theories A. Salam; 23. Dirac's influence on unified field theory B. N. Kursunoglu; Index.
Dunkl–Darboux differential-difference operators
NASA Astrophysics Data System (ADS)
Khekalo, S. P.
2017-02-01
Using a natural generalization, we construct and study analogues of Dunkl differential-difference operators on the line. These analogues turn out to be closely connected with the so-called Burchnall– Chaundy–Adler–Moser polynomials and, therefore, with Darboux transforms. We find the eigenfunctions of these operators.
CREUTZ, M.
2006-01-26
It is popular to discuss low energy physics in lattice gauge theory ill terms of the small eigenvalues of the lattice Dirac operator. I play with some ensuing pitfalls in the interpretation of these eigenvalue spectra. In short, thinking about the eigenvalues of the Dirac operator in the presence of gauge fields can give some insight, for example the elegant Banks-Casher picture for chiral symmetry breaking. Nevertheless, care is necessary because the problem is highly non-linear. This manifests itself in the non-intuitive example of how adding flavors enhances rather than suppresses low eigenvalues. Issues involving zero mode suppression represent one facet of a set of connected unresolved issues. Are there non-perturbative ambiguities in quantities such as the topological susceptibility? How essential are rough gauge fields, i.e. gauge fields on which the winding number is ambiguous? How do these issues interplay with the quark masses? I hope the puzzles presented here will stimulate more thought along these lines.
Photoconductivity in Dirac materials
Shao, J. M.; Yang, G. W.
2015-11-15
Two-dimensional (2D) Dirac materials including graphene and the surface of a three-dimensional (3D) topological insulator, and 3D Dirac materials including 3D Dirac semimetal and Weyl semimetal have attracted great attention due to their linear Dirac nodes and exotic properties. Here, we use the Fermi’s golden rule and Boltzmann equation within the relaxation time approximation to study and compare the photoconductivity of Dirac materials under different far- or mid-infrared irradiation. Theoretical results show that the photoconductivity exhibits the anisotropic property under the polarized irradiation, but the anisotropic strength is different between 2D and 3D Dirac materials. The photoconductivity depends strongly on the relaxation time for different scattering mechanism, just like the dark conductivity.
Hopf, T.; Vassilevski, K. V. Escobedo-Cousin, E.; King, P. J.; Wright, N. G.; O'Neill, A. G.; Horsfall, A. B.; Goss, J. P.; Wells, G. H.; Hunt, M. R. C.
2014-10-21
Top-gated graphene field-effect transistors (GFETs) have been fabricated using bilayer epitaxial graphene grown on the Si-face of 4H-SiC substrates by thermal decomposition of silicon carbide in high vacuum. Graphene films were characterized by Raman spectroscopy, Atomic Force Microscopy, Scanning Tunnelling Microscopy, and Hall measurements to estimate graphene thickness, morphology, and charge transport properties. A 27 nm thick Al₂O₃ gate dielectric was grown by atomic layer deposition with an e-beam evaporated Al seed layer. Electrical characterization of the GFETs has been performed at operating temperatures up to 100 °C limited by deterioration of the gate dielectric performance at higher temperatures. Devices displayed stable operation with the gate oxide dielectric strength exceeding 4.5 MV/cm at 100 °C. Significant shifting of the charge neutrality point and an increase of the peak transconductance were observed in the GFETs as the operating temperature was elevated from room temperature to 100 °C.
NASA Astrophysics Data System (ADS)
Hopf, T.; Vassilevski, K. V.; Escobedo-Cousin, E.; King, P. J.; Wright, N. G.; O'Neill, A. G.; Horsfall, A. B.; Goss, J. P.; Wells, G. H.; Hunt, M. R. C.
2014-10-01
Top-gated graphene field-effect transistors (GFETs) have been fabricated using bilayer epitaxial graphene grown on the Si-face of 4H-SiC substrates by thermal decomposition of silicon carbide in high vacuum. Graphene films were characterized by Raman spectroscopy, Atomic Force Microscopy, Scanning Tunnelling Microscopy, and Hall measurements to estimate graphene thickness, morphology, and charge transport properties. A 27 nm thick Al2O3 gate dielectric was grown by atomic layer deposition with an e-beam evaporated Al seed layer. Electrical characterization of the GFETs has been performed at operating temperatures up to 100 °C limited by deterioration of the gate dielectric performance at higher temperatures. Devices displayed stable operation with the gate oxide dielectric strength exceeding 4.5 MV/cm at 100 °C. Significant shifting of the charge neutrality point and an increase of the peak transconductance were observed in the GFETs as the operating temperature was elevated from room temperature to 100 °C.
Ultrarelativistic decoupling transformation for generalized Dirac equations
NASA Astrophysics Data System (ADS)
Noble, J. H.; Jentschura, U. D.
2015-07-01
The Foldy-Wouthuysen transformation is known to uncover the nonrelativistic limit of a generalized Dirac Hamiltonian, lending an intuitive physical interpretation to the effective operators within Schrödinger-Pauli theory. We here discuss the opposite, ultrarelativistic limit which requires the use of a fundamentally different expansion where the leading kinetic term in the Dirac equation is perturbed by the mass of the particle and other interaction (potential) terms, rather than vice versa. The ultrarelativistic decoupling transformation is applied to free Dirac particles (in the Weyl basis) and to high-energy tachyons, which are faster-than-light particles described by a fully Lorentz-covariant equation. The effective gravitational interactions are found. For tachyons, the dominant gravitational interaction term in the high-energy limit is shown to be attractive and equal to the leading term for subluminal Dirac particles (tardyons) in the high-energy limit.
Three Dimensional Dirac Semimetals
NASA Astrophysics Data System (ADS)
Zaheer, Saad
2014-03-01
Dirac points on the Fermi surface of two dimensional graphene are responsible for its unique electronic behavior. One can ask whether any three dimensional materials support similar pseudorelativistic physics in their bulk electronic spectra. This possibility has been investigated theoretically and is now supported by two successful experimental demonstrations reported during the last year. In this talk, I will summarize the various ways in which Dirac semimetals can be realized in three dimensions with primary focus on a specific theory developed on the basis of representations of crystal spacegroups. A three dimensional Dirac (Weyl) semimetal can appear in the presence (absence) of inversion symmetry by tuning parameters to the phase boundary separating a bulk insulating and a topological insulating phase. More generally, we find that specific rules governing crystal symmetry representations of electrons with spin lead to robust Dirac points at high symmetry points in the Brillouin zone. Combining these rules with microscopic considerations identifies six candidate Dirac semimetals. Another method towards engineering Dirac semimetals involves combining crystal symmetry and band inversion. Several candidate materials have been proposed utilizing this mechanism and one of the candidates has been successfully demonstrated as a Dirac semimetal in two independent experiments. Work carried out in collaboration with: Julia A. Steinberg, Steve M. Young, J.C.Y. Teo, C.L. Kane, E.J. Mele and Andrew M. Rappe.
On nonautonomous Dirac equation
Hovhannisyan, Gro; Liu Wen
2009-12-15
We construct the fundamental solution of time dependent linear ordinary Dirac system in terms of unknown phase functions. This construction gives approximate representation of solutions which is useful for the study of asymptotic behavior. Introducing analog of Rayleigh quotient for differential equations we generalize Hartman-Wintner asymptotic integration theorems with the error estimates for applications to the Dirac system. We also introduce the adiabatic invariants for the Dirac system, which are similar to the adiabatic invariant of Lorentz's pendulum. Using a small parameter method it is shown that the change in the adiabatic invariants approaches zero with the power speed as a small parameter approaches zero. As another application we calculate the transition probabilities for the Dirac system. We show that for the special choice of electromagnetic field, the only transition of an electron to the positron with the opposite spin orientation is possible.
Feng, Baojie; Sugino, Osamu; Liu, Ro-Ya; Zhang, Jin; Yukawa, Ryu; Kawamura, Mitsuaki; Iimori, Takushi; Kim, Howon; Hasegawa, Yukio; Li, Hui; Chen, Lan; Wu, Kehui; Kumigashira, Hiroshi; Komori, Fumio; Chiang, Tai-Chang; Meng, Sheng; Matsuda, Iwao
2017-03-03
Honeycomb structures of group IV elements can host massless Dirac fermions with nontrivial Berry phases. Their potential for electronic applications has attracted great interest and spurred a broad search for new Dirac materials especially in monolayer structures. We present a detailed investigation of the β_{12} sheet, which is a borophene structure that can form spontaneously on a Ag(111) surface. Our tight-binding analysis revealed that the lattice of the β_{12} sheet could be decomposed into two triangular sublattices in a way similar to that for a honeycomb lattice, thereby hosting Dirac cones. Furthermore, each Dirac cone could be split by introducing periodic perturbations representing overlayer-substrate interactions. These unusual electronic structures were confirmed by angle-resolved photoemission spectroscopy and validated by first-principles calculations. Our results suggest monolayer boron as a new platform for realizing novel high-speed low-dissipation devices.
NASA Astrophysics Data System (ADS)
Feng, Baojie; Sugino, Osamu; Liu, Ro-Ya; Zhang, Jin; Yukawa, Ryu; Kawamura, Mitsuaki; Iimori, Takushi; Kim, Howon; Hasegawa, Yukio; Li, Hui; Chen, Lan; Wu, Kehui; Kumigashira, Hiroshi; Komori, Fumio; Chiang, Tai-Chang; Meng, Sheng; Matsuda, Iwao
2017-03-01
Honeycomb structures of group IV elements can host massless Dirac fermions with nontrivial Berry phases. Their potential for electronic applications has attracted great interest and spurred a broad search for new Dirac materials especially in monolayer structures. We present a detailed investigation of the β12 sheet, which is a borophene structure that can form spontaneously on a Ag(111) surface. Our tight-binding analysis revealed that the lattice of the β12 sheet could be decomposed into two triangular sublattices in a way similar to that for a honeycomb lattice, thereby hosting Dirac cones. Furthermore, each Dirac cone could be split by introducing periodic perturbations representing overlayer-substrate interactions. These unusual electronic structures were confirmed by angle-resolved photoemission spectroscopy and validated by first-principles calculations. Our results suggest monolayer boron as a new platform for realizing novel high-speed low-dissipation devices.
Dirac's quantum electrodynamics
NASA Astrophysics Data System (ADS)
Kojevnikov, Alexei
In the present paper I examine Dirac's contribution to quantum electrodynamics during the years 1926 to 1933, paying attention to the importance and the specificity of his approach and also tracing the roots of his dissatisfaction with the theory, which goes back to the same time and which, as I see it, in many ways influenced his attitude to its subsequent development. Some of Dirac's crucial accomplishments of that period, in particular his theory of the relativistic electron, have already been studied by historians in much detail. I will describe them more briefly, placing them in the context of Dirac's other works and of the general situation in quantum theory and leaving more room for other, less studied works, such as the 1932 Dirac-Fock-Podolsky theory.
Dynamical supersymmetric Dirac Hamiltonians
Ginocchio, J.N.
1986-01-01
Using the language of quantum electrodynamics, the Dirac Hamiltonian of a neutral fermion interacting with a tensor field is examined. A supersymmetry found for a general Dirac Hamiltonian of this type is discussed, followed by consideration of the special case of a harmonic electric potential. The square of the Dirac Hamiltonian of a neutral fermion interacting via an anomalous magnetic moment in an electric potential is shown to be equivalent to a three-dimensional supersymmetric Schroedinger equation. It is found that for a potential that grows as a power of r, the lowest energy of the Hamiltonian equals the rest mass of the fermion, and the Dirac eigenfunction has only an upper component which is normalizable. It is also found that the higher energy states have upper and lower components which form a supersymmetric doublet. 15 refs. (LEW)
NASA Astrophysics Data System (ADS)
Casajus Ramo, A.; Graciani Diaz, R.
2012-12-01
DIRAC framework for distributed computing has been designed as a group of collaborating components, agents and servers, with persistent database back-end. Components communicate with each other using DISET, an in-house protocol that provides Remote Procedure Call (RPC) and file transfer capabilities. This approach has provided DIRAC with a modular and stable design by enforcing stable interfaces across releases. But it made complicated to scale further with commodity hardware. To further scale DIRAC, components needed to send more queries between them. Using RPC to do so requires a lot of processing power just to handle the secure handshake required to establish the connection. DISET now provides a way to keep stable connections and send and receive queries between components. Only one handshake is required to send and receive any number of queries. Using this new communication mechanism DIRAC now provides a new type of component called Executor. Executors process any task (such as resolving the input data of a job) sent to them by a task dispatcher. This task dispatcher takes care of persisting the state of the tasks to the storage backend and distributing them among all the Executors based on the requirements of each task. In case of a high load, several Executors can be started to process the extra load and stop them once the tasks have been processed. This new approach of handling tasks in DIRAC makes Executors easy to replace and replicate, thus enabling DIRAC to further scale beyond the current approach based on polling agents.
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}.
The Clifford algebra of physical space and Dirac theory
NASA Astrophysics Data System (ADS)
Vaz, Jayme, Jr.
2016-09-01
The claim found in many textbooks that the Dirac equation cannot be written solely in terms of Pauli matrices is shown to not be completely true. It is only true as long as the term β \\psi in the usual Dirac factorization of the Klein-Gordon equation is assumed to be the product of a square matrix β and a column matrix ψ. In this paper we show that there is another possibility besides this matrix product, in fact a possibility involving a matrix operation, and show that it leads to another possible expression for the Dirac equation. We show that, behind this other possible factorization is the formalism of the Clifford algebra of physical space. We exploit this fact, and discuss several different aspects of Dirac theory using this formalism. In particular, we show that there are four different possible sets of definitions for the parity, time reversal, and charge conjugation operations for the Dirac equation.
Filling-Enforced Magnetic Dirac Semimetals in Two Dimensions
NASA Astrophysics Data System (ADS)
Young, Steve M.; Wieder, Benjamin J.
2017-05-01
Filling-enforced Dirac semimetals, or those required at specific fillings by the combination of crystalline and time-reversal symmetries, have been proposed in numerous materials. However, Dirac points in these materials are not generally robust against breaking or modifying time-reversal symmetry. We present a new class of two-dimensional Dirac semimetal protected by the combination of crystal symmetries and a special, antiferromagnetic time-reversal symmetry. Systems in this class of magnetic layer groups, while having broken time-reversal symmetry, still respect the operation of time-reversal followed by a half-lattice translation. In contrast to 2D time-reversal-symmetric Dirac semimetal phases, this magnetic Dirac phase is capable of hosting just a single isolated Dirac point at the Fermi level, one that can be stabilized solely by symmorphic crystal symmetries. We find that this Dirac point represents a new quantum critical point, existing at the boundary between Chern insulating, antiferromagnetic topological crystalline insulating, and trivial insulating phases, and we discuss its relationship with condensed matter fermion doubling theorems. We present density functional theoretic calculations which demonstrate the presence of these 2D magnetic Dirac points in FeSe monolayers and discuss the implications for engineering quantum phase transitions in these materials.
Filling-Enforced Magnetic Dirac Semimetals in Two Dimensions.
Young, Steve M; Wieder, Benjamin J
2017-05-05
Filling-enforced Dirac semimetals, or those required at specific fillings by the combination of crystalline and time-reversal symmetries, have been proposed in numerous materials. However, Dirac points in these materials are not generally robust against breaking or modifying time-reversal symmetry. We present a new class of two-dimensional Dirac semimetal protected by the combination of crystal symmetries and a special, antiferromagnetic time-reversal symmetry. Systems in this class of magnetic layer groups, while having broken time-reversal symmetry, still respect the operation of time-reversal followed by a half-lattice translation. In contrast to 2D time-reversal-symmetric Dirac semimetal phases, this magnetic Dirac phase is capable of hosting just a single isolated Dirac point at the Fermi level, one that can be stabilized solely by symmorphic crystal symmetries. We find that this Dirac point represents a new quantum critical point, existing at the boundary between Chern insulating, antiferromagnetic topological crystalline insulating, and trivial insulating phases, and we discuss its relationship with condensed matter fermion doubling theorems. We present density functional theoretic calculations which demonstrate the presence of these 2D magnetic Dirac points in FeSe monolayers and discuss the implications for engineering quantum phase transitions in these materials.
Dirac cones in two-dimensional acoustic metamaterials
NASA Astrophysics Data System (ADS)
Dai, Hongqing; Xia, Baizhan; Yu, Dejie
2017-08-01
Dirac cones show many extraordinary properties, including Klein tunneling, pseudo-diffusive behavior, phase reconstruction, and topological edge states, and are thus attracting increasing research attention. However, no studies of Dirac cones on a subwavelength scale have been reported to date. In this paper, subwavelength-scale Dirac cones are realized using acoustic metamaterials that consist of hexagonal arrays of hexagonal columns with Helmholtz resonators. We have calculated the band structures of the three types of unit cells that are yielded by space group symmetry operations of the triangular Helmholtz resonators. The results show that these acoustic metamaterials with Helmholtz resonators can be used successfully to reduce the Dirac cone frequencies. Subwavelength Dirac cones of acoustic metamaterials with p6 mm or p6 symmetries are robust to rotation, while subwavelength Dirac cones of acoustic metamaterials with p31m symmetry are sensitive to rotation. In addition, the Dirac cone frequency decreases gradually with increasing filling ratio, which indicates a possible way to control wave propagation on the subwavelength scale. Numerical simulation results show that acoustic metamaterials can behave like zero-refractive-index media and can be applied to acoustic tunneling. The acoustic metamaterials designed in this work offer a route towards the design of functional acoustic devices operating on subwavelength scales.
NASA Astrophysics Data System (ADS)
Trzetrzelewski, Maciej
2016-11-01
Starting with a Nambu-Goto action, a Dirac-like equation can be constructed by taking the square-root of the momentum constraint. The eigenvalues of the resulting Hamiltonian are real and correspond to masses of the excited string. In particular there are no tachyons. A special case of radial oscillations of a closed string in Minkowski space-time admits exact solutions in terms of wave functions of the harmonic oscillator.
NASA Astrophysics Data System (ADS)
Mao, Pu-Jian; Jia, Lin-Yu; Ren, Ji-Rong
We investigate the separability of massive Dirac equation in the charged AdS-Kerr-Taub-NUT black hole. It is shown that the Dirac equation can be separated by variables into purely radial and purely angular parts in this background spacetime. From the separated solutions for massive Dirac equation, a first-order symmetric operator that commutes with the Dirac operator is constructed and expressed in terms of Killing-Yano tensor admitted by the charged AdS-Kerr-Taub-NUT spacetime. Then the Hawking radiation of Dirac particles in the background of charged AdS-Kerr-Taub-NUT black hole is investigated via the Damour-Ruffini-Sannan method. It is shown that quantum thermal effect of the Dirac particles in the charged AdS-Kerr-Taub-NUT black hole has the same character with that of the scalar particles.
Dirac Semimetals in Two Dimensions.
Young, Steve M; Kane, Charles L
2015-09-18
Graphene is famous for being a host of 2D Dirac fermions. However, spin-orbit coupling introduces a small gap, so that graphene is formally a quantum spin Hall insulator. Here we present symmetry-protected 2D Dirac semimetals, which feature Dirac cones at high-symmetry points that are not gapped by spin-orbit interactions and exhibit behavior distinct from both graphene and 3D Dirac semimetals. Using a two-site tight-binding model, we construct representatives of three possible distinct Dirac semimetal phases and show that single symmetry-protected Dirac points are impossible in two dimensions. An essential role is played by the presence of nonsymmorphic space group symmetries. We argue that these symmetries tune the system to the boundary between a 2D topological and trivial insulator. By breaking the symmetries we are able to access trivial and topological insulators as well as Weyl semimetal phases.
The connection between Dirac dynamic and parity symmetry
NASA Astrophysics Data System (ADS)
Coronado Villalobos, C. H.; Bueno Rogerio, R. J.
2016-12-01
Dirac spinors are important objects in the current literature, the algebraic structure presented in the text-books is a general method to write it, however, not unique. The purpose of the present work is to show an alternative approach to construct Dirac spinors, considering the interchange between the Lorentz representation space (1/2, 0) and (0, 1/2) made by the magic of Pauli matrices and not by parity, as was commonly thought. As is well known, the parity operator is related with the Dirac dynamics, as can be seen in Sperança L. D., Int. J. Mod. Phys. D, 2 (2014) 1444003. The major focus is to establish the relation between the Dirac dynamics with the parity operator, i.e., the reverse path shown in the paper by Sperança.
Dirac structures in vakonomic mechanics
NASA Astrophysics Data System (ADS)
Jiménez, Fernando; Yoshimura, Hiroaki
2015-08-01
In this paper, we explore dynamics of the nonholonomic system called vakonomic mechanics in the context of Lagrange-Dirac dynamical systems using a Dirac structure and its associated Hamilton-Pontryagin variational principle. We first show the link between vakonomic mechanics and nonholonomic mechanics from the viewpoints of Dirac structures as well as Lagrangian submanifolds. Namely, we clarify that Lagrangian submanifold theory cannot represent nonholonomic mechanics properly, but vakonomic mechanics instead. Second, in order to represent vakonomic mechanics, we employ the space TQ ×V∗, where a vakonomic Lagrangian is defined from a given Lagrangian (possibly degenerate) subject to nonholonomic constraints. Then, we show how implicit vakonomic Euler-Lagrange equations can be formulated by the Hamilton-Pontryagin variational principle for the vakonomic Lagrangian on the extended Pontryagin bundle (TQ ⊕T∗ Q) ×V∗. Associated with this variational principle, we establish a Dirac structure on (TQ ⊕T∗ Q) ×V∗ in order to define an intrinsic vakonomic Lagrange-Dirac system. Furthermore, we also establish another construction for the vakonomic Lagrange-Dirac system using a Dirac structure on T∗ Q ×V∗, where we introduce a vakonomic Dirac differential. Finally, we illustrate our theory of vakonomic Lagrange-Dirac systems by some examples such as the vakonomic skate and the vertical rolling coin.
Qualitative analysis of trapped Dirac fermions in graphene
Jakubský, Vít Krejčiřík, David
2014-10-15
We study the confinement of Dirac fermions in graphene and in carbon nanotubes by an external magnetic field, mechanical deformations or inhomogeneities in the substrate. By applying variational principles to the square of the Dirac operator, we obtain sufficient and necessary conditions for confinement of the quasi-particles. The rigorous theoretical results are illustrated on the realistic examples of the three classes of traps.
Zero-energy eigenstates for the Dirac boundary problem
NASA Astrophysics Data System (ADS)
Hortaçsu, M.; Rothe, K. D.; Schroer, B.
1980-10-01
As an alternative to the method of spherical compactification for the Dirac operator in instanton background fields we study the correct method of "box-quantization": the Atiyah-Patodi-Singer spectral boundary condition. This is the only self-adjoint boundary condition which respects the charge conjugation property and the γ 5 symmetry, apart from the usual breaking due to zero modes. We point out the relevance of this approach to the computation of instanton determinants and other problems involving Dirac spinors.
An Effective Theory of Dirac Dark Matter
Harnik, Roni; Kribs, Graham D.; /Oregon U.
2010-06-11
A stable Dirac fermion with four-fermion interactions to leptons suppressed by a scale {Lambda} {approx} 1 TeV is shown to provide a viable candidate for dark matter. The thermal relic abundance matches cosmology, while nuclear recoil direct detection bounds are automatically avoided in the absence of (large) couplings to quarks. The annihilation cross section in the early Universe is the same as the annihilation in our galactic neighborhood. This allows Dirac fermion dark matter to naturally explain the positron ratio excess observed by PAMELA with a minimal boost factor, given present astrophysical uncertainties. We use the Galprop program for propagation of signal and background; we discuss in detail the uncertainties resulting from the propagation parameters and, more importantly, the injected spectra. Fermi/GLAST has an opportunity to see a feature in the gamma-ray spectrum at the mass of the Dirac fermion. The excess observed by ATIC/PPB-BETS may also be explained with Dirac dark matter that is heavy. A supersymmetric model with a Dirac bino provides a viable UV model of the effective theory. The dominance of the leptonic operators, and thus the observation of an excess in positrons and not in anti-protons, is naturally explained by the large hypercharge and low mass of sleptons as compared with squarks. Minimizing the boost factor implies the right-handed selectron is the lightest slepton, which is characteristic of our model. Selectrons (or sleptons) with mass less than a few hundred GeV are an inescapable consequence awaiting discovery at the LHC.
NASA Astrophysics Data System (ADS)
Schmidt, M.; Peano, V.; Marquardt, F.
2015-02-01
Recent progress in optomechanical systems may soon allow the realization of optomechanical arrays, i.e. periodic arrangements of interacting optical and vibrational modes. We show that photons and phonons on a honeycomb lattice will produce an optically tunable Dirac-type band structure. Transport in such a system can exhibit transmission through an optically created barrier, similar to Klein tunneling, but with interconversion between light and sound. In addition, edge states at the sample boundaries are dispersive and enable controlled propagation of photon-phonon polaritons.
'Parabolic' trapped modes and steered Dirac cones in platonic crystals.
McPhedran, R C; Movchan, A B; Movchan, N V; Brun, M; Smith, M J A
2015-05-08
This paper discusses the properties of flexural waves governed by the biharmonic operator, and propagating in a thin plate pinned at doubly periodic sets of points. The emphases are on the design of dispersion surfaces having the Dirac cone topology, and on the related topic of trapped modes in plates for a finite set (cluster) of pinned points. The Dirac cone topologies we exhibit have at least two cones touching at a point in the reciprocal lattice, augmented by another band passing through the point. We show that these Dirac cones can be steered along symmetry lines in the Brillouin zone by varying the aspect ratio of rectangular lattices of pins, and that, as the cones are moved, the involved band surfaces tilt. We link Dirac points with a parabolic profile in their neighbourhood, and the characteristic of this parabolic profile decides the direction of propagation of the trapped mode in finite clusters.
The DIRAC Data Management System and the Gaudi dataset federation
NASA Astrophysics Data System (ADS)
Haen, Christophe; Charpentier, Philippe; Frank, Markus; Tsaregorodtsev, Andrei
2015-12-01
The DIRAC Interware provides a development framework and a complete set of components for building distributed computing systems. The DIRAC Data Management System (DMS) offers all the necessary tools to ensure data handling operations for small and large user communities. It supports transparent access to storage resources based on multiple technologies, and is easily expandable. The information on data files and replicas is kept in a File Catalog of which DIRAC offers a powerful and versatile implementation (DFC). Data movement can be performed using third party services including FTS3. Bulk data operations are resilient with respect to failures due to the use of the Request Management System (RMS) that keeps track of ongoing tasks. In this contribution we will present an overview of the DIRAC DMS capabilities and its connection with other DIRAC subsystems such as the Transformation System. This paper also focuses on the DIRAC File Catalog, for which a lot of new developments have been carried out, so that LHCb could migrate its replica catalog from the LCG File Catalog to the DFC. Finally, we will present how LHCb achieves a dataset federation without the need of an extra infrastructure.
NASA Astrophysics Data System (ADS)
Casajus, A.; Ciba, K.; Fernandez, V.; Graciani, R.; Hamar, V.; Mendez, V.; Poss, S.; Sapunov, M.; Stagni, F.; Tsaregorodtsev, A.; Ubeda, M.
2012-12-01
The DIRAC Project was initiated to provide a data processing system for the LHCb Experiment at CERN. It provides all the necessary functionality and performance to satisfy the current and projected future requirements of the LHCb Computing Model. A considerable restructuring of the DIRAC software was undertaken in order to turn it into a general purpose framework for building distributed computing systems that can be used by various user communities in High Energy Physics and other scientific application domains. The CLIC and ILC-SID detector projects started to use DIRAC for their data production system. The Belle Collaboration at KEK, Japan, has adopted the Computing Model based on the DIRAC system for its second phase starting in 2015. The CTA Collaboration uses DIRAC for the data analysis tasks. A large number of other experiments are starting to use DIRAC or are evaluating this solution for their data processing tasks. DIRAC services are included as part of the production infrastructure of the GISELA Latin America grid. Similar services are provided for the users of the France-Grilles and IBERGrid National Grid Initiatives in France and Spain respectively. The new communities using DIRAC started to provide important contributions to its functionality. Among recent additions can be mentioned the support of the Amazon EC2 computing resources as well as other Cloud management systems; a versatile File Replica Catalog with File Metadata capabilities; support for running MPI jobs in the pilot based Workload Management System. Integration with existing application Web Portals, like WS-PGRADE, is demonstrated. In this paper we will describe the current status of the DIRAC Project, recent developments of its framework and functionality as well as the status of the rapidly evolving community of the DIRAC users.
Quantum critical point of Dirac fermion mass generation without spontaneous symmetry breaking
NASA Astrophysics Data System (ADS)
He, Yuan-Yao; Wu, Han-Qing; You, Yi-Zhuang; Xu, Cenke; Meng, Zi Yang; Lu, Zhong-Yi
2016-12-01
We study a lattice model of interacting Dirac fermions in (2 +1 ) dimensions space-time with an SU(4) symmetry. While increasing the interaction strength, this model undergoes a continuous quantum phase transition from a weakly interacting Dirac semimetal to a fully gapped and nondegenerate phase without condensing any Dirac fermion bilinear mass operator. This unusual mechanism for mass generation is consistent with recent studies of interacting topological insulators/superconductors, and also consistent with recent progress in the lattice QCD community.
DIRAC3 - the new generation of the LHCb grid software
NASA Astrophysics Data System (ADS)
Tsaregorodtsev, A.; Brook, N.; Casajus Ramo, A.; Charpentier, Ph; Closier, J.; Cowan, G.; Graciani Diaz, R.; Lanciotti, E.; Mathe, Z.; Nandakumar, R.; Paterson, S.; Romanovsky, V.; Santinelli, R.; Sapunov, M.; Smith, A. C.; Seco Miguelez, M.; Zhelezov, A.
2010-04-01
DIRAC, the LHCb community Grid solution, was considerably reengineered in order to meet all the requirements for processing the data coming from the LHCb experiment. It is covering all the tasks starting with raw data transportation from the experiment area to the grid storage, data processing up to the final user analysis. The reengineered DIRAC3 version of the system includes a fully grid security compliant framework for building service oriented distributed systems; complete Pilot Job framework for creating efficient workload management systems; several subsystems to manage high level operations like data production and distribution management. The user interfaces of the DIRAC3 system providing rich command line and scripting tools are complemented by a full-featured Web portal providing users with a secure access to all the details of the system status and ongoing activities. We will present an overview of the DIRAC3 architecture, new innovative features and the achieved performance. Extending DIRAC3 to manage computing resources beyond the WLCG grid will be discussed. Experience with using DIRAC3 by other user communities than LHCb and in other application domains than High Energy Physics will be shown to demonstrate the general-purpose nature of the system.
Quantum logic gates from Dirac quasiparticles
NASA Astrophysics Data System (ADS)
Marino, E. C.; Brozeguini, J. C.
2015-03-01
We show that one of the fundamental operations of topological quantum computation, namely the non-Abelian braiding of identical particles, can be physically realized in a general system of Dirac quasiparticles in 1 + 1D. Our method is based on the study of the analytic structure of the different Euclidean correlation functions of Dirac fields, which are conveniently expressed as functions of a complex variable. When the Dirac field is an (Abelian) anyon with statistics parameter s (2s not an integer), we show that the associated Majorana states of such a field present non-Abelian statistics. The explicit form of the unitary, non-commuting (monodromy) matrices generated upon braiding is derived as a function of s and is shown to satisfy the Yang-Baxter algebra. For the special case of s = 1/4, we show that the braiding matrices become the logic gates NOT, CNOT,… required in the algorithms of universal quantum computation. We suggest that maybe polyacetylene, alternately doped with alkali and halogen atoms, is a potential candidate for a physical material realization of the system studied here.
Adjunctation and Scalar Product in the Dirac Equation - II
NASA Astrophysics Data System (ADS)
Dima, M.
2017-02-01
Part-I Dima (Int. J. Theor. Phys. 55, 949, 2016) of this paper showed in a representation independent way that γ 0 is the Bergmann-Pauli adjunctator of the Dirac { γ μ } set. The distiction was made between similarity (MATH) transformations and PHYS transformations - related to the (covariant) transformations of physical quantities. Covariance is due solely to the gauging of scalar products between systems of reference and not to the particular action of γ 0 on Lorentz boosts - a matter that in the past led inadvertently to the definition of a second scalar product (the Dirac-bar product). Part-II shows how two scalar products lead to contradictions and eliminates this un-natural duality in favour of the canonical scalar product and its gauge between systems of reference. What constitutes a proper observable is analysed and for instance spin is revealed not to embody one (except as projection on the boost direction - helicity). A thorough investigation into finding a proper-observable current for the theory shows that the Dirac equation does not possess one in operator form. A number of problems with the Dirac current operator are revealed - its Klein-Gordon counterpart being significantly more physical. The alternative suggested is finding a current for the Dirac theory in scalar form j^{μ } = < ρ rangle _{_{ψ }}v^{μ }_{ψ }.
Non-Abelian statistics of vortices with non-Abelian Dirac fermions.
Yasui, Shigehiro; Hirono, Yuji; Itakura, Kazunori; Nitta, Muneto
2013-05-01
We extend our previous analysis on the exchange statistics of vortices having a single Dirac fermion trapped in each core to the case where vortices trap two Dirac fermions with U(2) symmetry. Such a system of vortices with non-Abelian Dirac fermions appears in color superconductors at extremely high densities and in supersymmetric QCD. We show that the exchange of two vortices having doublet Dirac fermions in each core is expressed by non-Abelian representations of a braid group, which is explicitly verified in the matrix representation of the exchange operators when the number of vortices is up to four. We find that the result contains the matrices previously obtained for the vortices with a single Dirac fermion in each core as a special case. The whole braid group does not immediately imply non-Abelian statistics of identical particles because it also contains exchanges between vortices with different numbers of Dirac fermions. However, we find that it does contain, as its subgroup, genuine non-Abelian statistics for the exchange of the identical particles, that is, vortices with the same number of Dirac fermions. This result is surprising compared with conventional understanding because all Dirac fermions are defined locally at each vortex, unlike the case of Majorana fermions for which Dirac fermions are defined nonlocally by Majorana fermions located at two spatially separated vortices.
NASA Astrophysics Data System (ADS)
Yanagisawa, Takashi
2015-07-01
We investigate the Kondo effect in Dirac systems, where Dirac electrons interact with the localized spin via the s-d exchange coupling. The Dirac electron in solid state has the linear dispersion and is described typically by the Hamiltonian such as Hk = vk · σ for the wave number k where σj are Pauli matrices. We derived the formula of the Kondo temperature TK by means of the Green's function theory for small J. The TK is determined from a singularity of Green's functions in the form TK ≃ bar{D}exp ( - const./ρ |J|) when the exchange coupling |J| is small where bar{D} = D/√{1 + D2/(2μ )2} for a cutoff D and ρ is the density of states at the Fermi surface. When |μ| ≪ D, TK is proportional to |μ|: TK ≃ |μ| exp(-const./ρ|J|). The Kondo screening will, however, disappear when the Fermi surface shrinks to a point called the Dirac point, that is, TK vanishes when the chemical potential μ is just at the Dirac point. The resistivity and the specific heat exhibit a log-T singularity in the range TK < T ≪ |μ|/kB. Instead, for T ˜ O(|μ|) or T > |μ|, they never show log-T.
Neutron scattering by Dirac multipoles
NASA Astrophysics Data System (ADS)
Lovesey, S. W.; Khalyavin, D. D.
2017-06-01
Scattering by magnetic charge formed by Dirac multipoles that are magnetic and polar is examined in the context of materials with properties that challenge conventional concepts. An order parameter composed of Dirac quadrupoles has been revealed in the pseudo-gap phase of ceramic, high-T c superconductors on the basis of Kerr effect and magnetic neutron Bragg diffraction measurements. Construction of Dirac quadrupoles that emerge from centrosymmetric sites used by Cu ions in the ceramic superconductor Hg1201 is illustrated, together with selection rules for excitations that will feature in neutron inelastic scattering, and RIXS experiments. We report magnetic scattering amplitudes for diffraction by polar multipoles that have universal value, because they are not specific to ceramic superconductors. To illustrate this attribute, we consider neutron Bragg diffraction from a magnetically ordered iridate (Sr2IrO4) and discuss shortcomings in published interpretations of diffraction data.
Stability problem for singular Dirac equation system on finite interval
NASA Astrophysics Data System (ADS)
Ercan, Ahu; Panakhov, Etibar
2017-01-01
In this study, we show the stability problem for the singular Dirac equation system respect to two spectra on finite interval. The meaning of the stability problem of differential operators is to estimate difference of the spectral functions which considered problems when a finite number of eigenvalues of these problems coincide. The method is based on work by Ryabushko in [12]. The author in [12] studied to what extent only finitely many eigenvalues in one or both spectra determine the potential. We obtain a bound on variation of difference of the spectral functions for singular Dirac equation system.
Scalable implementation of spectral methods for the Dirac equation
Wells, J.C.
1998-10-01
The author discusses the implementation and performance on massively parallel, distributed-memory computers of a message-passing program to solve the time-dependent dirac equation in three Cartesian coordinates. Luses pseudo-spectral methods to obtain a discrete representation of the dirac spinor wavefunction and all coordinate-space operators. Algorithms for the solution of the discrete equations are iterative and depend critically on the dirac hamiltonian-wavefunction product, which he implements as a series of parallel matrix products using MPI. He investigated two communication algorithms, a ring algorithm and a collective-communication algorithm, and present performance results for each on a Paragon-MP (1024 nodes) and a Cray T3E-900 (512 nodes). The ring algorithm achieves very good performance, scaling up to the maximum number of nodes on each machine. However, the collective-communication algorithm scales effectively only on the Paragon.
Ruokokoski, E.; Moettoenen, M.
2011-12-15
We show theoretically that a monopole defect, analogous to the Dirac magnetic monopole, may exist as the ground state of a dilute spin-1 Bose-Einstein condensate. The ground-state monopole is not attached to a single semi-infinite Dirac string but forms a point where the circulation of a single vortex line is reversed. Furthermore, the three-dimensional dynamics of this monopole defect is studied after the magnetic field pinning the monopole is removed and the emergence of antimonopoles is observed. Our scheme is realizable with the current experimental facilities.
Dirac Loops in Carbon Allotropes
NASA Astrophysics Data System (ADS)
Mullen, Kieran; Uchoa, Bruno; Glatzhofer, D.
2015-03-01
We propose a family of structures that have ``Dirac loops'': closed lines in momentum space with Dirac-like quasiparticles, on which the density of states vanishes linearly with energy. The structures all possess the planar trigonal connectivity present in graphene, but are three dimensional. We discuss the consequences of their multiply-connected Fermi surface for transport, including the presence of three dimensional Integer Quantum Hall effect. In the presence of spin-orbit coupling, we show that those structures may have topological surface states. We discuss the feasibility of realizing the structures as an allotrope of carbon. Work supported by NSF Grants DMR-1310407 and DMR-1352604.
Realization of Dirac Cones in Few Bilayer Sb(111) Films by Surface Modification.
Pan, Hui; Wang, Xue-Sen
2015-12-01
We report the first-principle study on the recovery and linearization of Dirac cones in the electronic band structures of a few bilayer Sb(111) films (n-BL Sb) by surface modification. Due to the interaction between the surface states on the two surfaces of a free-standing film, the distorted Dirac cone in n-BL Sb(111) (n < 5) disappears. We demonstrate that the Dirac cone can be restored by functionalizing one surface with certain atoms including H, Ag, and Au, to reduce the inter-surface interaction. We further show that an ideal Dirac cone with linear dispersion of topological surface states near the zone center can be realized by functionalizing both surfaces of the film with oxygen, which enhances spin-orbital coupling. The realization of Dirac cone by surface functionalization shows promise for applications of topologic materials to spintronic devices and their operation in complicated conditions.
Generalized electromagnetism and Dirac algebra
Fryberger, D.
1989-02-01
Using a framework of Dirac algebra, the Clifford algebra appropriate for Minkowski space-time, the formulation of classical electromagnetism including both electric and magnetic charge is explored. Employing the two-potential approach of Cabibbo and Ferrari, a Lagrangian is obtained that is dyality invariant and from which it is possible to derive by Hamilton's principle both the symmetrized Maxwell's equations and the equations of motion for both electrically and magnetically charged particles. This latter result is achieved by defining the variation of the action associated with the cross terms of the interaction Lagrangian in terms of a surface integral. The surface integral has an equivalent path-integral form, showing that the contribution of the cross terms is local in nature. The form of these cross terms derives in a natural way from a Dirac algebraic formulation, and, in fact, the use of the geometric product of Dirac algebra is an essential aspect of this derivation. No kinematic restrictions are associated with the derivation, and no relationship between magnetic and electric charge evolves from the (classical) formulations. However, it is indicated that in bound states quantum mechanical considerations will lead to a version of Dirac's quantization condition. A discussion of parity violation of the generalized electromagnetic theory is given, and a new approach to the incorporation of this violation into the formalism is suggested. Possibilities for extensions are mentioned.
Superconductivity in doped Dirac semimetals
NASA Astrophysics Data System (ADS)
Hashimoto, Tatsuki; Kobayashi, Shingo; Tanaka, Yukio; Sato, Masatoshi
2016-07-01
We theoretically study intrinsic superconductivity in doped Dirac semimetals. Dirac semimetals host bulk Dirac points, which are formed by doubly degenerate bands, so the Hamiltonian is described by a 4 ×4 matrix and six types of k -independent pair potentials are allowed by the Fermi-Dirac statistics. We show that the unique spin-orbit coupling leads to characteristic superconducting gap structures and d vectors on the Fermi surface and the electron-electron interaction between intra and interorbitals gives a novel phase diagram of superconductivity. It is found that when the interorbital attraction is dominant, an unconventional superconducting state with point nodes appears. To verify the experimental signature of possible superconducting states, we calculate the temperature dependence of bulk physical properties such as electronic specific heat and spin susceptibility and surface state. In the unconventional superconducting phase, either dispersive or flat Andreev bound states appear between point nodes, which leads to double peaks or a single peak in the surface density of states, respectively. As a result, possible superconducting states can be distinguished by combining bulk and surface measurements.
Cloud flexibility using DIRAC interware
NASA Astrophysics Data System (ADS)
Fernandez Albor, Víctor; Seco Miguelez, Marcos; Fernandez Pena, Tomas; Mendez Muñoz, Victor; Saborido Silva, Juan Jose; Graciani Diaz, Ricardo
2014-06-01
Communities of different locations are running their computing jobs on dedicated infrastructures without the need to worry about software, hardware or even the site where their programs are going to be executed. Nevertheless, this usually implies that they are restricted to use certain types or versions of an Operating System because either their software needs an definite version of a system library or a specific platform is required by the collaboration to which they belong. On this scenario, if a data center wants to service software to incompatible communities, it has to split its physical resources among those communities. This splitting will inevitably lead to an underuse of resources because the data centers are bound to have periods where one or more of its subclusters are idle. It is, in this situation, where Cloud Computing provides the flexibility and reduction in computational cost that data centers are searching for. This paper describes a set of realistic tests that we ran on one of such implementations. The test comprise software from three different HEP communities (Auger, LHCb and QCD phenomelogists) and the Parsec Benchmark Suite running on one or more of three Linux flavors (SL5, Ubuntu 10.04 and Fedora 13). The implemented infrastructure has, at the cloud level, CloudStack that manages the virtual machines (VM) and the hosts on which they run, and, at the user level, the DIRAC framework along with a VM extension that will submit, monitorize and keep track of the user jobs and also requests CloudStack to start or stop the necessary VM's. In this infrastructure, the community software is distributed via the CernVM-FS, which has been proven to be a reliable and scalable software distribution system. With the resulting infrastructure, users are allowed to send their jobs transparently to the Data Center. The main purpose of this system is the creation of flexible cluster, multiplatform with an scalable method for software distribution for several
Transport experiments with Dirac electrons
NASA Astrophysics Data System (ADS)
Checkelsky, Joseph George
This thesis presents transport experiments performed on solid state systems in which the behavior of the charge carriers can be described by the Dirac equation. Unlike the massive carriers in a typical material, in these systems the carriers behave like massless fermions with a photon-like dispersion predicted to greatly modify their spin and charge transport properties. The first system studied is graphene, a crystalline monolayer of carbon arranged in a hexagonal lattice. The band structure calculated from the hexagonal lattice has the form of the massless Dirac Hamiltonian. At the charge neutral Dirac point, we find that application of a magnetic field drives a transition to an insulating state. We also study the thermoelectric properties of graphene and find that the states near the Dirac point have a unique response compared to those at higher charge density. The second system is the 3D topological insulator Bi2Se3, where a Dirac-like dispersion for states on the 2D surface of the insulating 3D crystal arises as a result of the topology of the 3D bands and time reversal symmetry. To access the transport properties of the 2D states, we suppress the remnant bulk conduction channel by chemical doping and electrostatic gating. In bulk crystals we find strong quantum corrections to transport at low temperature when the bulk conduction channel is maximally suppressed. In microscopic crystals we are able better to isolate the surface conduction channel properties. We identify in-gap conducting states that have relatively high mobility compared to the bulk and exhibit weak anti-localization, consistent with predictions for protected 2D surface states with strong spin-orbit coupling.
Spawning rings of exceptional points out of Dirac cones.
Zhen, Bo; Hsu, Chia Wei; Igarashi, Yuichi; Lu, Ling; Kaminer, Ido; Pick, Adi; Chua, Song-Liang; Joannopoulos, John D; Soljačić, Marin
2015-09-17
The Dirac cone underlies many unique electronic properties of graphene and topological insulators, and its band structure--two conical bands touching at a single point--has also been realized for photons in waveguide arrays, atoms in optical lattices, and through accidental degeneracy. Deformation of the Dirac cone often reveals intriguing properties; an example is the quantum Hall effect, where a constant magnetic field breaks the Dirac cone into isolated Landau levels. A seemingly unrelated phenomenon is the exceptional point, also known as the parity-time symmetry breaking point, where two resonances coincide in both their positions and widths. Exceptional points lead to counter-intuitive phenomena such as loss-induced transparency, unidirectional transmission or reflection, and lasers with reversed pump dependence or single-mode operation. Dirac cones and exceptional points are connected: it was theoretically suggested that certain non-Hermitian perturbations can deform a Dirac cone and spawn a ring of exceptional points. Here we experimentally demonstrate such an 'exceptional ring' in a photonic crystal slab. Angle-resolved reflection measurements of the photonic crystal slab reveal that the peaks of reflectivity follow the conical band structure of a Dirac cone resulting from accidental degeneracy, whereas the complex eigenvalues of the system are deformed into a two-dimensional flat band enclosed by an exceptional ring. This deformation arises from the dissimilar radiation rates of dipole and quadrupole resonances, which play a role analogous to the loss and gain in parity-time symmetric systems. Our results indicate that the radiation existing in any open system can fundamentally alter its physical properties in ways previously expected only in the presence of material loss and gain.
DIRAC File Replica and Metadata Catalog
NASA Astrophysics Data System (ADS)
Tsaregorodtsev, A.; Poss, S.
2012-12-01
File replica and metadata catalogs are essential parts of any distributed data management system, which are largely determining its functionality and performance. A new File Catalog (DFC) was developed in the framework of the DIRAC Project that combines both replica and metadata catalog functionality. The DFC design is based on the practical experience with the data management system of the LHCb Collaboration. It is optimized for the most common patterns of the catalog usage in order to achieve maximum performance from the user perspective. The DFC supports bulk operations for replica queries and allows quick analysis of the storage usage globally and for each Storage Element separately. It supports flexible ACL rules with plug-ins for various policies that can be adopted by a particular community. The DFC catalog allows to store various types of metadata associated with files and directories and to perform efficient queries for the data based on complex metadata combinations. Definition of file ancestor-descendent relation chains is also possible. The DFC catalog is implemented in the general DIRAC distributed computing framework following the standard grid security architecture. In this paper we describe the design of the DFC and its implementation details. The performance measurements are compared with other grid file catalog implementations. The experience of the DFC Catalog usage in the CLIC detector project are discussed.
Snapshots of Dirac fermions near the Dirac point in topological insulators.
Luo, C W; Wang, H J; Ku, S A; Chen, H-J; Yeh, T T; Lin, J-Y; Wu, K H; Juang, J Y; Young, B L; Kobayashi, T; Cheng, C-M; Chen, C-H; Tsuei, K-D; Sankar, R; Chou, F C; Kokh, K A; Tereshchenko, O E; Chulkov, E V; Andreev, Yu M; Gu, G D
2013-01-01
The recent focus on topological insulators is due to the scientific interest in the new state of quantum matter as well as the technology potential for a new generation of THz optoelectronics, spintronics and quantum computations. It is important to elucidate the dynamics of the Dirac fermions in the topologically protected surface state. Hence we utilized a novel ultrafast optical pump mid-infrared probe to explore the dynamics of Dirac fermions near the Dirac point. The femtosecond snapshots of the relaxation process were revealed by the ultrafast optics. Specifically, the Dirac fermion-phonon coupling strength in the Dirac cone was found to increase from 0.08 to 0.19 while Dirac fermions were away from the Dirac point into higher energy states. Further, the energy-resolved transient reflectivity spectra disclosed the energy loss rate of Dirac fermions at room temperature was about 1 meV/ps. These results are crucial to the design of Dirac fermion devices.
Gravitational Repulsion and Dirac Antimatter
NASA Astrophysics Data System (ADS)
Kowitt, Mark E.
1996-03-01
Based on an analogy with electron and hole dynamics in semiconductors, Dirac's relativistic electron equation is generalized to include a gravitational interaction using an electromagnetic-type approximation of the gravitational potential. With gravitational and inertial masses decoupled, the equation serves to extend Dirac's deduction of antimatter parameters to include the possibility of gravitational repulsion between matter and antimatter. Consequences for general relativity and related “antigravity” issues are considered, including the nature and gravitational behavior of virtual photons, virtual pairs, and negative-energy particles. Basic cosmological implications of antigravity are explored—in particular, potential contributions to inflation, expansion, and the general absence of detectable antimatter. Experimental and observational tests are noted, and new ones suggested.
Dirac sigma models from gauging
NASA Astrophysics Data System (ADS)
Salnikov, Vladimir; Strobl, Thomas
2013-11-01
The G/G WZW model results from the WZW-model by a standard procedure of gauging. G/G WZW models are members of Dirac sigma models, which also contain twisted Poisson sigma models as other examples. We show how the general class of Dirac sigma models can be obtained from a gauging procedure adapted to Lie algebroids in the form of an equivariantly closed extension. The rigid gauge groups are generically infinite dimensional and a standard gauging procedure would give a likewise infinite number of 1-form gauge fields; the proposed construction yields the requested finite number of them. Although physics terminology is used, the presentation is kept accessible also for a mathematical audience.
Hydrodynamics of the Dirac spectrum
Liu, Yizhuang; Warchoł, Piotr; Zahed, Ismail
2015-12-15
We discuss a hydrodynamical description of the eigenvalues of the Dirac spectrum in even dimensions in the vacuum and in the large N (volume) limit. The linearized hydrodynamics supports sound waves. The hydrodynamical relaxation of the eigenvalues is captured by a hydrodynamical (tunneling) minimum configuration which follows from a pertinent form of Euler equation. As a result, the relaxation from a phase of unbroken chiral symmetry to a phase of broken chiral symmetry occurs over a time set by the speed of sound.
DIRAC: Secure web user interface
NASA Astrophysics Data System (ADS)
Casajus Ramo, A.; Sapunov, M.
2010-04-01
Traditionally the interaction between users and the Grid is done with command line tools. However, these tools are difficult to use by non-expert users providing minimal help and generating outputs not always easy to understand especially in case of errors. Graphical User Interfaces are typically limited to providing access to the monitoring or accounting information and concentrate on some particular aspects failing to cover the full spectrum of grid control tasks. To make the Grid more user friendly more complete graphical interfaces are needed. Within the DIRAC project we have attempted to construct a Web based User Interface that provides means not only for monitoring the system behavior but also allows to steer the main user activities on the grid. Using DIRAC's web interface a user can easily track jobs and data. It provides access to job information and allows performing actions on jobs such as killing or deleting. Data managers can define and monitor file transfer activity as well as check requests set by jobs. Production managers can define and follow large data productions and react if necessary by stopping or starting them. The Web Portal is build following all the grid security standards and using modern Web 2.0 technologies which allow to achieve the user experience similar to the desktop applications. Details of the DIRAC Web Portal architecture and User Interface will be presented and discussed.
Dirac fermions in nontrivial topology black hole backgrounds
Gozdz, Marek; Nakonieczny, Lukasz; Rogatko, Marek
2010-05-15
We discuss the behavior of the Dirac fermions in a general spherically symmetric black hole background with a nontrivial topology of the event horizon. Both massive and massless cases are taken into account. We will conduct an analytical study of intermediate and late-time behavior of massive Dirac hair in the background of a black hole with a global monopole and dilaton black hole pierced by a cosmic string. In the case of a global monopole swallowed by a static black hole, the intermediate late-time behavior depends on the mass of the Dirac field, the multiple number of the wave mode, and the global monopole parameter. The late-time behavior is quite independent of these factors and has a decay rate proportional to t{sup -5/6}. As far as the black hole pierced by a cosmic string is concerned, the intermediate late-time behavior depends only on the hair mass and the multipole number of the wave mode, while the late-time behavior dependence is the same as in the previous case. The main modification stems from the topology of the S{sup 2} sphere pierced by a cosmic string. This factor modifies the eigenvalues of the Dirac operator acting on the transverse manifold.
A two-dimensional Dirac fermion microscope
NASA Astrophysics Data System (ADS)
Bøggild, Peter; Caridad, José M.; Stampfer, Christoph; Calogero, Gaetano; Papior, Nick Rübner; Brandbyge, Mads
2017-06-01
The electron microscope has been a powerful, highly versatile workhorse in the fields of material and surface science, micro and nanotechnology, biology and geology, for nearly 80 years. The advent of two-dimensional materials opens new possibilities for realizing an analogy to electron microscopy in the solid state. Here we provide a perspective view on how a two-dimensional (2D) Dirac fermion-based microscope can be realistically implemented and operated, using graphene as a vacuum chamber for ballistic electrons. We use semiclassical simulations to propose concrete architectures and design rules of 2D electron guns, deflectors, tunable lenses and various detectors. The simulations show how simple objects can be imaged with well-controlled and collimated in-plane beams consisting of relativistic charge carriers. Finally, we discuss the potential of such microscopes for investigating edges, terminations and defects, as well as interfaces, including external nanoscale structures such as adsorbed molecules, nanoparticles or quantum dots.
A two-dimensional Dirac fermion microscope
Bøggild, Peter; Caridad, José M.; Stampfer, Christoph; Calogero, Gaetano; Papior, Nick Rübner; Brandbyge, Mads
2017-01-01
The electron microscope has been a powerful, highly versatile workhorse in the fields of material and surface science, micro and nanotechnology, biology and geology, for nearly 80 years. The advent of two-dimensional materials opens new possibilities for realizing an analogy to electron microscopy in the solid state. Here we provide a perspective view on how a two-dimensional (2D) Dirac fermion-based microscope can be realistically implemented and operated, using graphene as a vacuum chamber for ballistic electrons. We use semiclassical simulations to propose concrete architectures and design rules of 2D electron guns, deflectors, tunable lenses and various detectors. The simulations show how simple objects can be imaged with well-controlled and collimated in-plane beams consisting of relativistic charge carriers. Finally, we discuss the potential of such microscopes for investigating edges, terminations and defects, as well as interfaces, including external nanoscale structures such as adsorbed molecules, nanoparticles or quantum dots. PMID:28598421
A two-dimensional Dirac fermion microscope.
Bøggild, Peter; Caridad, José M; Stampfer, Christoph; Calogero, Gaetano; Papior, Nick Rübner; Brandbyge, Mads
2017-06-09
The electron microscope has been a powerful, highly versatile workhorse in the fields of material and surface science, micro and nanotechnology, biology and geology, for nearly 80 years. The advent of two-dimensional materials opens new possibilities for realizing an analogy to electron microscopy in the solid state. Here we provide a perspective view on how a two-dimensional (2D) Dirac fermion-based microscope can be realistically implemented and operated, using graphene as a vacuum chamber for ballistic electrons. We use semiclassical simulations to propose concrete architectures and design rules of 2D electron guns, deflectors, tunable lenses and various detectors. The simulations show how simple objects can be imaged with well-controlled and collimated in-plane beams consisting of relativistic charge carriers. Finally, we discuss the potential of such microscopes for investigating edges, terminations and defects, as well as interfaces, including external nanoscale structures such as adsorbed molecules, nanoparticles or quantum dots.
Dirac fermions in an antiferromagnetic semimetal
Tang, Peizhe; Zhou, Quan; Xu, Gang; Zhang, Shou-Cheng
2016-08-08
Analogues of the elementary particles have been extensively searched for in condensed-matter systems for both scientific interest and technological applications. Recently, massless Dirac fermions were found to emerge as low-energy excitations in materials now known as Dirac semimetals. All of the currently known Dirac semimetals are non-magnetic with both time-reversal symmetry and inversion symmetry. Here in this paper, we show that Dirac fermions can exist in one type of antiferromagnetic system, where both and are broken but their combination is respected. We propose orthorhombic antiferromagnet CuMnAs as a candidate, analyse the robustness of the Dirac points under symmetry protections and demonstrate its distinctive bulk dispersions, as well as the corresponding surface states, by ab initio calculations. Our results provide a possible platform to study the interplay of Dirac fermion physics and magnetism.
Dirac fermions in an antiferromagnetic semimetal
Tang, Peizhe; Zhou, Quan; Xu, Gang; ...
2016-08-08
Analogues of the elementary particles have been extensively searched for in condensed-matter systems for both scientific interest and technological applications. Recently, massless Dirac fermions were found to emerge as low-energy excitations in materials now known as Dirac semimetals. All of the currently known Dirac semimetals are non-magnetic with both time-reversal symmetry and inversion symmetry. Here in this paper, we show that Dirac fermions can exist in one type of antiferromagnetic system, where both and are broken but their combination is respected. We propose orthorhombic antiferromagnet CuMnAs as a candidate, analyse the robustness of the Dirac points under symmetry protections andmore » demonstrate its distinctive bulk dispersions, as well as the corresponding surface states, by ab initio calculations. Our results provide a possible platform to study the interplay of Dirac fermion physics and magnetism.« less
Mapping curved spacetimes into Dirac spinors
Sabín, Carlos
2017-01-01
We show how to transform a Dirac equation in a curved static spacetime into a Dirac equation in flat spacetime. In particular, we show that any solution of the free massless Dirac equation in a 1 + 1 dimensional flat spacetime can be transformed via a local phase transformation into a solution of the corresponding Dirac equation in a curved static background, where the spacetime metric is encoded into the phase. In this way, the existing quantum simulators of the Dirac equation can naturally incorporate curved static spacetimes. As a first example we use our technique to obtain solutions of the Dirac equation in a particular family of interesting spacetimes in 1 + 1 dimensions. PMID:28074908
Mapping curved spacetimes into Dirac spinors.
Sabín, Carlos
2017-01-11
We show how to transform a Dirac equation in a curved static spacetime into a Dirac equation in flat spacetime. In particular, we show that any solution of the free massless Dirac equation in a 1 + 1 dimensional flat spacetime can be transformed via a local phase transformation into a solution of the corresponding Dirac equation in a curved static background, where the spacetime metric is encoded into the phase. In this way, the existing quantum simulators of the Dirac equation can naturally incorporate curved static spacetimes. As a first example we use our technique to obtain solutions of the Dirac equation in a particular family of interesting spacetimes in 1 + 1 dimensions.
Dirac fermions in an antiferromagnetic semimetal
NASA Astrophysics Data System (ADS)
Tang, Peizhe; Zhou, Quan; Xu, Gang; Zhang, Shou-Cheng
2016-12-01
Analogues of the elementary particles have been extensively searched for in condensed-matter systems for both scientific interest and technological applications. Recently, massless Dirac fermions were found to emerge as low-energy excitations in materials now known as Dirac semimetals. All of the currently known Dirac semimetals are non-magnetic with both time-reversal symmetry and inversion symmetry . Here we show that Dirac fermions can exist in one type of antiferromagnetic system, where both and are broken but their combination is respected. We propose orthorhombic antiferromagnet CuMnAs as a candidate, analyse the robustness of the Dirac points under symmetry protections and demonstrate its distinctive bulk dispersions, as well as the corresponding surface states, by ab initio calculations. Our results provide a possible platform to study the interplay of Dirac fermion physics and magnetism.
A Short Biography of Paul A. M. Dirac and Historical Development of Dirac Delta Function
ERIC Educational Resources Information Center
Debnath, Lokenath
2013-01-01
This paper deals with a short biography of Paul Dirac, his first celebrated work on quantum mechanics, his first formal systematic use of the Dirac delta function and his famous work on quantum electrodynamics and quantum statistics. Included are his first discovery of the Dirac relativistic wave equation, existence of positron and the intrinsic…
A Short Biography of Paul A. M. Dirac and Historical Development of Dirac Delta Function
ERIC Educational Resources Information Center
Debnath, Lokenath
2013-01-01
This paper deals with a short biography of Paul Dirac, his first celebrated work on quantum mechanics, his first formal systematic use of the Dirac delta function and his famous work on quantum electrodynamics and quantum statistics. Included are his first discovery of the Dirac relativistic wave equation, existence of positron and the intrinsic…
Functional integral method in quantum field theory of Dirac fermions in graphene
NASA Astrophysics Data System (ADS)
Duoc Phan, Nguyen Duc; Dat Nguyen, Nhu; Hau Tran, Van; Thang Nguyen, Toan; Hieu Nguyen, Van
2017-09-01
The purpose of this work is to elaborate the functional integral method in quantum field theory of Dirac fermions in the Dirac fermion gas of a graphene single layer at vanishing absolute temperature. The starting point to be assumed as the fundamental principle of the theory is the explicit expression of the action functional of this system. The efficient mathematical tool to be used in the study is the generating functional containing the Grassmann parameters anticommuting with the Dirac fermion field operators. The analytical expression of the generating functional of free Dirac fermion system is exactly derived and efficiently used in the study of 2n-point Green functions of free Dirac fermions. Then the celebrated Hubbard-Stratonovich transformation is applied to rewrite the functional integral of the interacting system of Dirac fermions in a new form expressing in terms of a scalar Hermitian quantum field describing the collective excitations in the interacting Dirac fermion gas and related to the graphene plasmons.
Dirac solutions for quaternionic potentials
De Leo, Stefano Giardino, Sergio
2014-02-15
The Dirac equation is solved for quaternionic potentials, i V{sub 0} + j W{sub 0} (V{sub 0}∈R , W{sub 0}∈C). The study shows two different solutions. The first one contains particle and anti-particle solutions and leads to the diffusion, tunneling, and Klein energy zones. The standard solution is recovered taking the complex limit of this solution. The second solution, which does not have a complex counterpart, can be seen as a V{sub 0}-antiparticle or |W{sub 0}|-particle solution.
Dirac's aether in curved spacetime.
Oliveira; Teixeira
2000-06-01
Proca's equations for two types of fields in a Dirac's aether with electric conductivity sigma are solved exactly. The Proca electromagnetic fields are assumed with cylindrical symmetry. The background is a static, curved spacetime whose spatial section is homogeneous and has the topology of either the three-sphere S 3 or the projective three-space P 3. Simple relations between the range of Proca field lambda, the Universe radius R, the limit of photon rest mass mgamma and the conductivity sigma are written down.
Phenomenology of pseudo Dirac neutrinos
NASA Astrophysics Data System (ADS)
Joshipura, A. S.; Rindani, S. D.
2000-11-01
We formulate general conditions on /3×3 neutrino mass matrices under which a degenerate pair of neutrinos at a high scale would split at low scale by radiative corrections involving only the standard model fields. This generalizes the original observations of Wolfenstein on pseudo Dirac neutrinos to three generations. A specific model involving partially broken discrete symmetry and solving the solar and atmospheric anomalies is proposed. The symmetry pattern of the model naturally generates two large angles one of which can account for the large angle MSW solution to the solar neutrino problem.
A fractional Dirac equation and its solution
NASA Astrophysics Data System (ADS)
Muslih, Sami I.; Agrawal, Om P.; Baleanu, Dumitru
2010-02-01
This paper presents a fractional Dirac equation and its solution. The fractional Dirac equation may be obtained using a fractional variational principle and a fractional Klein-Gordon equation; both methods are considered here. We extend the variational formulations for fractional discrete systems to fractional field systems defined in terms of Caputo derivatives. By applying the variational principle to a fractional action S, we obtain the fractional Euler-Lagrange equations of motion. We present a Lagrangian and a Hamiltonian for the fractional Dirac equation of order α. We also use a fractional Klein-Gordon equation to obtain the fractional Dirac equation which is the same as that obtained using the fractional variational principle. Eigensolutions of this equation are presented which follow the same approach as that for the solution of the standard Dirac equation. We also provide expressions for the path integral quantization for the fractional Dirac field which, in the limit α → 1, approaches to the path integral for the regular Dirac field. It is hoped that the fractional Dirac equation and the path integral quantization of the fractional field will allow further development of fractional relativistic quantum mechanics.
Dirac-Kaehler Theory and Massless Fields
Pletyukhov, V. A.; Strazhev, V. I.
2010-03-24
Three massless limits of the Dirac-Kaehler theory are considered. It is shown that the Dirac-Kaehler equation for massive particles can be represented as a result of the gauge-invariant mixture (topological interaction) of the above massless fields.
The DIRAC Language: Concepts and Facilities.
ERIC Educational Resources Information Center
Vallee, Jacques; Ludwig, Herbert
The three documents contained in this report describe an interactive retrieval language implemented for the IBM 360/67 of the Campus Faculty at Stanford University, between October 1969 and May 1970. The three reports are: (1) DIRAC--An Interactive Retrieval Language with Computational Interface, (2) DIRAC--An Overview of an Interactive Retrieval…
Two dimensional Dirac carbon allotropes from graphene.
Xu, Li-Chun; Wang, Ru-Zhi; Miao, Mao-Sheng; Wei, Xiao-Lin; Chen, Yuan-Ping; Yan, Hui; Lau, Woon-Ming; Liu, Li-Min; Ma, Yan-Ming
2014-01-21
Using a structural search method in combination with first-principles calculations, we found lots of low energy 2D carbon allotropes and examined all possible Dirac points around their Fermi levels. Three amazing 2D Dirac carbon allotropes have been discovered, named as S-graphene, D-graphene and E-graphene. By analyzing the topology correlations among S-, T, net W graphene and graphene, we found that a general rule is valuable for constructing 2D carbon allotropes that are keen to possess Dirac cones in their electronic structures. Based on this rule, we have successfully designed many new 2D carbon allotropes possessing Dirac cones. Their energy order can be well described by an Ising-like model, and some allotropes are energetically more stable than those recently reported. The related electronic structures of these Dirac allotropes are anisotropy distinguished from those of graphene. Moreover, the fact that D- and E-graphene present Dirac cones suggests that sp hybridization or sp(3) hybridization could not suppress the emerging of Dirac features. Our results demonstrate that the Dirac cone and carrier linear dispersion is a very common feature in 2D carbon allotropes and can exist beyond the limitations of fundamental structure features of graphene.
‘Parabolic’ trapped modes and steered Dirac cones in platonic crystals
McPhedran, R. C.; Movchan, A. B.; Movchan, N. V.; Brun, M.; Smith, M. J. A.
2015-01-01
This paper discusses the properties of flexural waves governed by the biharmonic operator, and propagating in a thin plate pinned at doubly periodic sets of points. The emphases are on the design of dispersion surfaces having the Dirac cone topology, and on the related topic of trapped modes in plates for a finite set (cluster) of pinned points. The Dirac cone topologies we exhibit have at least two cones touching at a point in the reciprocal lattice, augmented by another band passing through the point. We show that these Dirac cones can be steered along symmetry lines in the Brillouin zone by varying the aspect ratio of rectangular lattices of pins, and that, as the cones are moved, the involved band surfaces tilt. We link Dirac points with a parabolic profile in their neighbourhood, and the characteristic of this parabolic profile decides the direction of propagation of the trapped mode in finite clusters. PMID:27547089
Pierantozzi, T.; Vazquez, L.
2005-11-01
Through fractional calculus and following the method used by Dirac to obtain his well-known equation from the Klein-Gordon equation, we analyze a possible interpolation between the Dirac and the diffusion equations in one space dimension. We study the transition between the hyperbolic and parabolic behaviors by means of the generalization of the D'Alembert formula for the classical wave equation and the invariance under space and time inversions of the interpolating fractional evolution equations Dirac like. Such invariance depends on the values of the fractional index and is related to the nonlocal property of the time fractional differential operator. For this system of fractional evolution equations, we also find an associated conserved quantity analogous to the Hamiltonian for the classical Dirac case.
Dirac particle in gravitational quantum mechanics
NASA Astrophysics Data System (ADS)
Pedram, Pouria
2011-08-01
In this Letter, we consider the effects of the Generalized (Gravitational) Uncertainty Principle (GUP) on the eigenvalues and the eigenfunctions of the Dirac equation. This form of GUP is consistent with various candidates of quantum gravity such as string theory, loop quantum gravity, doubly special relativity and black hole physics and predicts both a minimum measurable length and a maximum measurable momentum. The modified Hamiltonian contains two additional terms proportional to a( and a( where αi are Dirac matrices and a∼1/MPlc is the GUP parameter. For the case of the Dirac free particle and the Dirac particle in a box, we solve the generalized Dirac equation and find the modified energy eigenvalues and eigenfunctions.
Double Dirac Semimetals in Three Dimensions.
Wieder, Benjamin J; Kim, Youngkuk; Rappe, A M; Kane, C L
2016-05-06
We study a class of Dirac semimetals that feature an eightfold-degenerate double Dirac point. We show that 7 of the 230 space groups can host such Dirac points and argue that they all generically display linear dispersion. We introduce an explicit tight-binding model for space groups 130 and 135. Space group 135 can host an intrinsic double Dirac semimetal with no additional states at the Fermi energy. This defines a symmetry-protected topological critical point, and we show that a uniaxial compressive strain applied in different directions leads to topologically distinct insulating phases. In addition, the double Dirac semimetal can accommodate topological line defects that bind helical modes. Connections are made to theories of strongly interacting filling-enforced semimetals, and potential materials realizations are discussed.
Highly Anisotropic Dirac Fermions in Square Graphynes.
Zhang, L Z; Wang, Z F; Wang, Zhiming M; Du, S X; Gao, H-J; Liu, Feng
2015-08-06
We predict a family of 2D carbon (C) allotropes, square graphynes (S-graphynes) that exhibit highly anisotropic Dirac fermions, using first-principle calculations within density functional theory. They have a square unit-cell containing two sizes of square C rings. The equal-energy contour of their 3D band structure shows a crescent shape, and the Dirac crescent has varying Fermi velocities from 0.6 × 10(5) to 7.2 × 10(5) m/s along different k directions. Near the Fermi level, the Dirac crescent can be nicely expressed by an extended 2D Dirac model Hamiltonian. Furthermore, tight-binding band fitting reveals that the Dirac crescent originates from the next-nearest-neighbor interactions between C atoms. S-graphynes may be used to build new 2D electronic devices taking advantages of their highly directional charge transport.
Tunable Dirac Fermion Dynamics in Topological Insulators
NASA Astrophysics Data System (ADS)
Chen, Chaoyu; Xie, Zhuojin; Feng, Ya; Yi, Hemian; Liang, Aiji; He, Shaolong; Mou, Daixiang; He, Junfeng; Peng, Yingying; Liu, Xu; Liu, Yan; Zhao, Lin; Liu, Guodong; Dong, Xiaoli; Zhang, Jun; Yu, Li; Wang, Xiaoyang; Peng, Qinjun; Wang, Zhimin; Zhang, Shenjin; Yang, Feng; Chen, Chuangtian; Xu, Zuyan; Zhou, X. J.
2013-08-01
Three-dimensional topological insulators are characterized by insulating bulk state and metallic surface state involving relativistic Dirac fermions which are responsible for exotic quantum phenomena and potential applications in spintronics and quantum computations. It is essential to understand how the Dirac fermions interact with other electrons, phonons and disorders. Here we report super-high resolution angle-resolved photoemission studies on the Dirac fermion dynamics in the prototypical Bi2(Te,Se)3 topological insulators. We have directly revealed signatures of the electron-phonon coupling and found that the electron-disorder interaction dominates the scattering process. The Dirac fermion dynamics in Bi2(Te3-xSex) topological insulators can be tuned by varying the composition, x, or by controlling the charge carriers. Our findings provide crucial information in understanding and engineering the electron dynamics of the Dirac fermions for fundamental studies and potential applications.
Double Dirac Semimetals in Three Dimensions
NASA Astrophysics Data System (ADS)
Wieder, Benjamin J.; Kim, Youngkuk; Rappe, A. M.; Kane, C. L.
2016-05-01
We study a class of Dirac semimetals that feature an eightfold-degenerate double Dirac point. We show that 7 of the 230 space groups can host such Dirac points and argue that they all generically display linear dispersion. We introduce an explicit tight-binding model for space groups 130 and 135. Space group 135 can host an intrinsic double Dirac semimetal with no additional states at the Fermi energy. This defines a symmetry-protected topological critical point, and we show that a uniaxial compressive strain applied in different directions leads to topologically distinct insulating phases. In addition, the double Dirac semimetal can accommodate topological line defects that bind helical modes. Connections are made to theories of strongly interacting filling-enforced semimetals, and potential materials realizations are discussed.
Tunable Dirac Fermion Dynamics in Topological Insulators
Chen, Chaoyu; Xie, Zhuojin; Feng, Ya; Yi, Hemian; Liang, Aiji; He, Shaolong; Mou, Daixiang; He, Junfeng; Peng, Yingying; Liu, Xu; Liu, Yan; Zhao, Lin; Liu, Guodong; Dong, Xiaoli; Zhang, Jun; Yu, Li; Wang, Xiaoyang; Peng, Qinjun; Wang, Zhimin; Zhang, Shenjin; Yang, Feng; Chen, Chuangtian; Xu, Zuyan; Zhou, X. J.
2013-01-01
Three-dimensional topological insulators are characterized by insulating bulk state and metallic surface state involving relativistic Dirac fermions which are responsible for exotic quantum phenomena and potential applications in spintronics and quantum computations. It is essential to understand how the Dirac fermions interact with other electrons, phonons and disorders. Here we report super-high resolution angle-resolved photoemission studies on the Dirac fermion dynamics in the prototypical Bi2(Te,Se)3 topological insulators. We have directly revealed signatures of the electron-phonon coupling and found that the electron-disorder interaction dominates the scattering process. The Dirac fermion dynamics in Bi2(Te3−xSex) topological insulators can be tuned by varying the composition, x, or by controlling the charge carriers. Our findings provide crucial information in understanding and engineering the electron dynamics of the Dirac fermions for fundamental studies and potential applications. PMID:23934507
Tunable Dirac fermion dynamics in topological insulators.
Chen, Chaoyu; Xie, Zhuojin; Feng, Ya; Yi, Hemian; Liang, Aiji; He, Shaolong; Mou, Daixiang; He, Junfeng; Peng, Yingying; Liu, Xu; Liu, Yan; Zhao, Lin; Liu, Guodong; Dong, Xiaoli; Zhang, Jun; Yu, Li; Wang, Xiaoyang; Peng, Qinjun; Wang, Zhimin; Zhang, Shenjin; Yang, Feng; Chen, Chuangtian; Xu, Zuyan; Zhou, X J
2013-01-01
Three-dimensional topological insulators are characterized by insulating bulk state and metallic surface state involving relativistic Dirac fermions which are responsible for exotic quantum phenomena and potential applications in spintronics and quantum computations. It is essential to understand how the Dirac fermions interact with other electrons, phonons and disorders. Here we report super-high resolution angle-resolved photoemission studies on the Dirac fermion dynamics in the prototypical Bi2(Te,Se)3 topological insulators. We have directly revealed signatures of the electron-phonon coupling and found that the electron-disorder interaction dominates the scattering process. The Dirac fermion dynamics in Bi2(Te3-xSex) topological insulators can be tuned by varying the composition, x, or by controlling the charge carriers. Our findings provide crucial information in understanding and engineering the electron dynamics of the Dirac fermions for fundamental studies and potential applications.
Revisiting double Dirac delta potential
NASA Astrophysics Data System (ADS)
Ahmed, Zafar; Kumar, Sachin; Sharma, Mayank; Sharma, Vibhu
2016-07-01
We study a general double Dirac delta potential to show that this is the simplest yet still versatile solvable potential to introduce double wells, avoided crossings, resonances and perfect transmission (T = 1). Perfect transmission energies turn out to be the critical property of symmetric and anti-symmetric cases wherein these discrete energies are found to correspond to the eigenvalues of a Dirac delta potential placed symmetrically between two rigid walls. For well(s) or barrier(s), perfect transmission (or zero reflectivity, R(E)) at energy E=0 is non-intuitive. However, this has been found earlier and called the ‘threshold anomaly’. Here we show that it is a critical phenomenon and we can have 0≤slant R(0)\\lt 1 when the parameters of the double delta potential satisfy an interesting condition. We also invoke a zero-energy and zero curvature eigenstate (\\psi (x)={Ax}+B) of the delta well between two symmetric rigid walls for R(0)=0. We resolve that the resonant energies and the perfect transmission energies are different and they arise differently.
Neutrino masses from a pseudo-Dirac bino
Coloma, Pilar; Ipek, Seyda
2016-09-09
We show that, in U(1)_{R}-symmetric supersymmetric models, the bino and its Dirac partner (the singlino) can play the role of right-handed neutrinos and generate the neutrino masses and mixing, without the need for traditional bilinear or trilinear R-parity violating operators. The two particles form a pseudo-Dirac pair, the “bi νo.” An inverse seesaw texture is generated for the neutrino-biνo sector, and the lightest neutrino is predicted to be massless. Lastly, unlike in most models with heavy right-handed neutrinos, the bi νo can be sizably produced at the LHC through its interactions with colored particles, while respecting low energy constraints from neutrinoless double-beta decay and charged lepton flavor violation.
Neutrino masses from a pseudo-Dirac bino
Coloma, Pilar; Ipek, Seyda
2016-09-09
We show that, in U(1)_{R}-symmetric supersymmetric models, the bino and its Dirac partner (the singlino) can play the role of right-handed neutrinos and generate the neutrino masses and mixing, without the need for traditional bilinear or trilinear R-parity violating operators. The two particles form a pseudo-Dirac pair, the “bi νo.” An inverse seesaw texture is generated for the neutrino-biνo sector, and the lightest neutrino is predicted to be massless. Lastly, unlike in most models with heavy right-handed neutrinos, the bi νo can be sizably produced at the LHC through its interactions with colored particles, while respecting low energy constraints from neutrinoless double-beta decay and charged lepton flavor violation.
Neutrino masses from a pseudo-Dirac bino
Coloma, Pilar; Ipek, Seyda
2016-09-09
We show that, in U(1)R-symmetric supersymmetric models, the bino and its Dirac partner (the singlino) can play the role of right-handed neutrinos and generate the neutrino masses and mixing, without the need for traditional bilinear or trilinear R-parity violating operators. The two particles form a pseudo-Dirac pair, the “bi νo.” An inverse seesaw texture is generated for the neutrino-biνo sector, and the lightest neutrino is predicted to be massless. Lastly, unlike in most models with heavy right-handed neutrinos, the bi νo can be sizably produced at the LHC through its interactions with colored particles, while respecting low energy constraints frommore » neutrinoless double-beta decay and charged lepton flavor violation.« less
Neutrino Masses from a Pseudo-Dirac Bino
NASA Astrophysics Data System (ADS)
Coloma, Pilar; Ipek, Seyda
2016-09-01
We show that, in U (1 )R -symmetric supersymmetric models, the bino and its Dirac partner (the singlino) can play the role of right-handed neutrinos and generate the neutrino masses and mixing, without the need for traditional bilinear or trilinear R -parity violating operators. The two particles form a pseudo-Dirac pair, the "bi ν o ." An inverse seesaw texture is generated for the neutrino-bi ν o sector, and the lightest neutrino is predicted to be massless. Unlike in most models with heavy right-handed neutrinos, the bi ν o can be sizably produced at the LHC through its interactions with colored particles, while respecting low energy constraints from neutrinoless double-beta decay and charged lepton flavor violation.
Neutrino Masses from a Pseudo-Dirac Bino.
Coloma, Pilar; Ipek, Seyda
2016-09-09
We show that, in U(1)_{R}-symmetric supersymmetric models, the bino and its Dirac partner (the singlino) can play the role of right-handed neutrinos and generate the neutrino masses and mixing, without the need for traditional bilinear or trilinear R-parity violating operators. The two particles form a pseudo-Dirac pair, the "biνo." An inverse seesaw texture is generated for the neutrino-biνo sector, and the lightest neutrino is predicted to be massless. Unlike in most models with heavy right-handed neutrinos, the biνo can be sizably produced at the LHC through its interactions with colored particles, while respecting low energy constraints from neutrinoless double-beta decay and charged lepton flavor violation.
Magnetotransport properties near the Dirac point of Dirac semimetal Cd3As2 nanowires
NASA Astrophysics Data System (ADS)
Wang, Li-Xian; Wang, Shuo; Li, Jin-Guang; Li, Cai-Zhen; Xu, Jun; Yu, Dapeng; Liao, Zhi-Min
2017-02-01
Three-dimensional (3D) Dirac semimetals are featured by 3D linear energy-momentum dispersion relation, which have been proposed to be a desirable system to study Dirac fermions in 3D space and Weyl fermions in solid-state materials. Significantly, to reveal exotic transport properties of Dirac semimetals, the Fermi level should be close to the Dirac point, around which the linear dispersion is retained. Here we report the magnetotransport properties near the Dirac point in Cd3As2 nanowires, manifesting the evolution of band structure under magnetic field. Ambipolar field effect is observed with the Dirac point at V g = 3.9 V. Under high magnetic field, there is a resistivity dip in transfer curve at the Dirac point, which is caused by the Zeeman splitting enhanced density of state around the Dirac point. Furthermore, the low carrier density in the nanowires makes it feasible to enter into the quantum limit regime, resulting in the quantum linear magnetoresistance being observed even at room temperature. Besides, the dramatic reduction of bulk conductivity due to the low carrier density, together with a large surface to volume ratio of the nanowire, collectively help to reveal the Shubnikov-de Haas oscillations from the surface states. Our studies on transport properties around the Dirac point therefore provide deep insights into the emerging exotic physics of Dirac and Weyl fermions.
Magnetotransport properties near the Dirac point of Dirac semimetal Cd3As2 nanowires.
Wang, Li-Xian; Wang, Shuo; Li, Jin-Guang; Li, Cai-Zhen; Xu, Jun; Yu, Dapeng; Liao, Zhi-Min
2017-02-01
Three-dimensional (3D) Dirac semimetals are featured by 3D linear energy-momentum dispersion relation, which have been proposed to be a desirable system to study Dirac fermions in 3D space and Weyl fermions in solid-state materials. Significantly, to reveal exotic transport properties of Dirac semimetals, the Fermi level should be close to the Dirac point, around which the linear dispersion is retained. Here we report the magnetotransport properties near the Dirac point in Cd3As2 nanowires, manifesting the evolution of band structure under magnetic field. Ambipolar field effect is observed with the Dirac point at V g = 3.9 V. Under high magnetic field, there is a resistivity dip in transfer curve at the Dirac point, which is caused by the Zeeman splitting enhanced density of state around the Dirac point. Furthermore, the low carrier density in the nanowires makes it feasible to enter into the quantum limit regime, resulting in the quantum linear magnetoresistance being observed even at room temperature. Besides, the dramatic reduction of bulk conductivity due to the low carrier density, together with a large surface to volume ratio of the nanowire, collectively help to reveal the Shubnikov-de Haas oscillations from the surface states. Our studies on transport properties around the Dirac point therefore provide deep insights into the emerging exotic physics of Dirac and Weyl fermions.
NASA Astrophysics Data System (ADS)
Cariglia, Marco; Krtouš, Pavel; Kubizňák, David
2011-07-01
We intrinsically characterize separability of the Dirac equation in Kerr-NUT-(A)dS spacetimes in all dimensions. Namely, we explicitly demonstrate that, in such spacetimes, there exists a complete set of first-order mutually commuting operators, one of which is the Dirac operator, that allows for common eigenfunctions which can be found in a separated form and correspond precisely to the general solution of the Dirac equation found by Oota and Yasui [Phys. Lett. BPYLBAJ0370-2693 659, 688 (2008)10.1016/j.physletb.2007.11.057]. Since all the operators in the set can be generated from the principal conformal Killing-Yano tensor, this establishes the (up-to-now) missing link among the existence of hidden symmetry, presence of a complete set of commuting operators, and separability of the Dirac equation in these spacetimes.
Antiferromagnetic Dirac semimetals in two dimensions
NASA Astrophysics Data System (ADS)
Wang, Jing
2017-03-01
The search for symmetry-protected two-dimensional (2D) Dirac semimetals analogous to graphene is important both for fundamental and practical interest. The 2D Dirac cones are protected by crystalline symmetries and magnetic ordering may destroy their robustness. Here we propose a general framework to classify stable 2D Dirac semimetals in spin-orbit coupled systems having the combined time-reversal and inversion symmetries, and show the existence of the stable Dirac points in 2D antiferromagnetic semimetals. Compared to 3D Dirac semimetals which fall into two distinct classes, Dirac semimetals in 2D with combined time-reversal and inversion symmetries belong to a single class which is closely related to the nonsymmorphic space-group symmetries. We further provide a concrete model in antiferromagnetic semimetals which supports symmetry-protected 2D Dirac points. The symmetry breaking in such systems leads to 2D chiral topological states such as quantum anomalous Hall insulator and chiral topological superconductor phases.
LHCbDirac: distributed computing in LHCb
NASA Astrophysics Data System (ADS)
Stagni, F.; Charpentier, P.; Graciani, R.; Tsaregorodtsev, A.; Closier, J.; Mathe, Z.; Ubeda, M.; Zhelezov, A.; Lanciotti, E.; Romanovskiy, V.; Ciba, K. D.; Casajus, A.; Roiser, S.; Sapunov, M.; Remenska, D.; Bernardoff, V.; Santana, R.; Nandakumar, R.
2012-12-01
We present LHCbDirac, an extension of the DIRAC community Grid solution that handles LHCb specificities. The DIRAC software has been developed for many years within LHCb only. Nowadays it is a generic software, used by many scientific communities worldwide. Each community wanting to take advantage of DIRAC has to develop an extension, containing all the necessary code for handling their specific cases. LHCbDirac is an actively developed extension, implementing the LHCb computing model and workflows handling all the distributed computing activities of LHCb. Such activities include real data processing (reconstruction, stripping and streaming), Monte-Carlo simulation and data replication. Other activities are groups and user analysis, data management, resources management and monitoring, data provenance, accounting for user and production jobs. LHCbDirac also provides extensions of the DIRAC interfaces, including a secure web client, python APIs and CLIs. Before putting in production a new release, a number of certification tests are run in a dedicated setup. This contribution highlights the versatility of the system, also presenting the experience with real data processing, data and resources management, monitoring for activities and resources.
NASA Astrophysics Data System (ADS)
Benoit-Lévy, Aurélien; Chardin, Gabriel
2014-05-01
We study an unconventional cosmology, in which we investigate the consequences that antigravity would pose to cosmology. We present the main characteristics of the Dirac-Milne Universe, a cosmological model where antimatter has a negative active gravitational mass. In this non-standard Universe, separate domains of matter and antimatter coexist at our epoch without annihilation, separated by a gravitationally induced depletion zone. We show that this cosmology does not require a priori the Dark Matter and Dark Energy components of the standard model of cosmology. Additionally, inflation becomes an unnecessary ingredient. Investigating this model, we show that the classical cosmological tests such as primordial nucleosynthesis, Type Ia supernovæ and Cosmic Microwave Background are surprisingly concordant.
Conformable fractional Dirac system on time scales.
Gulsen, Tuba; Yilmaz, Emrah; Goktas, Sertac
2017-01-01
We study the conformable fractional (CF) Dirac system with separated boundary conditions on an arbitrary time scale [Formula: see text]. Then we extend some basic spectral properties of the classical Dirac system to the CF case. Eventually, some asymptotic estimates for the eigenfunction of the CF Dirac eigenvalue problem are obtained on [Formula: see text]. So, we provide a constructive procedure for the solution of this problem. These results are important steps to consolidate the link between fractional calculus and time scale calculus in spectral theory.
Krylov subspace methods for the Dirac equation
NASA Astrophysics Data System (ADS)
Beerwerth, Randolf; Bauke, Heiko
2015-03-01
The Lanczos algorithm is evaluated for solving the time-independent as well as the time-dependent Dirac equation with arbitrary electromagnetic fields. We demonstrate that the Lanczos algorithm can yield very precise eigenenergies and allows very precise time propagation of relativistic wave packets. The unboundedness of the Dirac Hamiltonian does not hinder the applicability of the Lanczos algorithm. As the Lanczos algorithm requires only matrix-vector products and inner products, which both can be efficiently parallelized, it is an ideal method for large-scale calculations. The excellent parallelization capabilities are demonstrated by a parallel implementation of the Dirac Lanczos propagator utilizing the Message Passing Interface standard.
Spurious Roots in the Algebraic Dirac Equation
NASA Astrophysics Data System (ADS)
Pestka, Grzegorz
The nature of spurious roots discovered by Drake and Goldman [G. W. F. Drake and S. P. Goldman, Phys. Rev. A 23, 2093 (1981)] among solutions of the algebraic Dirac Hamiltonian eigenvalue problem is discussed. It is shown that the spurious roots represent the positive spectrum states of the Dirac Hamiltonian and that each of them has its variational non-relativistic counterpart. Sufficient conditions to avoid the appearance of the spuriouses in the forbidden gap of Dirac energies are formulated. Numerical examples for κ = 1 ( P1/2) states of an electron in a spherical Coulomb potential (in Slater-type bases) are presented.
Helicity oscillations of Dirac and Majorana neutrinos
NASA Astrophysics Data System (ADS)
Dobrynina, Alexandra; Kartavtsev, Alexander; Raffelt, Georg
2016-06-01
The helicity of a Dirac neutrino with mass m evolves under the influence of a B field because it has a magnetic dipole moment proportional to m . Moreover, it was recently shown that a polarized or anisotropic medium engenders the same effect for both Dirac and Majorana neutrinos. Because a B field polarizes a background medium, it instigates helicity oscillations even for Majorana neutrinos unless the medium is symmetric between matter and antimatter. Motivated by these observations, we review the impact of a B field and of an anisotropic or polarized medium on helicity oscillations for Dirac and Majorana neutrinos from the common perspective of in-medium dispersion.
Dirac Nodal Lines and Tilted Semi-Dirac Cones Coexisting in a Striped Boron Sheet.
Zhang, Honghong; Xie, Yuee; Zhang, Zhongwei; Zhong, Chengyong; Li, Yafei; Chen, Zhongfang; Chen, Yuanping
2017-04-20
The enchanting Dirac fermions in graphene stimulated us to seek other 2D Dirac materials, and boron monolayers may be a good candidate. So far, a number of monolayer boron sheets have been theoretically predicted, and three have been experimentally prepared. However, none of intrinsic sheets possess Dirac electrons near the Fermi level. Herein, by means of density functional theory computations, we identified a new boron monolayer, namely, hr-sB, with two types of Dirac fermions coexisting in the sheet: One type is related to Dirac nodal lines traversing Brillouin zone (BZ) with velocities approaching 10(6) m/s, and the other is related to tilted semi-Dirac cones with strong anisotropy. This newly predicted boron monolayer consists of hexagon and rhombus stripes. With an exceptional stability comparable to the experimentally achieved boron sheets, it is rather optimistic to grow hr-sB on some suitable substrates such as the Ag (111) surface.
Yu, Hongyi; Liu, Gui-Bin; Gong, Pu; Xu, Xiaodong; Yao, Wang
2014-05-12
In monolayer transition metal dichalcogenides, tightly bound excitons have been discovered with a valley pseudospin optically addressable through polarization selection rules. Here, we show that this valley pseudospin is strongly coupled to the exciton centre-of-mass motion through electron-hole exchange. This coupling realizes a massless Dirac cone with chirality index I = 2 for excitons inside the light cone, that is, bright excitons. Under moderate strain, the I = 2 Dirac cone splits into two degenerate I = 1 Dirac cones, and saddle points with a linear Dirac spectrum emerge. After binding an extra electron, the charged exciton becomes a massive Dirac particle associated with a large valley Hall effect protected from intervalley scattering. Our results point to unique opportunities to study Dirac physics, with exciton's optical addressability at specifiable momentum, energy and pseudospin. The strain-tunable valley-orbit coupling also implies new structures of exciton condensates, new functionalities of excitonic circuits and mechanical control of valley pseudospin.
On the Neuberger overlap operator
NASA Astrophysics Data System (ADS)
Boriçi, Artan
1999-04-01
We compute Neuberger's overlap operator by the Lanczos algorithm applied to the Wilson-Dirac operator. Locality of the operator for quenched QCD data and its eigenvalue spectrum in an instanton background are studied.
Condensed-matter trio scoop Dirac prize
NASA Astrophysics Data System (ADS)
Durrani, Matin
2012-09-01
Three condensed-matter physicists, who have advanced our understanding of a strange type of material known as a "topological insulator", have won this year's Dirac medal from the International Centre for Theoretical Physics (ICTP) in Trieste, Italy.
Dirac State in Giant Magnetoresistive Materials
NASA Astrophysics Data System (ADS)
Wu, Y.; Jo, N. H.; Ochi, M.; Huang, L.; Mou, D.; Kong, T.; Mun, E.; Wang, L.; Lee, Y.; Bud'Ko, S. L.; Canfield, P. C.; Trivedi, N.; Arito, R.; Kaminski, A.
We use ultrahigh resolution, tunable, vacuum ultraviolet laser-based angle-resolved photoemission spectroscopy (ARPES) to study the electronic properties of materials that recently were discovered to display titanic magnetoresistance. We find that that several of these materials have Dirac-like features in their band structure. In some materials those features are ``ordinary'' Dirac cones, while in others the linear Dirac dispersion of two crossing bands forms a linear object in 3D momentum space. Our observation poses an important question about the role of Dirac dispersion in the unusually high, non-saturating magnetoresistance of these materials. Research was supported by the US DOE, Office of Basic Energy Sciences under Contract No. DE-AC02-07CH11358; Gordon and Betty Moore Foundation EPiQS Initiative (Grant No. GBMF4411); CEM, a NSF MRSEC, under Grant No. DMR-1420451.
The degeneracy of the free Dirac equation
Gupta, V. . School of Physics Tata Inst. of Fundamental Research, Bombay ); McKellar, B.H.J. . School of Physics); Wu, D.D. . School of Physics Institute of High Energy Physics, Beijing, BJ . Electron LINAC Dept. General Atomics, San Diego, CA )
1991-08-01
Parity-mixed solutions of the free Dirac equation with the same 4-momentum are considered. The first-order EM energy has an electric dipole moment term whose value depends on the mixing angle. Further implications of this degeneracy to perturbative calculations are discussed. It is argued that the properties of the Dirac equation with the Coulomb potential can be used to decide the mixing angle, which should be zero.
Pathways to naturally small Dirac neutrino masses
NASA Astrophysics Data System (ADS)
Ma, Ernest; Popov, Oleg
2017-01-01
If neutrinos are truly Dirac fermions, the smallness of their masses may still be natural if certain symmetries exist beyond those of the standard model of quarks and leptons. We perform a systematic study of how this may occur at tree level and in one loop. We also propose a scotogenic version of the left-right gauge model with naturally small Dirac neutrino masses in one loop.
Phenomenology of Dirac Neutralino Dark Matter
Buckley, Matthew R.; Hooper, Dan; Kumar, Jason
2013-09-01
In supersymmetric models with an unbroken R-symmetry (rather than only R-parity), the neutralinos are Dirac fermions rather than Majorana. In this article, we discuss the phenomenology of neutralino dark matter in such models, including the calculation of the thermal relic abundance, and constraints and prospects for direct and indirect searches. Due to the large elastic scattering cross sections with nuclei predicted in R-symmetric models, we are forced to consider a neutralino that is predominantly bino, with very little higgsino mixing. We find a large region of parameter space in which bino-like Dirac neutralinos with masses between 10 and 380 GeV can annihilate through slepton exchange to provide a thermal relic abundance in agreement with the observed cosmological density, without relying on coannihilations or resonant annihilations. The signatures for the indirect detection of Dirac neutralinos are very different than predicted in the Majorana case, with annihilations proceeding dominately to $\\tau^+ \\tau^-$, $\\mu^+ \\mu^-$ and $e^+ e^-$ final states, without the standard chirality suppression. And unlike Majorana dark matter candidates, Dirac neutralinos experience spin-independent scattering with nuclei through vector couplings (via $Z$ and squark exchange), leading to potentially large rates at direct detection experiments. These and other characteristics make Dirac neutralinos potentially interesting within the context of recent direct and indirect detection anomalies. We also discuss the case in which the introduction of a small Majorana mass term breaks the $R$-symmetry, splitting the Dirac neutralino into a pair of nearly degenerate Majorana states.
Phenomenology of Dirac neutralino dark matter
NASA Astrophysics Data System (ADS)
Buckley, Matthew R.; Hooper, Dan; Kumar, Jason
2013-09-01
In supersymmetric models with an unbroken R symmetry (rather than only R parity), the neutralinos are Dirac fermions rather than Majorana. In this article, we discuss the phenomenology of neutralino dark matter in such models, including the calculation of the thermal relic abundance, and constraints and prospects for direct and indirect searches. Because of the large elastic scattering cross sections with nuclei predicted in R-symmetric models, we are forced to consider a neutralino that is predominantly bino, with very little Higgsino mixing. We find a large region of parameter space in which binolike Dirac neutralinos with masses between 10 and 380 GeV can annihilate through slepton exchange to provide a thermal relic abundance in agreement with the observed cosmological density, without relying on coannihilations or resonant annihilations. The signatures for the indirect detection of Dirac neutralinos are very different than predicted in the Majorana case, with annihilations proceeding dominantly to τ+τ-, μ+μ- and e+e- final states, without the standard chirality suppression. And unlike Majorana dark matter candidates, Dirac neutralinos experience spin-independent scattering with nuclei through vector couplings (via Z and squark exchange), leading to potentially large rates at direct detection experiments. These and other characteristics make Dirac neutralinos potentially interesting within the context of recent direct and indirect detection anomalies. We also discuss the case in which the introduction of a small Majorana mass term breaks the R symmetry, splitting the Dirac neutralino into a pair of nearly degenerate Majorana states.
Bosonic Dirac Materials in 2 dimensions
NASA Astrophysics Data System (ADS)
Banerjee, Saikat; Black-Schaffer, A. M.; Fransson, J.; Agren, H.; Balatsky, A. V.
We examine the low energy effective theory of phase oscillations in a two dimensional granular superconducting sheet where the grains are arranged in honeycomb lattice structure. Two different types of collective phase oscillations are obtained, which are analogous to the massive Leggett and massless Bogoliubov-Anderson-Gorkov modes for two-band superconductor. It is explicitly shown that the spectra of these collective Bosonic modes cross each other at K and K' points in the Brillouin zone and form a Dirac node. This Dirac node behavior in Bosonic excitations represent the case of Bosonic Dirac Materials (BDM). Dirac node is preserved in presence of an inter-grain interaction despite induced changes of the qualitative features of the two collective modes. Finally, breaking the sub lattice symmetry by choosing different on-site potentials for the two sub lattices leads to a gap opening near the Dirac node, in analogy with Fermionic Dirac material. Supported by US DOE E304, ERC DM 321031, KAW, VR2012-3447.
NASA Astrophysics Data System (ADS)
Mathe, Z.; Casajus Ramo, A.; Lazovsky, N.; Stagni, F.
2015-12-01
For many years the DIRAC interware (Distributed Infrastructure with Remote Agent Control) has had a web interface, allowing the users to monitor DIRAC activities and also interact with the system. Since then many new web technologies have emerged, therefore a redesign and a new implementation of the DIRAC Web portal were necessary, taking into account the lessons learnt using the old portal. These new technologies allowed to build a more compact, robust and responsive web interface that enables users to have better control over the whole system while keeping a simple interface. The web framework provides a large set of “applications”, each of which can be used for interacting with various parts of the system. Communities can also create their own set of personalised web applications, and can easily extend already existing ones with a minimal effort. Each user can configure and personalise the view for each application and save it using the DIRAC User Profile service as RESTful state provider, instead of using cookies. The owner of a view can share it with other users or within a user community. Compatibility between different browsers is assured, as well as with mobile versions. In this paper, we present the new DIRAC Web framework as well as the LHCb extension of the DIRAC Web portal.
Viability of Dirac phase leptogenesis
Anisimov, Alexey; Blanchet, Steve; Di Bari, Pasquale E-mail: blanchet@mppmu.mpg.de
2008-04-15
We discuss the conditions for a non-vanishing Dirac phase {delta} and mixing angle {theta}{sub 13}, sources of CP violation in neutrino oscillations, to be uniquely responsible for the observed matter-antimatter asymmetry of the Universe through leptogenesis. We show that this scenario, that we call {delta}-leptogenesis, is viable when the degenerate limit for the heavy right-handed (RH) neutrino spectrum is considered. We derive an interesting joint condition on sin{theta}{sub 13} and the absolute neutrino mass scale that can be tested in future neutrino oscillation experiments. In the limit of the hierarchical heavy RH neutrino spectrum, we strengthen the previous result that {delta}-leptogenesis is only very marginally allowed, even when the production from the two heavier RH neutrinos is taken into account. An improved experimental upper bound on sin{theta}{sub 13} and/or an account of quantum kinetic effects could completely rule out this option in the future. Therefore, {delta}-leptogenesis can be also regarded as motivation for models with degenerate heavy neutrino spectrum.
First-principles study of Dirac and Dirac-like cones in phononic and photonic crystals
NASA Astrophysics Data System (ADS)
Mei, Jun; Wu, Ying; Chan, C. T.; Zhang, Zhao-Qing
2012-07-01
By using the k⇀·p⇀ method, we propose a first-principles theory to study the linear dispersions in phononic and photonic crystals. The theory reveals that only those linear dispersions created by doubly degenerate states can be described by a reduced Hamiltonian that can be mapped into the Dirac Hamiltonian and possess a Berry phase of -π. Linear dispersions created by triply degenerate states cannot be mapped into the Dirac Hamiltonian and carry no Berry phase, and, therefore should be called Dirac-like cones. Our theory is capable of predicting accurately the linear slopes of Dirac and Dirac-like cones at various symmetry points in a Brillouin zone, independent of frequency and lattice structure.
Generic Friedberg-Lee symmetry of Dirac neutrinos
NASA Astrophysics Data System (ADS)
Luo, Shu; Xing, Zhi-Zhong; Li, Xin
2008-12-01
We write out the generic Dirac neutrino mass operator which possesses the Friedberg-Lee symmetry and find that its corresponding neutrino mass matrix is asymmetric. Following a simple way to break the Friedberg-Lee symmetry, we calculate the neutrino mass eigenvalues and show that the resultant neutrino mixing pattern is nearly tri-bimaximal. Imposing the Hermitian condition on the neutrino mass matrix, we also show that the simplified ansatz is consistent with current experimental data and favors the normal neutrino mass hierarchy.
The LHCb Experience on the Grid from the DIRAC Accounting Data
NASA Astrophysics Data System (ADS)
Casajús, Adrian; Graciani, Ricardo; Puig, Albert; Vázquez, Ricardo; LHCb Collaboration
2011-12-01
DIRAC is the software framework developed by LHCb to manage all its computing operations on the Grid. Since 2003 it has been used for large scale Monte Carlo simulation productions and for user analysis of these data. Since the end of 2009, with the start-up of LHC, DIRAC also takes care of the distribution, reconstruction, selection and analysis of the physics data taken by the detector apparatus. During 2009, DIRAC executed almost 5 million jobs for LHCb. In order to execute this workload slightly over 6 million of pilot jobs were submitted, out of which approximately one third were aborted by the Grid infrastructure. In 2010, thanks to their improved efficiency, DIRAC pilots are able, on average, to match and execute between 2 and 3 LHCb jobs during their lifetime, largely reducing the load on the Grid infrastructure. Given the large amount of submitted jobs and used resources, it becomes essential to store detailed information about their execution to track the behaviour of the system. The DIRAC Accounting system takes care, among other things, to collect and store data concerning the execution of jobs and pilots, making it available to everyone via the public interface of the LHCb DIRAC web portal in the form of time-binned accumulated distributions. The analysis of the raw accounting data stored allow us to improve and debug the system performance, as well as, to give a detailed picture on how LHCb uses its Grid resources. A new tool has been developed to extract the raw records from the DIRAC Accounting database and to transform them into ROOT files for subsequent study. This contribution presents an analysis of such data both for LHCb jobs and the corresponding pilots, including resource usage, number of pilots per job, job efficiency and other relevant variables that will help to further improving the LHCb Grid experience.
NASA Astrophysics Data System (ADS)
Volfson, Boris
2013-09-01
The hypothesis of transition from a chaotic Dirac Sea, via highly unstable positronium, into a Simhony Model of stable face-centered cubic lattice structure of electrons and positrons securely bound in vacuum space, is considered. 13.75 Billion years ago, the new lattice, which, unlike a Dirac Sea, is permeable by photons and phonons, made the Universe detectable. Many electrons and positrons ended up annihilating each other producing energy quanta and neutrino-antineutrino pairs. The weak force of the electron-positron crystal lattice, bombarded by the chirality-changing neutrinos, may have started capturing these neutrinos thus transforming from cubic crystals into a quasicrystal lattice. Unlike cubic crystal lattice, clusters of quasicrystals are "slippery" allowing the formation of centers of local torsion, where gravity condenses matter into galaxies, stars and planets. In the presence of quanta, in a quasicrystal lattice, the Majorana neutrinos' rotation flips to the opposite direction causing natural transformations in a category comprised of three components; two others being positron and electron. In other words, each particle-antiparticle pair "e-" and "e+", in an individual crystal unit, could become either a quasi- component "e- ve e+", or a quasi- component "e+ - ve e-". Five-to-six six billion years ago, a continuous stimulation of the quasicrystal aetherial lattice by the same, similar, or different, astronomical events, could have triggered Hebbian and anti-Hebbian learning processes. The Universe may have started writing script into its own aether in a code most appropriate for the quasicrystal aether "hardware": Eight three-dimensional "alphabet" characters, each corresponding to the individual quasi-crystal unit shape. They could be expressed as quantum Turing machine qubits, or, alternatively, in a binary code. The code numerals could contain terminal and nonterminal symbols of the Chomsky's hierarchy, wherein, the showers of quanta, forming the
Pairing instabilities of Dirac composite fermions
NASA Astrophysics Data System (ADS)
Milovanović, M. V.; Ćirić, M. Dimitrijević; Juričić, V.
2016-09-01
Recently, a Dirac (particle-hole symmetric) description of composite fermions in the half-filled Landau level (LL) was proposed [D. T. Son, Phys. Rev. X 5, 031027 (2015), 10.1103/PhysRevX.5.031027], and we study its possible consequences on BCS (Cooper) pairing of composite fermions (CFs). One of the main consequences is the existence of anisotropic states in single-layer and bilayer systems, which was previously suggested in Jeong and Park [J. S. Jeong and K. Park, Phys. Rev. B 91, 195119 (2015), 10.1103/PhysRevB.91.195119]. We argue that in the half-filled LL in the single-layer case the gapped states may sustain anisotropy, because isotropic pairings may coexist with anisotropic ones. Furthermore, anisotropic pairings with the addition of a particle-hole symmetry-breaking mass term may evolve into rotationally symmetric states, i.e., Pfaffian states of Halperin-Lee-Read (HLR) ordinary CFs. On the basis of the Dirac formalism, we argue that in the quantum Hall bilayer at total filling factor 1, with decreasing distance between the layers, weak pairing of p -wave paired CFs is gradually transformed from Dirac to ordinary, HLR-like, with a concomitant decrease in the CF number. Global characterization of low-energy spectra based on the Dirac CFs agrees well with previous calculations performed by exact diagonalization on a torus. Finally, we discuss features of the Dirac formalism when applied in this context.
Gravitationally coupled Dirac equation for antimatter
NASA Astrophysics Data System (ADS)
Jentschura, U. D.
2013-03-01
The coupling of antimatter to gravity is of general interest because of conceivable cosmological consequences (“surprises”) related to dark energy and the cosmological constant. Here, we revisit the derivation of the gravitationally coupled Dirac equation and find that the prefactor of a result given previously by Brill and Wheeler [Rev. Mod. Phys.RMPHAT0034-686110.1103/RevModPhys.29.465 29, 465 (1957)] for the affine connection matrix is in need of a correction. We also discuss the conversion of the curved-space Dirac equation from the so-called “East-Coast” to the “West-Coast” convention, in order to bring the gravitationally coupled Dirac equation to a form where it can easily be unified with the electromagnetic coupling as it is commonly used in modern particle physics calculations. The Dirac equation describes antiparticles as negative-energy states. We find a symmetry of the gravitationally coupled Dirac equation, which connects particle and antiparticle solutions for a general space-time metric of the Schwarzschild type and implies that particles and antiparticles experience the same coupling to the gravitational field, including all relativistic quantum corrections of motion. Our results demonstrate the consistency of quantum mechanics with general relativity and imply that a conceivable difference of gravitational interaction of hydrogen and antihydrogen should directly be attributed to a a “fifth force” (“quintessence”).
Strain engineering of Dirac cones in graphyne
Wang, Gaoxue; Kumar, Ashok; Pandey, Ravindra; Si, Mingsu
2014-05-26
6,6,12-graphyne, one of the two-dimensional carbon allotropes with the rectangular lattice structure, has two kinds of non-equivalent anisotropic Dirac cones in the first Brillouin zone. We show that Dirac cones can be tuned independently by the uniaxial compressive strain applied to graphyne, which induces n-type and p-type self-doping effect, by shifting the energy of the Dirac cones in the opposite directions. On the other hand, application of the tensile strain results into a transition from gapless to finite gap system for the monolayer. For the AB-stacked bilayer, the results predict tunability of Dirac-cones by in-plane strains as well as the strain applied perpendicular to the plane. The group velocities of the Dirac cones show enhancement in the resistance anisotropy for bilayer relative to the case of monolayer. Such tunable and direction-dependent electronic properties predicted for 6,6,12-graphyne make it to be competitive for the next-generation electronic devices at nanoscale.
Assili, M; Haddad, S
2013-09-11
We theoretically study the effect of the motion and the merging of Dirac cones on the interlayer magnetoresistance in multilayer graphene-like systems. This merging, which can be induced by a uniaxial strain, gives rise in a monolayer Dirac electron system to a topological transition from a semi-metallic phase to an insulating phase whereby Dirac points disappear. Based on a universal Hamiltonian, proposed to describe the motion and the merging of Dirac points in two-dimensional Dirac electron crystals, we calculate the interlayer conductivity of a stack of deformed graphene-like layers using the Kubo formula in the quantum limit where only the contribution of the n = 0 Landau level is relevant. A crossover from a negative to a positive interlayer magnetoresistance is found to take place as the merging is approached. This sign change of the magnetoresistance can also result from a coupling between the Dirac valleys, which is enhanced as the magnetic field amplitude increases. Our results describe the behavior of the magnetotransport in the organic conductor α-(BEDT)2I3 and in a stack of deformed graphene-like systems. The latter can be simulated by optical lattices or microwave experiments in which the merging of Dirac cones can be observed.
NASA Technical Reports Server (NTRS)
Turner, Michael S.
1991-01-01
Previous work has shown that the cooling of SN 1987A excludes a Dirac-neutrino mass greater than theta(20 keV) for nu(sub e), nu(sub mu), or nu(sub tau). The emission of wrong-helicity, Dirac neutrinos from SN 1987A, is re-examined. It is concluded that the effect of a Dirac neutrino on the cooling of SN 1987A has been underestimated due to neutrino degeneracy and additional emission processes. The limit that follows from the cooling of SN 1987A is believed to be greater (probably much greater) than 10 keV. This result is significant in light of the recent evidence for a 17 keV mass eigenstate that mixes with the electron neutrino.
White dwarfs, the Galaxy and Dirac's cosmology
NASA Technical Reports Server (NTRS)
Stothers, R.
1976-01-01
The additive and multiplicative versions of Dirac's cosmological hypothesis relating the gravitational constant variation with elapsed time and number of particles populating the universe is invoked to account for the deficiency or absence of white dwarfs fainter than about 0.0001 solar luminosity. An estimate is made of white dwarf luminosity in accordance with the two evolutionary models, and it is conjectured that some old white dwarfs with high space velocities may be on the verge of gravitational collapse. Lack of a special mechanism to produce the vast numbers of black holes or other dead stars accounting for 'missing matter' in the vicinity of the sun and in the galactic halo is noted in Dirac's multiplicative model. Results indicate that either Dirac's theory is untenable, or that radiation and heating are of some unknown nature, or that the process of creation of new matter requires a corresponding input of energy.
Supersymmetry in the 6D Dirac action
NASA Astrophysics Data System (ADS)
Fujimoto, Yukihiro; Hasegawa, Kouhei; Nishiwaki, Kenji; Sakamoto, Makoto; Tatsumi, Kentaro
2017-07-01
We investigate a 6D Dirac fermion on a rectangle. It is found that the 4D spectrum is governed by N =2 supersymmetric quantum mechanics. Then we demonstrate that the supersymmetry is very useful for classifying all the allowed boundary conditions and to expand the 6D Dirac field in Kaluza-Klein modes. A striking feature of the model is that even though the 6D Dirac fermion has non-vanishing bulk mass, the 4D mass spectrum can contain degenerate massless chiral fermions, which may provide a hint to solve the problem of the generation of quarks and leptons. It is pointed out that zero-energy solutions are not affected by the presence of the boundaries, while the boundary conditions work well for determining the positive-energy solutions. We also provide a brief discussion on possible boundary conditions in the general case, especially those on polygons.
White dwarfs, the Galaxy and Dirac's cosmology
NASA Technical Reports Server (NTRS)
Stothers, R.
1976-01-01
The additive and multiplicative versions of Dirac's cosmological hypothesis relating the gravitational constant variation with elapsed time and number of particles populating the universe is invoked to account for the deficiency or absence of white dwarfs fainter than about 0.0001 solar luminosity. An estimate is made of white dwarf luminosity in accordance with the two evolutionary models, and it is conjectured that some old white dwarfs with high space velocities may be on the verge of gravitational collapse. Lack of a special mechanism to produce the vast numbers of black holes or other dead stars accounting for 'missing matter' in the vicinity of the sun and in the galactic halo is noted in Dirac's multiplicative model. Results indicate that either Dirac's theory is untenable, or that radiation and heating are of some unknown nature, or that the process of creation of new matter requires a corresponding input of energy.
Triplet fermions and Dirac fermions in borophene
NASA Astrophysics Data System (ADS)
Ezawa, Motohiko
2017-07-01
Borophene is a monolayer materials made of boron. A perfect planar boropehene called β12 borophene has Dirac cones and they are well reproduced by a tight-binding model according to recent experimental and first-principles calculation results. We explicitly derive a Dirac theory for β12 borophene. Dirac cones are gapless when the inversion symmetry exists, while they are gapped when it is broken. In addition, three-band touching points emerge together with pseudospin triplet fermions when all transfer energy is equal and all onsite energy is equal. The three-band touching is slightly resolved otherwise. We construct effective three-band theories for triplet fermions. We also study the edge states of borophene nanoribbons, which show various behaviors depending on the way of edge terminations.
Confluent Crum-Darboux transformations in Dirac Hamiltonians with P T -symmetric Bragg gratings
NASA Astrophysics Data System (ADS)
Correa, Francisco; Jakubský, Vít
2017-03-01
We consider optical systems where propagation of light can be described by a Dirac-like equation with P T -symmetric Hamiltonian. In order to construct exactly solvable configurations, we extend the confluent Crum-Darboux transformation for the one-dimensional Dirac equation. The properties of the associated intertwining operators are discussed and the explicit form for higher-order transformations is presented. We utilize the results to derive a multiparametric class of exactly solvable systems where the balanced gain and loss represented by the P T -symmetric refractive index can imply localization of the electric field in the material.
Criteria of separability of the variables in the Dirac equation in gravitation fields
Andrushkevich, I.E.; Shishkin, G.V.
1987-08-01
The conditions under which the variables can be separated in the Dirac equation in gravitational fields are investigated. Rigorous theorems establish necessary and sufficient conditions for separability of the variables for a diagonal tetrad gauge. Operators that determine the dependence of the wave function on the separated variables are obtained.
Is the Composite Fermion a Dirac Particle?
NASA Astrophysics Data System (ADS)
Son, Dam Thanh
2015-07-01
We propose a particle-hole symmetric theory of the Fermi-liquid ground state of a half-filled Landau level. This theory should be applicable for a Dirac fermion in the magnetic field at charge neutrality, as well as for the ν =1/2 quantum Hall ground state of nonrelativistic fermions in the limit of negligible inter-Landau-level mixing. We argue that when particle-hole symmetry is exact, the composite fermion is a massless Dirac fermion, characterized by a Berry phase of π around the Fermi circle. We write down a tentative effective field theory of such a fermion and discuss the discrete symmetries, in particular, C P . The Dirac composite fermions interact through a gauge, but non-Chern-Simons, interaction. The particle-hole conjugate pair of Jain-sequence states at filling factors n /(2 n +1 ) and (n +1 )/(2 n +1 ) , which in the conventional composite fermion picture corresponds to integer quantum Hall states with different filling factors, n and n +1 , is now mapped to the same half-integer filling factor n +1/2 of the Dirac composite fermion. The Pfaffian and anti-Pfaffian states are interpreted as d -wave Bardeen-Cooper-Schrieffer paired states of the Dirac fermion with orbital angular momentum of opposite signs, while s -wave pairing would give rise to a particle-hole symmetric non-Abelian gapped phase. When particle-hole symmetry is not exact, the Dirac fermion has a C P -breaking mass. The conventional fermionic Chern-Simons theory is shown to emerge in the nonrelativistic limit of the massive theory.
Generalized chiral symmetry and stability of zero modes for tilted Dirac cones
NASA Astrophysics Data System (ADS)
Kawarabayashi, Tohru; Hatsugai, Yasuhiro; Morimoto, Takahiro; Aoki, Hideo
2011-04-01
While it is well known that chirality is an important symmetry for Dirac-fermion systems that gives rise to the zero-mode Landau level in graphene, here we explore whether this notion can be extended to tilted Dirac cones as encountered in organic metals. We find that there exists a “generalized chiral symmetry” that encompasses tilted Dirac cones, where a generalized chiral operator γ, satisfying γ†H+Hγ=0 for Hamiltonian H, protects the zero mode. We use this to show that the n=0 Landau level is δ-function-like (with no broadening) by extending the Aharonov-Casher argument. We confirm numerically that a lattice model that possesses generalized chirality has an anomalously sharp Landau level for spatially correlated randomness.
Spin eigen-states of Dirac equation for quasi-two-dimensional electrons
Eremko, Alexander; Brizhik, Larissa; Loktev, Vadim
2015-10-15
Dirac equation for electrons in a potential created by quantum well is solved and the three sets of the eigen-functions are obtained. In each set the wavefunction is at the same time the eigen-function of one of the three spin operators, which do not commute with each other, but do commute with the Dirac Hamiltonian. This means that the eigen-functions of Dirac equation describe three independent spin eigen-states. The energy spectrum of electrons confined by the rectangular quantum well is calculated for each of these spin states at the values of energies relevant for solid state physics. It is shown that the standard Rashba spin splitting takes place in one of such states only. In another one, 2D electron subbands remain spin degenerate, and for the third one the spin splitting is anisotropic for different directions of 2D wave vector.
Dirac equations for generalised Yang-Mills systems
NASA Astrophysics Data System (ADS)
Lechtenfeld, O.; Nahm, W.; Tchrakian, D. H.
1985-11-01
We present Dirac equations in 4 p dimensions for the generalised Yang-Mills (GYM) theories introduced earlier. These Dirac equations are related to the self-duality equations of the GYM and are checked to be elliptic in a “BPST” background. In this background these Dirac equations are integrated exactly. The possibility of imposing supersymmetry in the GYM-Dirac system is investigated, with negative results.
New routines for algebraic programming of the Dirac equation
Cotaescu, I.I.; Vulcanov, D.N.
1997-04-01
We present new procedures in the REDUCE language for algebraic programming of the Dirac equation on curved space-time. The main part of the program is a package of routines defining the Pauli and Dirac matrix algebras. Then the Dirac equation is obtained using the facilities of the EXCALC package. Finally we present some results obtained after running our procedures for the Dirac equation on several curved space-times.
Massive Dirac neutrinos and SN 1987A
NASA Technical Reports Server (NTRS)
Burrows, Adam; Gandhi, Raj; Turner, Michael S.
1992-01-01
The wrong-helicity states of a Dirac neutrino can provide an important cooling mechanism for young neutron stars. Based on numerical models of the early cooling of the neutron star associated with SN 1987A which self-consistently incorporate wrong-helicity neutrino emission, it is argued that a Dirac neutrino of mass greater than 30 keV (25 keV if it is degenerate) leads to shortening of the neutrino burst that is inconsistent with the Irvine-Michigan-Brookhaven and Kamiokande II data. If pions are as abundant as nucleons in the cores of neutron stars, the present limit improves to 15 keV.
Precise predictions for Dirac neutrino mixing
NASA Astrophysics Data System (ADS)
Abbas, Gauhar; Abyaneh, Mehran Zahiri; Srivastava, Rahul
2017-04-01
The neutrino mixing parameters are thoroughly studied using renormalization-group evolution of Dirac neutrinos with recently proposed parametrization of the neutrino mixing angles referred to as "high-scale mixing relations." The correlations among all neutrino mixing and C P violating observables are investigated. The predictions for the neutrino mixing angle θ23 are precise, and could be easily tested by ongoing and future experiments. We observe that the high-scale mixing unification hypothesis is incompatible with Dirac neutrinos due to updated experimental data.
Massive Dirac neutrinos and SN 1987A
NASA Technical Reports Server (NTRS)
Burrows, Adam; Gandhi, Raj; Turner, Michael S.
1992-01-01
The wrong-helicity states of a Dirac neutrino can provide an important cooling mechanism for young neutron stars. Based on numerical models of the early cooling of the neutron star associated with SN 1987A which self-consistently incorporate wrong-helicity neutrino emission, it is argued that a Dirac neutrino of mass greater than 30 keV (25 keV if it is degenerate) leads to shortening of the neutrino burst that is inconsistent with the Irvine-Michigan-Brookhaven and Kamiokande II data. If pions are as abundant as nucleons in the cores of neutron stars, the present limit improves to 15 keV.
Line of Dirac Nodes in Hyperhoneycomb Lattices.
Mullen, Kieran; Uchoa, Bruno; Glatzhofer, Daniel T
2015-07-10
We propose a family of structures that have "Dirac loops," closed lines of Dirac nodes in momentum space, on which the density of states vanishes linearly with energy. Those lattices all possess the planar trigonal connectivity present in graphene, but are three dimensional. We show that their highly anisotropic and multiply connected Fermi surface leads to quantized Hall conductivities in three dimensions for magnetic fields with toroidal geometry. In the presence of spin-orbit coupling, we show that those structures have topological surface states. We discuss the feasibility of realizing the structures as new allotropes of carbon.
Line of Dirac Nodes in Hyperhoneycomb Lattices
NASA Astrophysics Data System (ADS)
Mullen, Kieran; Uchoa, Bruno; Glatzhofer, Daniel T.
2015-07-01
We propose a family of structures that have "Dirac loops," closed lines of Dirac nodes in momentum space, on which the density of states vanishes linearly with energy. Those lattices all possess the planar trigonal connectivity present in graphene, but are three dimensional. We show that their highly anisotropic and multiply connected Fermi surface leads to quantized Hall conductivities in three dimensions for magnetic fields with toroidal geometry. In the presence of spin-orbit coupling, we show that those structures have topological surface states. We discuss the feasibility of realizing the structures as new allotropes of carbon.
Dirac particle tunneling from black rings
Jiang Qingquan
2008-08-15
Recent research shows that Hawking radiation can be treated as a quantum tunneling process, and Hawking temperatures of Dirac particles across the horizon of a black hole can be correctly recovered via the fermion tunneling method. In this paper, motivated by the fermion tunneling method, we attempt to apply the analysis to derive Hawking radiation of Dirac particles via tunneling from black ring solutions of 5-dimensional Einstein-Maxwell-dilaton gravity theory. Finally, it is interesting to find that, as in the black hole case, fermion tunneling can also result in correct Hawking temperatures for the rotating neutral, dipole, and charged black rings.
Kapitza-Dirac effect with traveling waves
NASA Astrophysics Data System (ADS)
Hayrapetyan, Armen G.; Grigoryan, Karen K.; Götte, Jörg B.; Petrosyan, Rubik G.
2015-08-01
We report on the possibility of diffracting electrons from light waves traveling inside a dielectric medium. We show that, in the frame of reference which moves with the group velocity of light, the traveling wave acts as a stationary diffraction grating from which electrons can diffract, similar to the conventional Kapitza-Dirac effect. To characterize the Kapitza-Dirac effect with traveling light waves, we make use of the Hamiltonian Analogy between electron optics and quantum mechanics and apply the Helmholtz-Kirchhoff theory of diffraction.
Search for Heavy Pointlike Dirac Monopoles
NASA Astrophysics Data System (ADS)
Abbott, B.; Abolins, M.; Acharya, B. S.; Adam, I.; Adams, D. L.; Adams, M.; Ahn, S.; Aihara, H.; Alves, G. A.; Amos, N.; Anderson, E. W.; Astur, R.; Baarmand, M. M.; Babukhadia, L.; Baden, A.; Balamurali, V.; Balderston, J.; Baldin, B.; Banerjee, S.; Bantly, J.; Barberis, E.; Bartlett, J. F.; Belyaev, A.; Beri, S. B.; Bertram, I.; Bezzubov, V. A.; Bhat, P. C.; Bhatnagar, V.; Bhattacharjee, M.; Biswas, N.; Blazey, G.; Blessing, S.; Bloom, P.; Boehnlein, A.; Bojko, N. I.; Borcherding, F.; Boswell, C.; Brandt, A.; Brock, R.; Bross, A.; Buchholz, D.; Burtovoi, V. S.; Butler, J. M.; Carvalho, W.; Casey, D.; Casilum, Z.; Castilla-Valdez, H.; Chakraborty, D.; Chang, S.-M.; Chekulaev, S. V.; Chen, L.-P.; Chen, W.; Choi, S.; Chopra, S.; Choudhary, B. C.; Christenson, J. H.; Chung, M.; Claes, D.; Clark, A. R.; Cobau, W. G.; Cochran, J.; Coney, L.; Cooper, W. E.; Cretsinger, C.; Cullen-Vidal, D.; Cummings, M. A.; Cutts, D.; Dahl, O. I.; Davis, K.; de, K.; del Signore, K.; Demarteau, M.; Denisov, D.; Denisov, S. P.; Diehl, H. T.; Diesburg, M.; di Loreto, G.; Draper, P.; Ducros, Y.; Dudko, L. V.; Dugad, S. R.; Edmunds, D.; Ellison, J.; Elvira, V. D.; Engelmann, R.; Eno, S.; Eppley, G.; Ermolov, P.; Eroshin, O. V.; Evdokimov, V. N.; Fahland, T.; Fatyga, M. K.; Feher, S.; Fein, D.; Ferbel, T.; Finocchiaro, G.; Fisk, H. E.; Fisyak, Y.; Flattum, E.; Forden, G. E.; Fortner, M.; Frame, K. C.; Fuess, S.; Gallas, E.; Galyaev, A. N.; Gartung, P.; Gavrilov, V.; Geld, T. L.; Genik, R. J.; Genser, K.; Gerber, C. E.; Gershtein, Y.; Gibbard, B.; Glenn, S.; Gobbi, B.; Goldschmidt, A.; Gómez, B.; Gómez, G.; Goncharov, P. I.; González Solís, J. L.; Gordon, H.; Goss, L. T.; Gounder, K.; Goussiou, A.; Graf, N.; Grannis, P. D.; Green, D. R.; Greenlee, H.; Grinstein, S.; Grudberg, P.; Grünendahl, S.; Guglielmo, G.; Guida, J. A.; Guida, J. M.; Gupta, A.; Gurzhiev, S. N.; Gutierrez, G.; Gutierrez, P.; Hadley, N. J.; Haggerty, H.; Hagopian, S.; Hagopian, V.; Hahn, K. S.; Hall, R. E.; Hanlet, P.; Hansen, S.; Hauptman, J. M.; Hedin, D.; Heinson, A. P.; Heintz, U.; Hernández-Montoya, R.; Heuring, T.; Hirosky, R.; Hobbs, J. D.; Hoeneisen, B.; Hoftun, J. S.; Hsieh, F.; Hu, Ting; Hu, Tong; Huehn, T.; Ito, A. S.; James, E.; Jaques, J.; Jerger, S. A.; Jesik, R.; Jiang, J. Z.-Y.; Joffe-Minor, T.; Johns, K.; Johnson, M.; Jonckheere, A.; Jones, M.; Jöstlein, H.; Jun, S. Y.; Jung, C. K.; Kahn, S.; Kalbfleisch, G.; Kang, J. S.; Karmanov, D.; Karmgard, D.; Kehoe, R.; Kelly, M. L.; Kim, C. L.; Kim, S. K.; Klima, B.; Klopfenstein, C.; Kohli, J. M.; Koltick, D.; Kostritskiy, A. V.; Kotcher, J.; Kotwal, A. V.; Kourlas, J.; Kozelov, A. V.; Kozlovsky, E. A.; Krane, J.; Krishnaswamy, M. R.; Krzywdzinski, S.; Kuleshov, S.; Kunori, S.; Landry, F.; Landsberg, G.; Lauer, B.; Leflat, A.; Li, H.; Li, J.; Li-Demarteau, Q. Z.; Lima, J. G.; Lincoln, D.; Linn, S. L.; Linnemann, J.; Lipton, R.; Liu, Y. C.; Lobkowicz, F.; Loken, S. C.; Lökös, S.; Lueking, L.; Lyon, A. L.; Maciel, A. K.; Madaras, R. J.; Madden, R.; Magaña-Mendoza, L.; Manankov, V.; Mani, S.; Mao, H. S.; Markeloff, R.; Marshall, T.; Martin, M. I.; Mauritz, K. M.; May, B.; Mayorov, A. A.; McCarthy, R.; McDonald, J.; McKibben, T.; McKinley, J.; McMahon, T.; Melanson, H. L.; Merkin, M.; Merritt, K. W.; Miettinen, H.; Mincer, A.; Mishra, C. S.; Mokhov, N.; Mondal, N. K.; Montgomery, H. E.; Mooney, P.; da Motta, H.; Murphy, C.; Nang, F.; Narain, M.; Narasimham, V. S.; Narayanan, A.; Neal, H. A.; Negret, J. P.; Nemethy, P.; Norman, D.; Oesch, L.; Oguri, V.; Oliveira, E.; Oltman, E.; Oshima, N.; Owen, D.; Padley, P.; Para, A.; Park, Y. M.; Partridge, R.; Parua, N.; Paterno, M.; Pawlik, B.; Perkins, J.; Peters, M.; Piegaia, R.; Piekarz, H.; Pischalnikov, Y.; Pope, B. G.; Prosper, H. B.; Protopopescu, S.; Qian, J.; Quintas, P. Z.; Raja, R.; Rajagopalan, S.; Ramirez, O.; Rasmussen, L.; Reucroft, S.; Rijssenbeek, M.; Rockwell, T.; Roco, M.; Rubinov, P.; Ruchti, R.; Rutherfoord, J.; Sánchez-Hernández, A.; Santoro, A.; Sawyer, L.; Schamberger, R. D.; Schellman, H.; Sculli, J.; Shabalina, E.; Shaffer, C.; Shankar, H. C.; Shivpuri, R. K.; Shupe, M.; Singh, H.; Singh, J. B.; Sirotenko, V.; Smart, W.; Smith, E.; Smith, R. P.; Snihur, R.; Snow, G. R.; Snow, J.; Snyder, S.; Solomon, J.; Sosebee, M.; Sotnikova, N.; Souza, M.; Spadafora, A. L.; Steinbrück, G.; Stephens, R. W.; Stevenson, M. L.; Stewart, D.; Stichelbaut, F.; Stoker, D.; Stolin, V.; Stoyanova, D. A.; Strauss, M.; Streets, K.; Strovink, M.; Sznajder, A.; Tamburello, P.; Tarazi, J.; Tartaglia, M.; Thomas, T. L.; Thompson, J.; Trippe, T. G.; Tuts, P. M.; Varelas, N.; Varnes, E. W.; Vititoe, D.; Volkov, A. A.; Vorobiev, A. P.; Wahl, H. D.; Wang, G.; Warchol, J.; Watts, G.; Wayne, M.; Weerts, H.; White, A.; White, J. T.; Wightman, J. A.; Willis, S.; Wimpenny, S. J.; Wirjawan, J. V.; Womersley, J.; Won, E.; Wood, D. R.; Xu, H.; Yamada, R.; Yamin, P.; Yang, J.; Yasuda, T.; Yepes, P.; Yoshikawa, C.; Youssef, S.; Yu, J.; Yu, Y.; Zhou, Z.; Zhu, Z. H.; Zieminska, D.; Zieminski, A.; Zverev, E. G.; Zylberstejn, A.
1998-07-01
We have searched for central production of a pair of photons with high transverse energies in pp¯ collisions at s = 1.8 TeV using 70 pb-1 of data collected with the D0 detector at the Fermilab Tevatron in 1994-1996. If they exist, virtual heavy pointlike Dirac monopoles could rescatter pairs of nearly real photons into this final state via a box diagram. We observe no excess of events above background, and set lower 95% C.L. limits of 610, 870, or 1580 GeV/c2 on the mass of a spin 0, 1/2, or 1 Dirac monopole.
Tuning Dirac points by strain in MoX2 nanoribbons (X = S, Se, Te) with a 1T' structure.
Sung, Ha-Jun; Choe, Duk-Hyun; Chang, K J
2016-06-28
For practical applications of two-dimensional topological insulators, large band gaps and Dirac states within the band gap are desirable because they allow for device operation at room temperature and quantum transport without dissipation. Based on first-principles density functional calculations, we report the tunability of the electronic structure by strain engineering in quasi-one-dimensional nanoribbons of transition metal dichalcogenides with a 1T' structure, MoX2 with X = (S, Se, Te). We find that both the band gaps and Dirac points in 1T'-MoX2 can be engineered by applying an external strain, thereby leading to a single Dirac cone within the bulk band gap. Considering the gap size and the location of the Dirac point, we suggest that, among 1T'-MoX2 nanoribbons, MoSe2 is the most suitable candidate for quantum spin Hall (QSH) devices.
Understanding Quaternions and the Dirac Belt Trick
ERIC Educational Resources Information Center
Staley, Mark
2010-01-01
The Dirac belt trick is often employed in physics classrooms to show that a 2n rotation is not topologically equivalent to the absence of rotation whereas a 4n rotation is, mirroring a key property of quaternions and their isomorphic cousins, spinors. The belt trick can leave the student wondering if a real understanding of quaternions and spinors…
Applications of Dirac's Delta Function in Statistics
ERIC Educational Resources Information Center
Khuri, Andre
2004-01-01
The Dirac delta function has been used successfully in mathematical physics for many years. The purpose of this article is to bring attention to several useful applications of this function in mathematical statistics. Some of these applications include a unified representation of the distribution of a function (or functions) of one or several…
Understanding Quaternions and the Dirac Belt Trick
ERIC Educational Resources Information Center
Staley, Mark
2010-01-01
The Dirac belt trick is often employed in physics classrooms to show that a 2n rotation is not topologically equivalent to the absence of rotation whereas a 4n rotation is, mirroring a key property of quaternions and their isomorphic cousins, spinors. The belt trick can leave the student wondering if a real understanding of quaternions and spinors…
On solvable Dirac equation with polynomial potentials
Stachowiak, Tomasz
2011-01-15
One-dimensional Dirac equation is analyzed with regard to the existence of exact (or closed-form) solutions for polynomial potentials. The notion of Liouvillian functions is used to define solvability, and it is shown that except for the linear potentials the equation in question is not solvable.
Applications of Dirac's Delta Function in Statistics
ERIC Educational Resources Information Center
Khuri, Andre
2004-01-01
The Dirac delta function has been used successfully in mathematical physics for many years. The purpose of this article is to bring attention to several useful applications of this function in mathematical statistics. Some of these applications include a unified representation of the distribution of a function (or functions) of one or several…
Emeritus trio scoops the 2013 Dirac Medal
NASA Astrophysics Data System (ADS)
Dacey, James
2013-09-01
The 2013 Dirac Medal has been awarded to three scientists whose wide-ranging work has brought profound advances in cosmology, astrophysics and fundamental physics. Thomas Kibble, James Peebles and Martin Rees all receive the honour, which is bestowed annually by the Abdus Salam International Centre for Theoretical Physics (ICTP) in Trieste, Italy.
Paul Dirac:. Building Bridges of the Mind
NASA Astrophysics Data System (ADS)
Brown, Laurie M.
2003-12-01
Paul Dirac was a brilliant and original thinker. He used his physical intuition and his ideal of mathematical beauty to construct bridges between major areas of physics. This article discusses several such important works, including the bridge between quantum mechanics and relativity that led to his prediction of the existence of antimatter.
Polymer Dirac field propagator: A model
NASA Astrophysics Data System (ADS)
García-Chung, Angel A.; Morales-Técotl, Hugo A.
2014-03-01
Polymer quantum mechanics, the mechanical analogue of the loop quantization of gravity, has been applied recently to scalar field modes yielding interesting behavior for its corresponding propagator at high, possibly Planck's, energy. Clearly other matter components are worth investigating along these lines, and thus we focus here on the Dirac field. To proceed to the polymer analysis of the Dirac field, a previous canonical analysis of its modes is advantageous. We show that this yields an energy spectrum suggesting a natural Fermi oscillator decomposition and, moreover, that both Fourier modes and Fermi oscillators lead to the corresponding free propagator in flat space-time. Finally, we advance a model entailing the polymer quantization of the Fermi oscillators that make up the Dirac field. It consists of a discrete set that replaces one of the two real anticommutative lines forming the reduced phase space of a Fermi oscillator. This is in analogy to the bosonic harmonic oscillator in which the corresponding polymer quantization involves replacing the real line by a regular lattice. The resulting polymer propagator contains as its body the standard Dirac field propagator plus soul terms involving up to second-order powers in two anticommutative parameters. Some possible physical implications are mentioned in the discussion.
Poisson geometry from a Dirac perspective
NASA Astrophysics Data System (ADS)
Meinrenken, Eckhard
2017-07-01
We present proofs of classical results in Poisson geometry using techniques from Dirac geometry. This article is based on mini-courses at the Poisson summer school in Geneva, June 2016, and at the workshop Quantum Groups and Gravity at the University of Waterloo, April 2016.
Barbier, Michaël; Vasilopoulos, Panagiotis; Peeters, François M
2010-12-13
We review the energy spectrum and transport properties of several types of one-dimensional superlattices (SLs) on single-layer and bilayer graphene. In single-layer graphene, for certain SL parameters an electron beam incident on an SL is highly collimated. On the other hand, there are extra Dirac points generated for other SL parameters. Using rectangular barriers allows us to find analytical expressions for the location of new Dirac points in the spectrum and for the renormalization of the electron velocities. The influence of these extra Dirac points on the conductivity is investigated. In the limit of δ-function barriers, the transmission T through and conductance G of a finite number of barriers as well as the energy spectra of SLs are periodic functions of the dimensionless strength P of the barriers, Pδ(x) = V(x)/ħv(F), with v(F) the Fermi velocity. For a Kronig-Penney SL with alternating sign of the height of the barriers, the Dirac point becomes a Dirac line for P = π/2+nπ with n an integer. In bilayer graphene, with an appropriate bias applied to the barriers and wells, we show that several new types of SLs are produced and two of them are similar to type I and type II semiconductor SLs. Similar to single-layer graphene SLs, extra 'Dirac' points are found in bilayer graphene SLs. Non-ballistic transport is also considered.
Identifying Dirac cones in carbon allotropes with square symmetry
Wang, Jinying; Huang, Huaqing; Duan, Wenhui; Liu, Zhirong
2013-11-14
A theoretical study is conducted to search for Dirac cones in two-dimensional carbon allotropes with square symmetry. By enumerating the carbon atoms in a unit cell up to 12, an allotrope with octatomic rings is recognized to possess Dirac cones under a simple tight-binding approach. The obtained Dirac cones are accompanied by flat bands at the Fermi level, and the resulting massless Dirac-Weyl fermions are chiral particles with a pseudospin of S = 1, rather than the conventional S = 1/2 of graphene. The spin-1 Dirac cones are also predicted to exist in hexagonal graphene antidot lattices.
Identifying Dirac cones in carbon allotropes with square symmetry.
Wang, Jinying; Huang, Huaqing; Duan, Wenhui; Liu, Zhirong
2013-11-14
A theoretical study is conducted to search for Dirac cones in two-dimensional carbon allotropes with square symmetry. By enumerating the carbon atoms in a unit cell up to 12, an allotrope with octatomic rings is recognized to possess Dirac cones under a simple tight-binding approach. The obtained Dirac cones are accompanied by flat bands at the Fermi level, and the resulting massless Dirac-Weyl fermions are chiral particles with a pseudospin of S = 1, rather than the conventional S = 1∕2 of graphene. The spin-1 Dirac cones are also predicted to exist in hexagonal graphene antidot lattices.
NASA Astrophysics Data System (ADS)
Wu, Yun; Wang, Lin-Lin; Mun, Eundeok; Johnson, D. D.; Mou, Daixiang; Huang, Lunan; Lee, Yongbin; Bud'Ko, S. L.; Canfield, P. C.; Kaminski, Adam
2016-07-01
In topological quantum materials the conduction and valence bands are connected at points or along lines in the momentum space. A number of studies have demonstrated that several materials are indeed Dirac/Weyl semimetals. However, there is still no experimental confirmation of materials with line nodes, in which the Dirac nodes form closed loops in the momentum space. Here we report the discovery of a novel topological structure--Dirac node arcs--in the ultrahigh magnetoresistive material PtSn4 using laser-based angle-resolved photoemission spectroscopy data and density functional theory calculations. Unlike the closed loops of line nodes, the Dirac node arc structure arises owing to the surface states and resembles the Dirac dispersion in graphene that is extended along a short line in the momentum space. We propose that this reported Dirac node arc structure is a novel topological state that provides an exciting platform for studying the exotic properties of Dirac fermions.
SARAH 3.2: Dirac gauginos, UFO output, and more
NASA Astrophysics Data System (ADS)
Staub, Florian
2013-07-01
SARAH is a Mathematica package optimized for the fast, efficient and precise study of supersymmetric models beyond the MSSM: a new model can be defined in a short form and all vertices are derived. This allows SARAH to create model files for FeynArts/FormCalc, CalcHep/CompHep and WHIZARD/O'Mega. The newest version of SARAH now provides the possibility to create model files in the UFO format which is supported by MadGraph 5, MadAnalysis 5, GoSam, and soon by Herwig++. Furthermore, SARAH also calculates the mass matrices, RGEs and 1-loop corrections to the mass spectrum. This information is used to write source code for SPheno in order to create a precision spectrum generator for the given model. This spectrum-generator-generator functionality as well as the output of WHIZARD and CalcHep model files has seen further improvement in this version. Also models including Dirac gauginos are supported with the new version of SARAH, and additional checks for the consistency of the implementation of new models have been created. Program summaryProgram title:SARAH Catalogue identifier: AEIB_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIB_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 3 22 411 No. of bytes in distributed program, including test data, etc.: 3 629 206 Distribution format: tar.gz Programming language: Mathematica. Computer: All for which Mathematica is available. Operating system: All for which Mathematica is available. Classification: 11.1, 11.6. Catalogue identifier of previous version: AEIB_v1_0 Journal reference of previous version: Comput. Phys. Comm. 182 (2011) 808 Does the new version supersede the previous version?: Yes, the new version includes all known features of the previous version but also provides the new features mentioned below
Plexciton Dirac points and topological modes
Yuen-Zhou, Joel; Saikin, Semion K.; Zhu, Tony; Onbasli, Mehmet C.; Ross, Caroline A.; Bulovic, Vladimir; Baldo, Marc A.
2016-06-09
Plexcitons are polaritonic modes that result from the strong coupling between excitons and plasmons. Here, we consider plexcitons emerging from the interaction of excitons in an organic molecular layer with surface plasmons in a metallic film. We predict the emergence of Dirac cones in the two-dimensional band-structure of plexcitons due to the inherent alignment of the excitonic transitions in the organic layer. An external magnetic field opens a gap between the Dirac cones if the plexciton system is interfaced with a magneto-optical layer. The resulting energy gap becomes populated with topologically protected one-way modes, which travel at the interface of this plexcitonic system. Furthermore, our theoretical proposal suggests that plexcitons are a convenient and simple platform for the exploration of exotic phases of matter and for the control of energy flow at the nanoscale.
Plexciton Dirac points and topological modes
Yuen-Zhou, Joel; Saikin, Semion K.; Zhu, Tony; ...
2016-06-09
Plexcitons are polaritonic modes that result from the strong coupling between excitons and plasmons. Here, we consider plexcitons emerging from the interaction of excitons in an organic molecular layer with surface plasmons in a metallic film. We predict the emergence of Dirac cones in the two-dimensional band-structure of plexcitons due to the inherent alignment of the excitonic transitions in the organic layer. An external magnetic field opens a gap between the Dirac cones if the plexciton system is interfaced with a magneto-optical layer. The resulting energy gap becomes populated with topologically protected one-way modes, which travel at the interface ofmore » this plexcitonic system. Furthermore, our theoretical proposal suggests that plexcitons are a convenient and simple platform for the exploration of exotic phases of matter and for the control of energy flow at the nanoscale.« less
Classical electromagnetic radiation of the Dirac electron
NASA Technical Reports Server (NTRS)
Lanyi, G.
1973-01-01
A wave-function-dependent four-vector potential is added to the Dirac equation in order to achieve conservation of energy and momentum for a Dirac electron and its emitted electromagnetic field. The resultant equation contains solutions which describe transitions between different energy states of the electron. As a consequence it is possible to follow the space-time evolution of such a process. This evolution is shown in the case of the spontaneous emission of an electromagnetic field by an electron bound in a hydrogen-like atom. The intensity of the radiation and the spectral distribution are calculated for transitions between two eigenstates. The theory gives a self-consistent deterministic description of some simple radiation processes without using quantum electrodynamics or the correspondence principle.
Chiral Scars in Chaotic Dirac Fermion Systems
NASA Astrophysics Data System (ADS)
Xu, Hongya; Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso
2013-02-01
Do relativistic quantum scars in classically chaotic systems possess unique features that are not shared by nonrelativistic quantum scars? We report a class of relativistic quantum scars in massless Dirac fermion systems whose phases return to the original values or acquire a 2π change only after circulating twice about some classical unstable periodic orbits. We name such scars chiral scars, the successful identification of which has been facilitated tremendously by our development of an analytic, conformal-mapping-based method to calculate an unprecedentedly large number of eigenstates with high accuracy. Our semiclassical theory indicates that the physical origin of chiral scars can be attributed to a combined effect of chirality intrinsic to massless Dirac fermions and the geometry of the underlying classical orbit.
Topological Dirac line nodes in centrosymmetric semimetals
NASA Astrophysics Data System (ADS)
Kim, Youngkuk; Wieder, Benjamin; Kane, Charles; Rappe, Andrew; TI seed Team
Dirac line nodes (DLNs) are one-dimensional lines of Dirac band-touching points, characterized by linear dispersion in only a single direction in momentum space. In the presence of inversion symmetry and time-reversal symmetry, crystals with vanishing spin-orbit coupling can host topologically protected DLNs. Recently, we have proposed and characterized a novel Z2 class of DLN semimetals [1]. We present Z2 topological invariants, dictating the presence of DLNs, based on the parity eigenvalues at the time-reversal invariant crystal momenta. Our first-principles calculations show that DLNs can be realized in Cu3N in an anti-ReO3 structure via a metal-insulator electronic transition, driven by transition metal doping. We also discuss the resultant surface states and the effects of spin-orbit coupling.
Plexciton Dirac points and topological modes
NASA Astrophysics Data System (ADS)
Yuen-Zhou, Joel; Saikin, Semion K.; Zhu, Tony; Onbasli, Mehmet C.; Ross, Caroline A.; Bulovic, Vladimir; Baldo, Marc A.
2016-06-01
Plexcitons are polaritonic modes that result from the strong coupling between excitons and plasmons. Here, we consider plexcitons emerging from the interaction of excitons in an organic molecular layer with surface plasmons in a metallic film. We predict the emergence of Dirac cones in the two-dimensional band-structure of plexcitons due to the inherent alignment of the excitonic transitions in the organic layer. An external magnetic field opens a gap between the Dirac cones if the plexciton system is interfaced with a magneto-optical layer. The resulting energy gap becomes populated with topologically protected one-way modes, which travel at the interface of this plexcitonic system. Our theoretical proposal suggests that plexcitons are a convenient and simple platform for the exploration of exotic phases of matter and for the control of energy flow at the nanoscale.
Plexciton Dirac points and topological modes.
Yuen-Zhou, Joel; Saikin, Semion K; Zhu, Tony; Onbasli, Mehmet C; Ross, Caroline A; Bulovic, Vladimir; Baldo, Marc A
2016-06-09
Plexcitons are polaritonic modes that result from the strong coupling between excitons and plasmons. Here, we consider plexcitons emerging from the interaction of excitons in an organic molecular layer with surface plasmons in a metallic film. We predict the emergence of Dirac cones in the two-dimensional band-structure of plexcitons due to the inherent alignment of the excitonic transitions in the organic layer. An external magnetic field opens a gap between the Dirac cones if the plexciton system is interfaced with a magneto-optical layer. The resulting energy gap becomes populated with topologically protected one-way modes, which travel at the interface of this plexcitonic system. Our theoretical proposal suggests that plexcitons are a convenient and simple platform for the exploration of exotic phases of matter and for the control of energy flow at the nanoscale.
Plexciton Dirac points and topological modes
Yuen-Zhou, Joel; Saikin, Semion K.; Zhu, Tony; Onbasli, Mehmet C.; Ross, Caroline A.; Bulovic, Vladimir; Baldo, Marc A.
2016-01-01
Plexcitons are polaritonic modes that result from the strong coupling between excitons and plasmons. Here, we consider plexcitons emerging from the interaction of excitons in an organic molecular layer with surface plasmons in a metallic film. We predict the emergence of Dirac cones in the two-dimensional band-structure of plexcitons due to the inherent alignment of the excitonic transitions in the organic layer. An external magnetic field opens a gap between the Dirac cones if the plexciton system is interfaced with a magneto-optical layer. The resulting energy gap becomes populated with topologically protected one-way modes, which travel at the interface of this plexcitonic system. Our theoretical proposal suggests that plexcitons are a convenient and simple platform for the exploration of exotic phases of matter and for the control of energy flow at the nanoscale. PMID:27278258
Classical electromagnetic radiation of the Dirac electron
NASA Technical Reports Server (NTRS)
Lanyi, G.
1973-01-01
A wave-function-dependent four-vector potential is added to the Dirac equation in order to achieve conservation of energy and momentum for a Dirac electron and its emitted electromagnetic field. The resultant equation contains solutions which describe transitions between different energy states of the electron. As a consequence it is possible to follow the space-time evolution of such a process. This evolution is shown in the case of the spontaneous emission of an electromagnetic field by an electron bound in a hydrogen-like atom. The intensity of the radiation and the spectral distribution are calculated for transitions between two eigenstates. The theory gives a self-consistent deterministic description of some simple radiation processes without using quantum electrodynamics or the correspondence principle.
Plexciton Dirac points and topological modes
Yuen-Zhou, Joel; Saikin, Semion K.; Zhu, Tony; Onbasli, Mehmet C.; Ross, Caroline A.; Bulovic, Vladimir; Baldo, Marc A.
2016-06-09
Plexcitons are polaritonic modes that result from the strong coupling between excitons and plasmons. Here, we consider plexcitons emerging from the interaction of excitons in an organic molecular layer with surface plasmons in a metallic film. We predict the emergence of Dirac cones in the two-dimensional band-structure of plexcitons due to the inherent alignment of the excitonic transitions in the organic layer. An external magnetic field opens a gap between the Dirac cones if the plexciton system is interfaced with a magneto-optical layer. The resulting energy gap becomes populated with topologically protected one-way modes, which travel at the interface of this plexcitonic system. Our theoretical proposal suggests that plexcitons are a convenient and simple platform for the exploration of exotic phases of matter and for the control of energy flow at the nanoscale.
Double Dirac point in a photonic graphene
NASA Astrophysics Data System (ADS)
Qiu, Pingping; Qiu, Weibin; Lin, Zhili; Chen, Houbo; Ren, Junbo; Wang, Jia-Xian; Kan, Qiang; Pan, Jiao-Qing
2017-08-01
The band structure of the photonic graphene composed of an array of dielectric cylinders in air with honeycomb lattice is computed in this work. The results reveal that there is a double Dirac point at the Brillouin zone center with a frequency of 0.870 61c/a in our proposed photonic graphene structure. By using average eigen-field calculation, we demonstrate that such a photonic graphene structure possesses both zero effective permittivity and effective permeability, which implied that this structure can serve as zero-index medium. Furthermore, applications including focusing, multidirectional emission and super-coupling are numerically demonstrated with the proposed structure at the double Dirac point frequency, which further conformed the zero-index properties of the photonic graphene structure.
Dirac gauginos in low scale supersymmetry breaking
NASA Astrophysics Data System (ADS)
Goodsell, Mark D.; Tziveloglou, Pantelis
2014-12-01
It has been claimed that Dirac gaugino masses are necessary for realistic models of low-scale supersymmetry breaking, and yet very little attention has been paid to the phenomenology of a light gravitino when gauginos have Dirac masses. We begin to address this deficit by investigating the couplings and phenomenology of the gravitino in the effective Lagrangian approach. We pay particular attention to the phenomenology of the scalar octets, where new decay channels open up. This leads us to propose a new simplified effective scenario including only light gluinos, sgluons and gravitinos, allowing the squarks to be heavy - with the possible exception of the third generation. Finally, we comment on the application of our results to Fake Split Supersymmetry.
Pseudoclassical description of the Dirac Oscillator
NASA Technical Reports Server (NTRS)
Delsolmesa, Antonio; Martinezyromero, R. P.
1995-01-01
In this paper we discuss the Dirac Oscillator wave equation in terms of pseudoclassical language, using Grassmann variables to describe the internal degrees of freedom of the oscillator. Regarding the original wave equation as a classical constraint, we use the theory of constrained systems, to develop a reparameterization invariant lagrangian, which is the pseudoclassical equivalent of the quantum case. The consistency of the Hamiltonian formalism and the quantization procedure are also analyzed.
Dirac particle in a pseudoscalar potential
Moreno, M.; Zentella-Dehesa, A.
1996-02-01
We study the problem of a Dirac particle with a pseudoscalar interaction in the potential approximation. It is shown how nonperturbative relativistic solutions arise. The case of the central pseudoscalar potential is explicitly worked out also in a closed form. The angular functions are worked out in general for this central case. Finally for the special case of the spherical well the radial solutions are shown to behave like Bessel-type functions. {copyright} {ital 1996 American Institute of Physics.}
Dirac particle in a pseudoscalar potential
Moreno, Matias; Zentella-Dehesa, Arturo
1996-02-20
We study the problem of a Dirac particle with a pseudoscalar interaction in the potential approximation. It is shown how nonperturbative relativistic solutions arise. The case of the central pseudoscalar potential is explicitly worked out also in a closed form. The angular functions are worked out in general for this central case. Finally for the special case of the spherical well the radial solutions are shown to behave like Bessel-type functions.
Photonic realization of the relativistic Dirac oscillator.
Longhi, S
2010-04-15
A photonic realization of the Dirac oscillator (DO), i.e., of the relativistic extension of the quantum harmonic oscillator, is proposed for light propagation in fiber Bragg gratings. Transmission spectra clearly show the existence of electron and positron bound states of the DO, corresponding to resonance modes above and below the Bragg frequency, as well as the asymmetry of the energy spectrum for electron and positron branches.
First Integrals, Liouville Theorem, and Dirac Brackets
NASA Astrophysics Data System (ADS)
Gleria, Iram; Filho, Tarcísio M. Rocha; Figueiredo Neto, Annibal D.; Vianna, José David M.
2017-08-01
In this paper, we discuss the conditions for the existence of first integrals of movement and the Liouville theorem on integrable systems. We revise the core results of the Hamilton-Jacobi theory and discuss the extension of the formalism to encompass constrained systems using Dirac brackets, originally developed in the context of the canonical quantization of constrained systems. As an application, we analyze a Hamiltonian that represents the classical limit of a Fermionic system of oscillators.
Manipulation of Dirac Cones in Mechanical Graphene
Kariyado, Toshikaze; Hatsugai, Yasuhiro
2015-01-01
Recently, quantum Hall state analogs in classical mechanics attract much attention from topological points of view. Topology is not only for mathematicians but also quite useful in a quantum world. Further it even governs the Newton’s law of motion. One of the advantages of classical systems over solid state materials is its clear controllability. Here we investigate mechanical graphene, which is a spring-mass model with the honeycomb structure as a typical mechanical model with nontrivial topological phenomena. The vibration spectrum of mechanical graphene is characterized by Dirac cones serving as sources of topological nontriviality. We find that the spectrum has dramatic dependence on the spring tension at equilibrium as a natural control parameter, i.e., creation and annihilation of the Dirac particles are realized as the tension increases. Just by rotating the system, the manipulated Dirac particles lead to topological transition, i.e., a jump of the “Chern number” occurs associated with flipping of propagating direction of chiral edge modes. This is a bulk-edge correspondence governed by the Newton’s law. A simple observation that in-gap edge modes exist only at the fixed boundary, but not at the free one, is attributed to the symmetry protection of topological phases. PMID:26667580
Manipulation of Dirac Cones in Mechanical Graphene
NASA Astrophysics Data System (ADS)
Kariyado, Toshikaze; Hatsugai, Yasuhiro
2015-12-01
Recently, quantum Hall state analogs in classical mechanics attract much attention from topological points of view. Topology is not only for mathematicians but also quite useful in a quantum world. Further it even governs the Newton’s law of motion. One of the advantages of classical systems over solid state materials is its clear controllability. Here we investigate mechanical graphene, which is a spring-mass model with the honeycomb structure as a typical mechanical model with nontrivial topological phenomena. The vibration spectrum of mechanical graphene is characterized by Dirac cones serving as sources of topological nontriviality. We find that the spectrum has dramatic dependence on the spring tension at equilibrium as a natural control parameter, i.e., creation and annihilation of the Dirac particles are realized as the tension increases. Just by rotating the system, the manipulated Dirac particles lead to topological transition, i.e., a jump of the “Chern number” occurs associated with flipping of propagating direction of chiral edge modes. This is a bulk-edge correspondence governed by the Newton’s law. A simple observation that in-gap edge modes exist only at the fixed boundary, but not at the free one, is attributed to the symmetry protection of topological phases.
Quantum transport through 3D Dirac materials
Salehi, M.; Jafari, S.A.
2015-08-15
Bismuth and its alloys provide a paradigm to realize three dimensional materials whose low-energy effective theory is given by Dirac equation in 3+1 dimensions. We study the quantum transport properties of three dimensional Dirac materials within the framework of Landauer–Büttiker formalism. Charge carriers in normal metal satisfying the Schrödinger equation, can be split into four-component with appropriate matching conditions at the boundary with the three dimensional Dirac material (3DDM). We calculate the conductance and the Fano factor of an interface separating 3DDM from a normal metal, as well as the conductance through a slab of 3DDM. Under certain circumstances the 3DDM appears transparent to electrons hitting the 3DDM. We find that electrons hitting the metal-3DDM interface from metallic side can enter 3DDM in a reversed spin state as soon as their angle of incidence deviates from the direction perpendicular to interface. However the presence of a second interface completely cancels this effect.
Manipulation of Dirac Cones in Mechanical Graphene.
Kariyado, Toshikaze; Hatsugai, Yasuhiro
2015-12-15
Recently, quantum Hall state analogs in classical mechanics attract much attention from topological points of view. Topology is not only for mathematicians but also quite useful in a quantum world. Further it even governs the Newton's law of motion. One of the advantages of classical systems over solid state materials is its clear controllability. Here we investigate mechanical graphene, which is a spring-mass model with the honeycomb structure as a typical mechanical model with nontrivial topological phenomena. The vibration spectrum of mechanical graphene is characterized by Dirac cones serving as sources of topological nontriviality. We find that the spectrum has dramatic dependence on the spring tension at equilibrium as a natural control parameter, i.e., creation and annihilation of the Dirac particles are realized as the tension increases. Just by rotating the system, the manipulated Dirac particles lead to topological transition, i.e., a jump of the "Chern number" occurs associated with flipping of propagating direction of chiral edge modes. This is a bulk-edge correspondence governed by the Newton's law. A simple observation that in-gap edge modes exist only at the fixed boundary, but not at the free one, is attributed to the symmetry protection of topological phases.
The Integration of CloudStack and OCCI/OpenNebula with DIRAC
NASA Astrophysics Data System (ADS)
Méndez Muñoz, Víctor; Fernández Albor, Víctor; Graciani Diaz, Ricardo; Casajús Ramo, Adriàn; Fernández Pena, Tomás; Merino Arévalo, Gonzalo; José Saborido Silva, Juan
2012-12-01
The increasing availability of Cloud resources is arising as a realistic alternative to the Grid as a paradigm for enabling scientific communities to access large distributed computing resources. The DIRAC framework for distributed computing is an easy way to efficiently access to resources from both systems. This paper explains the integration of DIRAC with two open-source Cloud Managers: OpenNebula (taking advantage of the OCCI standard) and CloudStack. These are computing tools to manage the complexity and heterogeneity of distributed data center infrastructures, allowing to create virtual clusters on demand, including public, private and hybrid clouds. This approach has required to develop an extension to the previous DIRAC Virtual Machine engine, which was developed for Amazon EC2, allowing the connection with these new cloud managers. In the OpenNebula case, the development has been based on the CernVM Virtual Software Appliance with appropriate contextualization, while in the case of CloudStack, the infrastructure has been kept more general, which permits other Virtual Machine sources and operating systems being used. In both cases, CernVM File System has been used to facilitate software distribution to the computing nodes. With the resulting infrastructure, the cloud resources are transparent to the users through a friendly interface, like the DIRAC Web Portal. The main purpose of this integration is to get a system that can manage cloud and grid resources at the same time. This particular feature pushes DIRAC to a new conceptual denomination as interware, integrating different middleware. Users from different communities do not need to care about the installation of the standard software that is available at the nodes, nor the operating system of the host machine which is transparent to the user. This paper presents an analysis of the overhead of the virtual layer, doing some tests to compare the proposed approach with the existing Grid solution. License
QED2+1 in Graphene: Symmetries of Dirac Equation in 2+1 Dimensions
NASA Astrophysics Data System (ADS)
Kosiński, P.; Maślanka, P.; S´nska, J.; Zasada, I.
2012-10-01
It is well-known that the tight-binding Hamiltonian of graphene describes the low-energy excitations that appear to be massless chiral Dirac fermions. Thus, in the continuum limit one can analyze the crystal properties using the formalism of quantum electrodynamics in 2+1 dimensions (QED_{2+1}) which provides the opportunity to verify the high energy physics phenomena in the condensed matter system. We study the symmetry properties of 2+1-dimensional Dirac equation, both in the noninteracting case and in the case with constant uniform magnetic field included in the model. The maximal symmetry group of the massless Dirac equation is considered by putting it in the Jordan block form and determining the algebra of operators leaving invariant the subspace of solutions. It is shown that the resulting symmetry operators expressed in terms of Dirac matrices cannot be described exclusively in terms of γ matrices (and their products) entering the corresponding Dirac equation. It is a consequence of the reducibility of the considered representation in contrast to the 3+1-dimensional case. Symmetry algebra is demonstrated to be a direct sum of two gL(2,C) algebras plus an eight-dimensional abelian ideal. Since the matrix structure which determines the rotational symmetry has all required properties of the spin algebra, the pseudospin related to the sublattices (M. Mecklenburg and B. C. Regan, Phys. Rev. Lett. 106 (2011), 116803) gains the character of the real angular momentum, although the degrees of freedom connected with the electron's spin are not included in the model. This seems to be graphene's analogue of the phenomenon called ``spin from isospin'' in high energy physics.
He, Junjie; Li, Xiao; Lyu, Pengbo; Nachtigall, Petr
2017-02-09
A great obstacle for practical applications of the quantum anomalous Hall (QAH) effect is the lack of suitable QAH materials (Chern insulators) with a large non-trivial band gap, room-temperature magnetic order and high carrier mobility. Based on first-principles calculations it is shown here that a nickel chloride (NiCl3) monolayer has all these characteristics. Thus, the NiCl3 monolayer represents a new class of Dirac materials with Dirac spin-gapless semiconducting properties and high-temperature ferromagnetism (∼400 K). Taking into account the spin-orbit coupling, the NiCl3 monolayer becomes an intrinsic Chern insulator with a large non-trivial band gap of ∼24 meV, corresponding to an operating temperature as high as ∼280 K at which the quantum anomalous Hall effect could be observed. The calculated large non-trivial gap, high Curie temperature and single-spin Dirac states reported herein for the NiCl3 monolayer led us to propose that this material gives a great promise for potential realization of a near-room temperature QAH effect and potential applications in spintronics. Last but not least the calculated Fermi velocities of Dirac fermions of about 4 × 10(5) m s(-1) indicate very high mobility in NiCl3 monolayers.
Lattice Dirac fermions on a simplicial Riemannian manifold
NASA Astrophysics Data System (ADS)
Brower, Richard C.; Weinberg, Evan S.; Fleming, George T.; Gasbarro, Andrew D.; Raben, Timothy G.; Tan, Chung-I.
2017-06-01
The lattice Dirac equation is formulated on a simplicial complex which approximates a smooth Riemann manifold by introducing a lattice vierbein on each site and a lattice spin connection on each link. Care is taken so the construction applies to any smooth D-dimensional Riemannian manifold that permits a spin connection. It is tested numerically in 2D for the projective sphere S2 in the limit of an increasingly refined sequence of triangles. The eigenspectrum and eigenvectors are shown to converge rapidly to the exact result in the continuum limit. In addition comparison is made with the continuum Ising conformal field theory on S2. Convergence is tested for the two point, ⟨ɛ (x1)ɛ (x2)⟩, and the four point, ⟨σ (x1)ɛ (x2)ɛ (x3)σ (x4)⟩, correlators for the energy, ɛ (x )=i ψ ¯(x )ψ (x ), and twist operators, σ (x ), respectively.
Type-II Symmetry-Protected Topological Dirac Semimetals.
Chang, Tay-Rong; Xu, Su-Yang; Sanchez, Daniel S; Tsai, Wei-Feng; Huang, Shin-Ming; Chang, Guoqing; Hsu, Chuang-Han; Bian, Guang; Belopolski, Ilya; Yu, Zhi-Ming; Yang, Shengyuan A; Neupert, Titus; Jeng, Horng-Tay; Lin, Hsin; Hasan, M Zahid
2017-07-14
The recent proposal of the type-II Weyl semimetal state has attracted significant interest. In this Letter, we propose the concept of the three-dimensional type-II Dirac fermion and theoretically identify this new symmetry-protected topological state in the large family of transition-metal icosagenides, MA_{3} (M=V, Nb, Ta; A=Al, Ga, In). We show that the VAl_{3} family features a pair of strongly Lorentz-violating type-II Dirac nodes and that each Dirac node can be split into four type-II Weyl nodes with chiral charge ±1 via symmetry breaking. Furthermore, we predict that the Landau level spectrum arising from the type-II Dirac fermions in VAl_{3} is distinct from that of known Dirac or Weyl semimetals. We also demonstrate a topological phase transition from a type-II Dirac semimetal to a quadratic Weyl semimetal or a topological crystalline insulator via crystalline distortions.
Pseudo-Dirac dark matter leaves a trace.
De Simone, Andrea; Sanz, Veronica; Sato, Hiromitsu Phil
2010-09-17
Pseudo-Dirac dark matter is a viable type of dark matter which originates from a new Dirac fermion whose two Weyl states get slightly split in mass by a small Majorana term. The decay of the heavier to the lighter state naturally occurs over a detectable length scale. Thus, whenever pseudo-Dirac dark matter is produced in a collider, it leaves a clear trace: a visible displaced vertex in association with missing energy. Moreover, pseudo-Dirac dark matter behaves Dirac-like for relic abundance and Majorana-like in direct detection experiments. We provide a general effective field theory treatment, specializing to a pseudo-Dirac bino. The dark matter mass and the mass splitting can be extracted from measurements of the decay length and the invariant mass of the products, even in the presence of missing energy.
Type-II Symmetry-Protected Topological Dirac Semimetals
NASA Astrophysics Data System (ADS)
Chang, Tay-Rong; Xu, Su-Yang; Sanchez, Daniel S.; Tsai, Wei-Feng; Huang, Shin-Ming; Chang, Guoqing; Hsu, Chuang-Han; Bian, Guang; Belopolski, Ilya; Yu, Zhi-Ming; Yang, Shengyuan A.; Neupert, Titus; Jeng, Horng-Tay; Lin, Hsin; Hasan, M. Zahid
2017-07-01
The recent proposal of the type-II Weyl semimetal state has attracted significant interest. In this Letter, we propose the concept of the three-dimensional type-II Dirac fermion and theoretically identify this new symmetry-protected topological state in the large family of transition-metal icosagenides, M A3 (M =V , Nb, Ta; A =Al , Ga, In). We show that the VAl3 family features a pair of strongly Lorentz-violating type-II Dirac nodes and that each Dirac node can be split into four type-II Weyl nodes with chiral charge ±1 via symmetry breaking. Furthermore, we predict that the Landau level spectrum arising from the type-II Dirac fermions in VAl3 is distinct from that of known Dirac or Weyl semimetals. We also demonstrate a topological phase transition from a type-II Dirac semimetal to a quadratic Weyl semimetal or a topological crystalline insulator via crystalline distortions.
Integrated optical Dirac physics via inversion symmetry breaking
NASA Astrophysics Data System (ADS)
Collins, Matthew J.; Zhang, Fan; Bojko, Richard; Chrostowski, Lukas; Rechtsman, Mikael C.
2016-12-01
Graphene and boron nitride are two-dimensional materials whose atoms are arranged in a honeycomb lattice. Their unique properties arise because their electrons behave like relativistic particles (without and with mass, respectively)—namely, they obey the Dirac equation. Here, we use a photonic analog of boron nitride to observe Dirac physics in a silicon integrated optical platform. This will allow for photonic applications of Dirac dispersions (gapped and ungapped) to be realized in an on-chip, integrated nanophotonic platform.
Dirac neutrinos and dark matter stability from lepton quarticity
NASA Astrophysics Data System (ADS)
Centelles Chuliá, Salvador; Ma, Ernest; Srivastava, Rahul; Valle, José W. F.
2017-04-01
We propose to relate dark matter stability to the possible Dirac nature of neutrinos. The idea is illustrated in a simple scheme where small Dirac neutrino masses arise from a type-I seesaw mechanism as a result of a Z4 discrete lepton number symmetry. The latter implies the existence of a viable WIMP dark matter candidate, whose stability arises from the same symmetry which ensures the Diracness of neutrinos.
Note on Generalized Fermi-Dirac Function and Its Derivatives
NASA Astrophysics Data System (ADS)
Gong, Zhigang; Zejda, Ladislav; Däppen, Werner
2000-04-01
Generalized Fermi-Dirac function and its derivatives are important in evaluating the thermodynamic functions of partially degenerate electrons in hot stellar plasmas. Because of the nature of the Fermi-Dirac functions, analytic expressions are only available for certain extreme cases, and regular numeric methods fail when degeneracy and temperature are relatively high (but not high enough to use approximative formulae). In this paper, recursion relations of the generalized Fermi-Dirac function are discussed, and an effective numerical method to evaluate the derivatives of the generalized Fermi-Dirac function is given, following the Aparicio (1998) scheme. Finally, accuracy and domain of reliability of some popular analytic approximations are investigated.
Orbital magnetization of interacting Dirac fermions in graphene
NASA Astrophysics Data System (ADS)
Yan, Xin-Zhong; Ting, C. S.
2017-09-01
We present a formalism to calculate the orbital magnetization of interacting Dirac fermions under a magnetic field. In this approach, the divergence difficulty is overcome with a special limit of the derivative of the thermodynamic potential with respect to the magnetic field. The formalism satisfies the particle-hole symmetry of the Dirac fermions system. We apply the formalism to the interacting Dirac fermions in graphene. The charge and spin orderings and the exchange interactions between all the Landau levels are taken into account by the mean-field theory. The results for the orbital magnetization of interacting Dirac fermions are compared with that of noninteracting cases.
Quasiparticle dynamics in reshaped helical Dirac cone of topological insulators.
Miao, Lin; Wang, Z F; Ming, Wenmei; Yao, Meng-Yu; Wang, Meixiao; Yang, Fang; Song, Y R; Zhu, Fengfeng; Fedorov, Alexei V; Sun, Z; Gao, C L; Liu, Canhua; Xue, Qi-Kun; Liu, Chao-Xing; Liu, Feng; Qian, Dong; Jia, Jin-Feng
2013-02-19
Topological insulators and graphene present two unique classes of materials, which are characterized by spin-polarized (helical) and nonpolarized Dirac cone band structures, respectively. The importance of many-body interactions that renormalize the linear bands near Dirac point in graphene has been well recognized and attracted much recent attention. However, renormalization of the helical Dirac point has not been observed in topological insulators. Here, we report the experimental observation of the renormalized quasiparticle spectrum with a skewed Dirac cone in a single Bi bilayer grown on Bi(2)Te(3) substrate from angle-resolved photoemission spectroscopy. First-principles band calculations indicate that the quasiparticle spectra are likely associated with the hybridization between the extrinsic substrate-induced Dirac states of Bi bilayer and the intrinsic surface Dirac states of Bi(2)Te(3) film at close energy proximity. Without such hybridization, only single-particle Dirac spectra are observed in a single Bi bilayer grown on Bi(2)Se(3), where the extrinsic Dirac states Bi bilayer and the intrinsic Dirac states of Bi(2)Se(3) are well separated in energy. The possible origins of many-body interactions are discussed. Our findings provide a means to manipulate topological surface states.
Quasiparticle dynamics in reshaped helical Dirac cone of topological insulators
Miao, Lin; Wang, Z. F.; Ming, Wenmei; Yao, Meng-Yu; Wang, Meixiao; Yang, Fang; Song, Y. R.; Zhu, Fengfeng; Fedorov, Alexei V.; Sun, Z.; Gao, C. L.; Liu, Canhua; Xue, Qi-Kun; Liu, Chao-Xing; Liu, Feng; Qian, Dong; Jia, Jin-Feng
2013-01-01
Topological insulators and graphene present two unique classes of materials, which are characterized by spin-polarized (helical) and nonpolarized Dirac cone band structures, respectively. The importance of many-body interactions that renormalize the linear bands near Dirac point in graphene has been well recognized and attracted much recent attention. However, renormalization of the helical Dirac point has not been observed in topological insulators. Here, we report the experimental observation of the renormalized quasiparticle spectrum with a skewed Dirac cone in a single Bi bilayer grown on Bi2Te3 substrate from angle-resolved photoemission spectroscopy. First-principles band calculations indicate that the quasiparticle spectra are likely associated with the hybridization between the extrinsic substrate-induced Dirac states of Bi bilayer and the intrinsic surface Dirac states of Bi2Te3 film at close energy proximity. Without such hybridization, only single-particle Dirac spectra are observed in a single Bi bilayer grown on Bi2Se3, where the extrinsic Dirac states Bi bilayer and the intrinsic Dirac states of Bi2Se3 are well separated in energy. The possible origins of many-body interactions are discussed. Our findings provide a means to manipulate topological surface states. PMID:23382185
Klein tunneling and Dirac potentials in trapped ions
Casanova, J.; Garcia-Ripoll, J. J.; Gerritsma, R.; Roos, C. F.; Solano, E.
2010-08-15
We propose the quantum simulation of the Dirac equation with potentials, allowing the study of relativistic scattering and Klein tunneling. This quantum relativistic effect permits a positive-energy Dirac particle to propagate through a repulsive potential via the population transfer to negative-energy components. We show how to engineer scalar, pseudoscalar, and other potentials in the 1+1 Dirac equation by manipulating two trapped ions. The Dirac spinor is represented by the internal states of one ion, while its position and momentum are described by those of a collective motional mode. The second ion is used to build the desired potentials with high spatial resolution.
Configurable Dirac-like conical dispersions in complex photonic crystals
NASA Astrophysics Data System (ADS)
Xu, Changqing; Lai, Yun
2017-01-01
We investigate Dirac-like conical dispersions in photonic crystals with complex unit cells. Comparing with photonic crystals with simple unit cells, the complex-unit-cell design can provide extra degrees of freedom to engineer the frequency of the Dirac-like point in a broad frequency regime. Interestingly, we find that many functionalities of double zero media associated with the Dirac-like point are well preserved in such complex photonic crystals, such as wave tunneling, cloaking, wave front control, etc. Different transmission behaviors, e.g., total reflection and negative refraction, can be achieved by shifting the frequency of the Dirac-like point.
Unpaired Dirac cones in photonic lattices and networks (Conference Presentation)
NASA Astrophysics Data System (ADS)
Chong, Yidong; Leykam, Daniel; Rechtsman, Mikael C.
2016-09-01
Unpaired Dirac cones are bandstructures with two bands crossing at a single point in the Brillouin zone. It is known that photonic bandstructures can exhibit pairs of Dirac cones, similar to graphene; unpaired cones, however, have not observed in photonics, and have been observed in condensed-matter systems only among topological insulator surface states. We show that unpaired Dirac cones occur in a 2D photonic lattice that is not the surface of a 3D system. These modes have unusual properties, including conical diffraction and antilocalization immune to short-range disorder, due to the absence of "intervalley" scattering between Dirac cones.
Prototype of a production system for Cherenkov Telescope Array with DIRAC
NASA Astrophysics Data System (ADS)
Arrabito, L.; Bregeon, J.; Haupt, A.; Graciani Diaz,
2015-12-01
The Cherenkov Telescope Array (CTA) — an array of many tens of Imaging Atmospheric Cherenkov Telescopes deployed on an unprecedented scale — is the next generation instrument in the field of very high energy gamma-ray astronomy. CTA will operate as an open observatory providing data products to the scientific community. An average data stream of about 10 GB/s for about 1000 hours of observation per year, thus producing several PB/year, is expected. Large CPU time is required for data-processing as well for massive Monte Carlo simulations needed for detector calibration purposes. The current CTA computing model is based on a distributed infrastructure for the archive and the data off-line processing. In order to manage the off-line data-processing in a distributed environment, CTA has evaluated the DIRAC (Distributed Infrastructure with Remote Agent Control) system, which is a general framework for the management of tasks over distributed heterogeneous computing environments. In particular, a production system prototype has been developed, based on the two main DIRAC components, i.e. the Workload Management and Data Management Systems. After three years of successful exploitation of this prototype, for simulations and analysis, we proved that DIRAC provides suitable functionalities needed for the CTA data processing. Based on these results, the CTA development plan aims to achieve an operational production system, based on the DIRAC Workload Management System, to be ready for the start of CTA operation phase in 2017-2018. One more important challenge consists of the development of a fully automatized execution of the CTA workflows. For this purpose, we have identified a third DIRAC component, the so-called Transformation System, which offers very interesting functionalities to achieve this automatisation. The Transformation System is a ’data-driven’ system, allowing to automatically trigger data-processing and data management operations according to pre
Algorithm for the solution of the Dirac equation on digital quantum computers
NASA Astrophysics Data System (ADS)
Fillion-Gourdeau, François; MacLean, Steve; Laflamme, Raymond
2017-04-01
A quantum algorithm that solves the time-dependent Dirac equation on a digital quantum computer is developed and analyzed. The time evolution is performed by an operator-splitting decomposition technique that allows for a mapping of the Dirac operator to a quantum walk supplemented by unitary rotation steps in spinor space. Every step of the splitting method is decomposed into sets of quantum gates. It is demonstrated that the algorithm has an exponential speed-up over the implementation of the same numerical scheme on a classical computer, as long as certain conditions are satisfied. Finally, an explicit decomposition of this algorithm into elementary gates from a universal set is carried out to determine the resource requirements. It is shown that a proof-of-principle calculation may be possible with actual quantum technologies.
Hawking radiation for Dirac spinors on the RP{sup 3} geon
Langlois, Paul
2004-11-15
We analyze the Hawking(-Unruh) effect for a massive Dirac spinor on the Z{sub 2} quotient of Kruskal spacetime known as the RP{sup 3} geon. There are two distinct Hartle-Hawking-like vacua, depending on the choice of the spin structure, and suitable measurements in the static region (which on its own has only one spin structure) distinguish these two vacua. However, both vacua appear thermal in the usual Hawking temperature to certain types of restricted operators, including operators with support in the asymptotic future (or past). Similar results hold in a family of topologically analogous flat spacetimes, where we show the two vacua to be distinguished also by the shear stresses in the zero-mass limit. As a by-product, we display the explicit Bogolubov transformation between the Rindler-basis and the Minkowski-basis for massive Dirac fermions in four-dimensional Minkowski spacetime.
A comparative study of numerical methods for the overlap Dirac operator—a status report
NASA Astrophysics Data System (ADS)
van den Eshof, J.; Frommer, A.; Lippert, Th.; Schilling, K.; van der Vorst, H.
2002-03-01
Improvements of various methods to compute the sign function of the hermitian Wilson-Dirac matrix within the overlap operator are presented. An optimal partial fraction expansion (PFE) based on a theorem of Zolotarev is given. Benchmarks show that this PFE together with removal of converged systems within a multi-shift CG appears to approximate the sign function times a vector most efficiently. A posteriori error bounds are given.
The Hamiltonian structure of Dirac's equation in tensor form and its Fermi quantization
NASA Technical Reports Server (NTRS)
Reifler, Frank; Morris, Randall
1992-01-01
Currently, there is some interest in studying the tensor forms of the Dirac equation to elucidate the possibility of the constrained tensor fields admitting Fermi quantization. We demonstrate that the bispinor and tensor Hamiltonian systems have equivalent Fermi quantizations. Although the tensor Hamiltonian system is noncanonical, representing the tensor Poisson brackets as commutators for the Heisenberg operators directly leads to Fermi quantization without the use of bispinors.
Local moment formation in Dirac electrons
NASA Astrophysics Data System (ADS)
Mashkoori, M.; Mahyaeh, I.; Jafari, S. A.
2015-04-01
Elemental bismuth and its compounds host strong spin-orbit interaction which is at the heart of topologically non-trivial alloys based on bismuth. These class of materials are described in terms of 4x4 matrices at each v point where spin and orbital labels of the underlying electrons are mixed. In this work we investigate the single impurity Anderson model (SIAM) within a mean field approximation to address the nature of local magnetic moment formation in a generic Dirac Hamiltonian. Despite the spin-mixing in the Hamiltonian, within the Hartree approximation it turns out that the impuritys Green function is diagonal in spin label. In the three dimensional Dirac materials defined over a bandwidth D and spin-orbit parameter γ, that hybridizes with impurity through V, a natural dimensionless parameter V2D/2πγ3 emerges. So neither the hybridization strength, V, nor the spin-orbit coupling γ, but a combination thereof governs the phase diagram. By tuning chemical potential and the impurity level, we present phase diagram for various values of Hubbard U. Numerical results suggest that strong spin-orbit coupling enhances the local moment formation both in terms of its strength and the area of the local moment region. In the case that we tune the chemical potential in a similar way as normal metal we find that magnetic region is confined to μ ≥ ε0, in sharp contrast to 2D Dirac fermions. If one fixes the chemical potential and tunes the impurity level, phase diagram has two magnetic regions which corresponds to hybridization of impurity level with lower and upper bands.
The Dirac Experiments - Results and Challenges
NASA Astrophysics Data System (ADS)
Clark, R. G.; O'Brien, J. L.; Dzurak, A. S.; Kane, B. E.; Lumpkin, N. E.; Reilley, D. J.; Starrett, R. P.; Rickel, D. G.; Goettee, J. D.; Campbell, L. J.; Fowler, C. M.; Mielke, C.; Harrison, N.; Zerwekh, W. D.; Clark, D.; Bartram, B. D.; King, J. C.; Parkin, D.; Nakagawa, H.; Miura, N.
2004-11-01
The 1997 international Dirac II Series held at Los Alamos National Laboratory involved low temperature electrical transport and optical experiments in magnetic fields exceeding 800 T, produced by explosive flux compression using Russian MC-1 generators. An overview of the scientific and technical advances achieved in this Series is given, together with a strategy for future work in this challenging experimental environment. A significant outcome was achieved in transport studies of microfabricated thin-film YBCO structures with the magnetic field in the CuO plane. Using a GHz transmission line technique at an ambient temperature of 1.6 K, an onset of dissipation was observed at 150 T (a new upper bound for superconductivity in any material), with a saturation of resistivity at 240 T. Comparison with the Pauli limit expected at B - 155 T in this material suggests that the critical field in this geometry is limited by spin paramagnetism. In preparation for a Dirac III series, a systematic temperature-dependent transport study of YBCO using in-plane magnetic fields of 150 T generated by single-turn coils, at temperatures over the range 10-100 K, has been undertaken in collaboration with the Japanese Megagauss Laboratory. The objective is to map out the phase diagram for this geometry, which is expected to be significantly different than the Werthamer-Helfand-Hohenberg model due to the presence of paramagnetic limiting. Nanofabricated magnetometers have also been developed in a UNSW-LANL collaboration for use in Dirac III for Fermi surface measurements of YBCO in megagauss fields, which are described.
New preshower detector for the DIRAC experiment
NASA Astrophysics Data System (ADS)
Pentia, M.; Aogaki, S.; Dumitriu, D.; Fluerasu, D.; Gugiu, M.; Yazkov, V.
2015-09-01
The Preshower (PSh) detector [1] is a component of the DIRAC setup [2]. It is designed to identify and reject the huge e-e+ pairs background in the ππ and Kπ pairs measurement produced in a hadronic atom ionization process. In the high energy region used for kaon detection, the small Nitrogen Cherenkov detector has low electron rejection efficiency. To increase the overall efficiency, a new two-layer scintillator Preshower detector has been developed and built. The new Preshower-Cherenkov combination ensures an electron rejection efficiency better than 99% in the momentum range 1-7 GeV/c.
Dirac oscillator interacting with a topological defect
Carvalho, J.; Furtado, C.; Moraes, F.
2011-09-15
In this work we study the interaction problem of a Dirac oscillator with gravitational fields produced by topological defects. The energy levels of the relativistic oscillator in the cosmic string and in the cosmic dislocation space-times are sensible to curvature and torsion associated to these defects and are important evidence of the influence of the topology on this system. In the presence of a localized magnetic field the energy levels acquire a term associated with the Aharonov-Bohm effect. We obtain the eigenfunctions and eigenvalues and see that in the nonrelativistic limit some results known in standard quantum mechanics are reached.
Cosmic String Global Superconducting Dirac Born Infeld
NASA Astrophysics Data System (ADS)
Ikrima, Ika; Ramadhan, Handhika S.; Mart, Terry
2016-08-01
Superconducting cosmic string possibly plays an important role in the formation of the universe structure. The physics of this phenomenon has been explored by studying the field theory in the string interior. Numerical solutions of superconducting strings with all relevant fields are presented in this paper. The field is constructed from a generalization of the usual field theory of superconducting global string, but the kinetic term consists of the Dirac Born Infeld (DBI). Some changes in the characteristic of the superconducting string DBI from the usual superconducting string case have been observed. The observation includes physical mechanism of all related fields.
Incomplete Dirac reduction of constrained Hamiltonian systems
Chandre, C.
2015-10-15
First-class constraints constitute a potential obstacle to the computation of a Poisson bracket in Dirac’s theory of constrained Hamiltonian systems. Using the pseudoinverse instead of the inverse of the matrix defined by the Poisson brackets between the constraints, we show that a Dirac–Poisson bracket can be constructed, even if it corresponds to an incomplete reduction of the original Hamiltonian system. The uniqueness of Dirac brackets is discussed. The relevance of this procedure for infinite dimensional Hamiltonian systems is exemplified.
Neutrino oscillations from Dirac and Majorana masses
Ring, D.
1997-05-01
We present a scenario of neutrino masses and mixing angles. Each generation includes a sterile right-handed neutrino in addition to the usual left-handed one. We assume a hierarchy in their Dirac masses similar to, but much larger than, the hierarchies in the quarks and charged leptons. In addition, we include a Majorana mass term for the sterile neutrinos only. These assumptions prove sufficient to accommodate scales of mass differences and mixing angles consistent with all existing neutrino oscillation data. {copyright} {ital 1997} {ital The American Physical Society}
Gavrilov, S.P.; Gitman, D.M.; Smirnov, A.A.
2003-02-01
We study solutions of Dirac equation in the field of Aharonov-Bohm solenoid and a collinear uniform magnetic field. On this base we construct self-adjoint extensions of the Dirac Hamiltonian using von Neumann's theory of deficiency indices. We reduce (3+1)-dimensional problem to (2+1)-dimensional one by a proper choice of spin operator. Then we study the problem doing a finite radius regularization of the solenoid field. We exploit solutions of the latter problem to specify boundary conditions in the singular case.
Dirac's equation and the nature of quantum field theory
NASA Astrophysics Data System (ADS)
Plotnitsky, Arkady
2012-11-01
This paper re-examines the key aspects of Dirac's derivation of his relativistic equation for the electron in order advance our understanding of the nature of quantum field theory. Dirac's derivation, the paper argues, follows the key principles behind Heisenberg's discovery of quantum mechanics, which, the paper also argues, transformed the nature of both theoretical and experimental physics vis-à-vis classical physics and relativity. However, the limit theory (a crucial consideration for both Dirac and Heisenberg) in the case of Dirac's theory was quantum mechanics, specifically, Schrödinger's equation, while in the case of quantum mechanics, in Heisenberg's version, the limit theory was classical mechanics. Dirac had to find a new equation, Dirac's equation, along with a new type of quantum variables, while Heisenberg, to find new theory, was able to use the equations of classical physics, applied to different, quantum-mechanical variables. In this respect, Dirac's task was more similar to that of Schrödinger in his work on his version of quantum mechanics. Dirac's equation reflects a more complex character of quantum electrodynamics or quantum field theory in general and of the corresponding (high-energy) experimental quantum physics vis-à-vis that of quantum mechanics and the (low-energy) experimental quantum physics. The final section examines this greater complexity and its implications for fundamental physics.
Upper-Division Student Difficulties with the Dirac Delta Function
ERIC Educational Resources Information Center
Wilcox, Bethany R.; Pollock, Steven J.
2015-01-01
The Dirac delta function is a standard mathematical tool that appears repeatedly in the undergraduate physics curriculum in multiple topical areas including electrostatics, and quantum mechanics. While Dirac delta functions are often introduced in order to simplify a problem mathematically, students still struggle to manipulate and interpret them.…
Decay of Dirac hair around a dilaton black hole
Gibbons, Gary W.; Rogatko, Marek
2008-02-15
The intermediate and late-time behavior of a massive Dirac field in the background of static spherically symmetric dilaton black hole solutions is investigated. The intermediate asymptotic behavior of a massive Dirac field depends on the mass parameter as well as the wave number of the mode, while the late-time behavior has a power-law decay rate independent of both.
Dirac point movement and topological phase transition in patterned graphene.
Dvorak, Marc; Wu, Zhigang
2015-02-28
The honeycomb lattice of graphene is characterized by linear dispersion and pseudospin chirality of fermions on the Dirac cones. If lattice anisotropy is introduced, the Dirac cones stay intact but move in reciprocal space. Dirac point movement can lead to a topological transition from semimetal to semiconductor when two inequivalent Dirac points merge, an idea that has attracted significant research interest. However, such movement normally requires unrealistically high lattice anisotropy. Here we show that anisotropic defects can break the C3 symmetry of graphene, leading to Dirac point drift in the Brillouin zone. Additionally, the long-range order in periodically patterned graphene can induce intervalley scattering between two inequivalent Dirac points, resulting in a semimetal-to-insulator topological phase transition. The magnitude and direction of Dirac point drift are predicted analytically, which are consistent with our first-principles electronic structure calculations. Thus, periodically patterned graphene can be used to study the fascinating physics associated with Dirac point movement and the corresponding phase transition.
Dirac oscillator and nonrelativistic Snyder-de Sitter algebra
Stetsko, M. M. E-mail: mykola@ktf.franko.lviv.ua
2015-01-15
Three dimensional Dirac oscillator was considered in space with deformed commutation relations known as Snyder-de Sitter algebra. Snyder-de Sitter commutation relations give rise to appearance of minimal uncertainties in position as well as in momentum. To derive energy spectrum and wavefunctions of the Dirac oscillator, supersymmetric quantum mechanics and shape invariance technique were applied.
Upper-Division Student Difficulties with the Dirac Delta Function
ERIC Educational Resources Information Center
Wilcox, Bethany R.; Pollock, Steven J.
2015-01-01
The Dirac delta function is a standard mathematical tool that appears repeatedly in the undergraduate physics curriculum in multiple topical areas including electrostatics, and quantum mechanics. While Dirac delta functions are often introduced in order to simplify a problem mathematically, students still struggle to manipulate and interpret them.…
The Dirac oscillator in a rotating frame of reference
NASA Astrophysics Data System (ADS)
Strange, P.; Ryder, L. H.
2016-10-01
The Dirac equation in a rotating frame of reference is derived from first principles within a linear approximation. This equation is employed to exhibit an equivalence between a particle in a Dirac oscillator potential and a free particle in a rotating frame of reference. A zero-point contribution to the energy of the particle, resulting from its spin, is also noted.
Strong topological metal material with multiple Dirac cones
Ji, Huiwen; Valla, T.; Pletikosic, I.; Gibson, Q. D.; Sahasrabudhe, Girija; Cava, R. J.
2016-01-25
We report a new, cleavable, strong topological metal, Zr_{2}Te_{2}P, which has the same tetradymite-type crystal structure as the topological insulator Bi_{2}Te_{2}Se. Instead of being a semiconductor, however, Zr_{2}Te_{2}P is metallic with a pseudogap between 0.2 and 0.7 eV above the Fermi energy (E_{F}). Inside this pseudogap, two Dirac dispersions are predicted: one is a surface-originated Dirac cone protected by time-reversal symmetry (TRS), while the other is a bulk-originated and slightly gapped Dirac cone with a largely linear dispersion over a 2 eV energy range. A third surface TRS-protected Dirac cone is predicted, and observed using angle-resolved photoemission spectroscopy, making Z_{r2}Te_{2}P the first system, to our knowledge, to realize TRS-protected Dirac cones at M¯ points. The high anisotropy of this Dirac cone is similar to the one in the hypothetical Dirac semimetal BiO_{2}. As a result, we propose that if E_{F} can be tuned into the pseudogap where the Dirac dispersions exist, it may be possible to observe ultrahigh carrier mobility and large magnetoresistance in this material.
Strong topological metal material with multiple Dirac cones
Ji, Huiwen; Valla, T.; Pletikosic, I.; ...
2016-01-25
We report a new, cleavable, strong topological metal, Zr2Te2P, which has the same tetradymite-type crystal structure as the topological insulator Bi2Te2Se. Instead of being a semiconductor, however, Zr2Te2P is metallic with a pseudogap between 0.2 and 0.7 eV above the Fermi energy (EF). Inside this pseudogap, two Dirac dispersions are predicted: one is a surface-originated Dirac cone protected by time-reversal symmetry (TRS), while the other is a bulk-originated and slightly gapped Dirac cone with a largely linear dispersion over a 2 eV energy range. A third surface TRS-protected Dirac cone is predicted, and observed using angle-resolved photoemission spectroscopy, making Zr2Te2Pmore » the first system, to our knowledge, to realize TRS-protected Dirac cones at M¯ points. The high anisotropy of this Dirac cone is similar to the one in the hypothetical Dirac semimetal BiO2. As a result, we propose that if EF can be tuned into the pseudogap where the Dirac dispersions exist, it may be possible to observe ultrahigh carrier mobility and large magnetoresistance in this material.« less
NASA Astrophysics Data System (ADS)
Liu, Jian; Kriegner, D.; Horak, L.; Puggioni, D.; Rayan Serrao, C.; Chen, R.; Yi, D.; Frontera, C.; Holy, V.; Vishwanath, A.; Rondinelli, J. M.; Marti, X.; Ramesh, R.
2016-02-01
By using a combination of heteroepitaxial growth, structure refinement based on synchrotron x-ray diffraction, and first-principles calculations, we show that the symmetry-protected Dirac line nodes in the topological semimetallic perovskite SrIrO3 can be lifted simply by applying epitaxial constraints. In particular, the Dirac gap opens without breaking the P b n m mirror symmetry. In virtue of a symmetry-breaking analysis, we demonstrate that the original symmetry protection is related to the n -glide operation, which can be selectively broken by different heteroepitaxial structures. This symmetry protection renders the nodal line a nonsymmorphic Dirac semimetallic state. The results highlight the vital role of crystal symmetry in spin-orbit-coupled correlated oxides and provide a foundation for experimental realization of topological insulators in iridate-based heterostructures.
Berry phase jumps and giant nonreciprocity in Dirac quantum dots
NASA Astrophysics Data System (ADS)
Rodriguez-Nieva, Joaquin F.; Levitov, Leonid S.
2016-12-01
We predict that a strong nonreciprocity in the resonance spectra of Dirac quantum dots can be induced by the Berry phase. The nonreciprocity arises in relatively weak magnetic fields and is manifest in anomalously large field-induced splittings of quantum dot resonances which are degenerate at B =0 due to time-reversal symmetry. This exotic behavior, which is governed by field-induced jumps in the Berry phase of confined electronic states, is unique to quantum dots in Dirac materials and is absent in conventional quantum dots. The effect is strong for gapless Dirac particles and can overwhelm the B -induced orbital and Zeeman splittings. A finite Dirac mass suppresses the effect. The nonreciprocity, predicted for generic two-dimensional Dirac materials, is accessible through Faraday and Kerr optical rotation measurements and scanning tunneling spectroscopy.
Discrete Dirac equation on a finite half-integer lattice
NASA Technical Reports Server (NTRS)
Smalley, L. L.
1986-01-01
The formulation of the Dirac equation on a discrete lattice with half-integer spacing and periodic boundary conditions is investigated analytically. The importance of lattice formulations for problems in field theory and quantum mechanics is explained; the concept of half-integer Fourier representation is introduced; the discrete Dirac equation for the two-dimensional case is derived; dispersion relations for the four-dimensional case are developed; and the spinor formulation for the Dirac fields on the half-integer lattice and the discrete time variable for the four-dimensional time-dependent Dirac equation are obtained. It is argued that the half-integer lattice, because it takes the Dirac Lagrangian into account, is more than a mere relabeling of the integer lattice and may have fundamental physical meaning (e.g., for the statistics of fermions). It is noted that the present formulation does not lead to species doubling, except in the continuum limit.
Z_{2} and Chiral Anomalies in Topological Dirac Semimetals.
Burkov, Anton A; Kim, Yong Baek
2016-09-23
We demonstrate that topological Dirac semimetals, which possess two Dirac nodes, separated in momentum space along a rotation axis and protected by rotational symmetry, exhibit an additional quantum anomaly, distinct from the chiral anomaly. This anomaly, which we call the Z_{2} anomaly, is a consequence of the fact that the Dirac nodes in topological Dirac semimetals carry a Z_{2} topological charge. The Z_{2} anomaly refers to nonconservation of this charge in the presence of external fields due to quantum effects and has observable consequences due to its interplay with the chiral anomaly. We discuss possible implications of this for the interpretation of magnetotransport experiments on topological Dirac semimetals. We also provide a possible explanation for the magnetic field dependent angular narrowing of the negative longitudinal magnetoresistance, observed in a recent experiment on Na_{3}Bi.
Optical analogue of relativistic Dirac solitons in binary waveguide arrays
Tran, Truong X.; Longhi, Stefano; Biancalana, Fabio
2014-01-15
We study analytically and numerically an optical analogue of Dirac solitons in binary waveguide arrays in the presence of Kerr nonlinearity. Pseudo-relativistic soliton solutions of the coupled-mode equations describing dynamics in the array are analytically derived. We demonstrate that with the found soliton solutions, the coupled mode equations can be converted into the nonlinear relativistic 1D Dirac equation. This paves the way for using binary waveguide arrays as a classical simulator of quantum nonlinear effects arising from the Dirac equation, something that is thought to be impossible to achieve in conventional (i.e. linear) quantum field theory. -- Highlights: •An optical analogue of Dirac solitons in nonlinear binary waveguide arrays is suggested. •Analytical solutions to pseudo-relativistic solitons are presented. •A correspondence of optical coupled-mode equations with the nonlinear relativistic Dirac equation is established.
Tilted anisotropic Dirac cones in partially hydrogenated graphene
NASA Astrophysics Data System (ADS)
Lu, Hong-Yan; Cuamba, Armindo S.; Lin, Shih-Yang; Hao, Lei; Wang, Rui; Li, Hai; Zhao, YuanYuan; Ting, C. S.
2016-11-01
By means of first-principles calculations, we predict a partially hydrogenated graphene system, C6H2 , and find the one in A B -trans configuration is a Dirac material with a tilted anisotropic Dirac cone electronic structure. Different from graphene, in which the Dirac points are located at K and K' and the Fermi surfaces are circular with doping, the A B -trans C6H2 exhibits Dirac points located on the lines from Γ to M with quasielliptical Fermi surfaces when doped. Around the Dirac point, the Fermi velocity varies along different directions. Therefore, the propagation of charge carriers in this system is highly anisotropic, creating a new tunability for novel transport properties.
On the spring and mass of the Dirac oscillator
NASA Technical Reports Server (NTRS)
Crawford, James P.
1993-01-01
The Dirac oscillator is a relativistic generalization of the quantum harmonic oscillator. In particular, the square of the Hamiltonian for the Dirac oscillator yields the Klein-Gordon equation with a potential of the form: (ar(sub 2) + b(L x S)), where a and b are constants. To obtain the Dirac oscillator, a 'minimal substitution' is made in the Dirac equation, where the ordinary derivative is replaced with a covariant derivative. However, an unusual feature of the covariant derivative in this case is that the potential is a non-trivial element of the Clifford algebra. A theory which naturally gives rise to gage potentials which are non-trivial elements of the Clifford algebra is that based on local automorphism invariance. An exact solution of the automorphism gage field equations which reproduces both the potential term and the mass term of the Dirac oscillator is presented.
Plasmon modes of a massive Dirac plasma, and their superlattices
NASA Astrophysics Data System (ADS)
Sachdeva, Rashi; Thakur, Anmol; Vignale, Giovanni; Agarwal, Amit
2015-05-01
We explore the collective density oscillations of a collection of charged massive Dirac particles, in one, two, and three dimensions, and their one-dimensional (1D) superlattice. We calculate the long-wavelength limit of the dynamical polarization function analytically, and use the random phase approximation to obtain the plasmon dispersion. The density dependence of the long-wavelength plasmon frequency in massive Dirac systems is found to be different compared to systems with parabolic and gapless Dirac dispersion. We also calculate the long-wavelength plasmon dispersion of a 1D metamaterial made from 1D and 2D massive Dirac plasma. Our analytical results will be useful for exploring the use of massive Dirac materials as electrostatically tunable plasmonic metamaterials and can be experimentally verified by infrared spectroscopy, as in the case of graphene [L. Ju et al., Nat. Nanotechnol. 6, 630 (2011), 10.1038/nnano.2011.146].
Discrete Dirac equation on a finite half-integer lattice
NASA Technical Reports Server (NTRS)
Smalley, L. L.
1986-01-01
The formulation of the Dirac equation on a discrete lattice with half-integer spacing and periodic boundary conditions is investigated analytically. The importance of lattice formulations for problems in field theory and quantum mechanics is explained; the concept of half-integer Fourier representation is introduced; the discrete Dirac equation for the two-dimensional case is derived; dispersion relations for the four-dimensional case are developed; and the spinor formulation for the Dirac fields on the half-integer lattice and the discrete time variable for the four-dimensional time-dependent Dirac equation are obtained. It is argued that the half-integer lattice, because it takes the Dirac Lagrangian into account, is more than a mere relabeling of the integer lattice and may have fundamental physical meaning (e.g., for the statistics of fermions). It is noted that the present formulation does not lead to species doubling, except in the continuum limit.
Isospin of topological defects in Dirac systems
NASA Astrophysics Data System (ADS)
Herbut, Igor F.
2012-02-01
We study the Dirac quasiparticles in d-dimensional lattice systems of electrons in the presence of domain walls (d=1), vortices (d=2), or hedgehogs (d=3) of superconducting and/or insulating, order parameters, which appear as mass terms in the Dirac equation. Such topological defects have been known to carry nontrivial quantum numbers, such as charge and spin. Here we discuss their additional internal degree of freedom: irrespective of the dimensionality of space and the nature of orders that support the defect, an extra mass order parameter is found to emerge in their core. Six linearly independent local orders, which close two mutually commuting three-dimensional Clifford algebras, are proven to be in general possible. We show how the particle-hole symmetry restricts the defects to always carry the quantum numbers of a single effective isospin 1/2, quite independently of the values of their electric charge or true spin. Examples of this new degree of freedom in graphene and on surfaces of topological insulators are discussed.
Terahertz Electrodynamics of Dirac Fermions in Graphene
NASA Astrophysics Data System (ADS)
Frenzel, Alex James
Charge carriers in graphene mimic two-dimensional massless Dirac fermions with linear energy dispersion, resulting in unique optical and electronic properties. They exhibit high mobility and strong interaction with electromagnetic radiation over a broad frequency range. Interband transitions in graphene give rise to pronounced optical absorption in the mid-infrared to visible spectral range, where the optical conductivity is close to a universal value sigma_0 = pi e. 2/2h. Free-carrier intraband transitions, on the otherhand, cause low-frequency absorption, which varies significantly with charge density and results in strong light extinction at high carrier density. These properties together suggest a rich variety of possible optoelectronic applications for graphene. In this thesis, we investigate the optoelectronic properties of graphene by measuring transient photoconductivity with optical pump-terahertz probe spectroscopy. We demonstrate that graphene exhibits semiconducting positive photoconductivity near zero carrier density, which crosses over to metallic negative photoconductivity at high carrier density. These observations are accounted for by the interplay between photoinduced changes of both the Drude weight and carrier scattering rate. Our findings provide a complete picture to explain the opposite photoconductivity behavior reported in (undoped) graphene grown epitaxially and (doped) graphene grown by chemical vapor deposition. Our measurements also reveal the non-monotonic temperature dependence of the Drude weight in graphene, a unique property of two-dimensional massless Dirac fermions.
The Dirac point electron in zero-gravity Kerr–Newman spacetime
Kiessling, M. K.-H.; Tahvildar-Zadeh, A. S.
2015-04-15
Dirac’s wave equation for a point electron in the topologically nontrivial maximal analytically extended electromagnetic Kerr–Newman spacetime is studied in a limit G → 0, where G is Newton’s constant of universal gravitation. The following results are obtained: the formal Dirac Hamiltonian on the static spacelike slices is essentially self-adjoint and the spectrum of the self-adjoint extension is symmetric about zero, featuring a continuum with a gap about zero that, under two smallness conditions, contains a point spectrum. The symmetry result extends to the Dirac operator on a generalization of the zero-G Kerr–Newman spacetime with different electric-monopole/magnetic-dipole-moment ratios.
NASA Astrophysics Data System (ADS)
Erdoğan, M. Burak; Green, William R.
2016-12-01
We investigate dispersive estimates for the two dimensional Dirac equation with a potential. In particular, we show that the Dirac evolution satisfies a t -1 decay rate as an operator from the Hardy space H 1 to BMO, the space of functions of bounded mean oscillation. This estimate, along with the L 2 conservation law allows one to deduce a family of Strichartz estimates. We classify the structure of threshold obstructions as being composed of s-wave resonances, p-wave resonances and eigenfunctions. We show that, as in the case of the Schrödinger evolution, the presence of a threshold s-wave resonance does not destroy the t -1 decay rate. As a consequence of our analysis we obtain a limiting absorption principle in the neighborhood of the threshold, and show that there are only finitely many eigenvalues in the spectral gap.
Unconventional spin Hall effect and axial current generation in a Dirac semimetal
NASA Astrophysics Data System (ADS)
Okuma, Nobuyuki; Ogata, Masao
2016-04-01
We investigate electrical transport in a three-dimensional massless Dirac fermion model that describes a Dirac semimetal state realized in topological materials. We derive a set of interdependent diffusion equations with eight local degrees of freedom, including the electric charge density and the spin density, that respond to an external electric field. By solving the diffusion equations for a system with a boundary, we demonstrate that a spin Hall effect with spin accumulation occurs even though the conventional spin current operator is zero. The Noether current associated with chiral symmetry, known as the axial current, is also discussed. We demonstrate that the axial current flows near the boundary and that it is perpendicular to the electric current.
NASA Astrophysics Data System (ADS)
Erdoğan, M. Burak; Green, William R.
2017-06-01
We investigate dispersive estimates for the two dimensional Dirac equation with a potential. In particular, we show that the Dirac evolution satisfies a t -1 decay rate as an operator from the Hardy space H 1 to BMO, the space of functions of bounded mean oscillation. This estimate, along with the L 2 conservation law allows one to deduce a family of Strichartz estimates. We classify the structure of threshold obstructions as being composed of s-wave resonances, p-wave resonances and eigenfunctions. We show that, as in the case of the Schrödinger evolution, the presence of a threshold s-wave resonance does not destroy the t -1 decay rate. As a consequence of our analysis we obtain a limiting absorption principle in the neighborhood of the threshold, and show that there are only finitely many eigenvalues in the spectral gap.
Wu, Yun; Wang, Lin -Lin; Mun, Eundeok; Johnson, D. D.; Mou, Daixiang; Huang, Lunan; Lee, Yongbin; Bud’ko, S. L.; Canfield, P. C.; Kaminski, Adam
2016-04-04
In topological quantum materials^{1,2,3} the conduction and valence bands are connected at points or along lines in the momentum space. A number of studies have demonstrated that several materials are indeed Dirac/Weyl semimetals^{4,5,6,7,8}. However, there is still no experimental confirmation of materials with line nodes, in which the Dirac nodes form closed loops in the momentum space^{2,3}. Here we report the discovery of a novel topological structure—Dirac node arcs—in the ultrahigh magnetoresistive material PtSn_{4} using laser-based angle-resolved photoemission spectroscopy data and density functional theory calculations. Unlike the closed loops of line nodes, the Dirac node arc structure arises owing to the surface states and resembles the Dirac dispersion in graphene that is extended along a short line in the momentum space. Here, we propose that this reported Dirac node arc structure is a novel topological state that provides an exciting platform for studying the exotic properties of Dirac fermions.
Wu, Yun; Wang, Lin -Lin; Mun, Eundeok; ...
2016-04-04
In topological quantum materials1,2,3 the conduction and valence bands are connected at points or along lines in the momentum space. A number of studies have demonstrated that several materials are indeed Dirac/Weyl semimetals4,5,6,7,8. However, there is still no experimental confirmation of materials with line nodes, in which the Dirac nodes form closed loops in the momentum space2,3. Here we report the discovery of a novel topological structure—Dirac node arcs—in the ultrahigh magnetoresistive material PtSn4 using laser-based angle-resolved photoemission spectroscopy data and density functional theory calculations. Unlike the closed loops of line nodes, the Dirac node arc structure arises owing tomore » the surface states and resembles the Dirac dispersion in graphene that is extended along a short line in the momentum space. Here, we propose that this reported Dirac node arc structure is a novel topological state that provides an exciting platform for studying the exotic properties of Dirac fermions.« less
Supersymmetric model with Dirac neutrino masses
Marshall, Gardner; McCaskey, Mathew; Sher, Marc
2010-03-01
New models have recently been proposed in which a second Higgs doublet couples only to the lepton doublets and right-handed neutrinos, yielding Dirac neutrino masses. The vacuum value of this second 'nu-Higgs' doublet is made very small by means of a very softly-broken Z{sub 2} or U(1) symmetry. The latter is technically natural and avoids fine-tuning and very light scalars. We consider a supersymmetric version of this model, in which two additional doublets are added to the minimal supersymmetric standard model (MSSM). If kinematically allowed, the decay of the heavy MSSM scalar into charged nu-Higgs scalars will yield dilepton events which can be separated from the W-pair background. In addition, the nu-Higgsinos can lead to very dramatic tetralepton, pentalepton, and hexalepton events which have negligible background and can be detected at the LHC and the Tevatron.
Absorbing layers for the Dirac equation
Pinaud, Olivier
2015-05-15
This work is devoted to the construction of perfectly matched layers (PML) for the Dirac equation, that not only arises in relativistic quantum mechanics but also in the dynamics of electrons in graphene or in topological insulators. While the resulting equations are stable at the continuous level, some care is necessary in order to obtain a stable scheme at the discrete level. This is related to the so-called fermion doubling problem. For this matter, we consider the numerical scheme introduced by Hammer et al. [19], and combine it with the discretized PML equations. We state some arguments for the stability of the resulting scheme, and perform simulations in two dimensions. The perfectly matched layers are shown to exhibit, in various configurations, superior absorption than the absorbing potential method and the so-called transport-like boundary conditions.
Pseudo Dirac neutrinos in the seesaw model
NASA Astrophysics Data System (ADS)
Dutta, Gautam; Joshipura, Anjan S.
1995-04-01
A specific class of textures for the Dirac and Majorana mass matrices in the seesaw model leading to a pair of almost degenerate neutrinos is discussed. These textures can be obtained by imposing a horizontal U(1) symmetry. A specific model is discussed in which (1) all three neutrino masses are similar in magnitude and could lie around 1 eV providing the hot component of the dark matter in the Universe, (2) two of these are highly degenerate and their (mass)2 difference could solve the solar neutrino problem through the large angle MSW solution, and (3) the electron neutrino mass may be observable through a Kurie plot as well as through a search of the neutrinoless double β decay.
Dirac neutrino in warped extra dimensions
NASA Astrophysics Data System (ADS)
Chang, We-Fu; Ng, John N.; Wu, Jackson M. S.
2009-12-01
We implement Dirac neutrinos in the minimal custodial Randall-Sundrum setting via the Krauss-Wilczek mechanism. We demonstrate by giving explicit lepton mass matrices that with neutrinos in the normal hierarchy, lepton mass and mixing patterns can be naturally reproduced at the scale set by the constraints from electroweak precision measurements, and at the same time without violating bounds set by lepton flavor violations. Our scenario generically predicts a nonzero neutrino mixing angle θ13, as well as the existence of sub-TeV right-handed Kaluza-Klein neutrinos, which partner the right-handed standard model charged leptons. These relatively light KK neutrinos may be searched for at the LHC.
Bosonic Analogue of Dirac Composite Fermi Liquid.
Mross, David F; Alicea, Jason; Motrunich, Olexei I
2016-09-23
We introduce a particle-hole-symmetric metallic state of bosons in a magnetic field at odd-integer filling. This state hosts composite fermions whose energy dispersion features a quadratic band touching and corresponding 2π Berry flux protected by particle-hole and discrete rotation symmetries. We also construct an alternative particle-hole symmetric state-distinct in the presence of inversion symmetry-without Berry flux. As in the Dirac composite Fermi liquid introduced by Son [Phys. Rev. X 5, 031027 (2015)], breaking particle-hole symmetry recovers the familiar Chern-Simons theory. We discuss realizations of this phase both in 2D and on bosonic topological insulator surfaces, as well as signatures in experiments and simulations.
Quantized charge pump of massive Dirac electrons
NASA Astrophysics Data System (ADS)
Wang, Jun; Liu, Jun-Feng
2017-05-01
We study a new scheme to realize a quantized two-parameter charge pump based on massive Dirac electrons. It is shown that the two time-dependent and out-of-phase staggered potentials introduced in graphene can pump out an integer number of electrons in a pumping cycle as long as the Fermi energy resides in the effective energy gap opened by pumping potentials. The dependence of the pumped charge per mode on the pumping phase or the dynamic phase exhibits a binary alternation from +e to -e . This quantization has a topological origin and can be accounted for by adiabatic evolution of the topologically protected interfacial state forming between the two pumping sources.
On regularizations of the Dirac delta distribution
NASA Astrophysics Data System (ADS)
Hosseini, Bamdad; Nigam, Nilima; Stockie, John M.
2016-01-01
In this article we consider regularizations of the Dirac delta distribution with applications to prototypical elliptic and hyperbolic partial differential equations (PDEs). We study the convergence of a sequence of distributions SH to a singular term S as a parameter H (associated with the support size of SH) shrinks to zero. We characterize this convergence in both the weak-* topology of distributions and a weighted Sobolev norm. These notions motivate a framework for constructing regularizations of the delta distribution that includes a large class of existing methods in the literature. This framework allows different regularizations to be compared. The convergence of solutions of PDEs with these regularized source terms is then studied in various topologies such as pointwise convergence on a deleted neighborhood and weighted Sobolev norms. We also examine the lack of symmetry in tensor product regularizations and effects of dissipative error in hyperbolic problems.
Warm Dirac-Born-Infeld inflation
Cai Yifu; Dent, James B.; Easson, Damien A.
2011-05-15
We propose a warm inflationary model in the context of relativistic D-brane inflation in a warped throat, which has Dirac-Born-Infeld (DBI) kinetic term and is coupled to radiation through a dissipation term. The perturbation freezes at the sound horizon and the power spectrum is determined by a combination of the dissipative parameter and the sound speed parameter. The thermal dissipation ameliorates the eta problem and softens theoretical constraints from the extra-dimensional volume and from observational bounds on the tensor-to-scalar ratio. The warm DBI model can lead to appreciable non-Gaussianity of the equilateral type. As a phenomenological model, ignoring compactification constraints, we show that large-field warm inflation models do not necessarily yield a large tensor-to-scalar ratio.
ERIC Educational Resources Information Center
Wilkins, Jesse L. M.; Norton, Anderson; Boyce, Steven J.
2013-01-01
Previous research has documented schemes and operations that undergird students' understanding of fractions. This prior research was based, in large part, on small-group teaching experiments. However, written assessments are needed in order for teachers and researchers to assess students' ways of operating on a whole-class scale. In this study,…
Spin Dynamics in the Kapitza-Dirac Effect
NASA Astrophysics Data System (ADS)
Ahrens, Sven; Bauke, Heiko; Keitel, Christoph H.; Müller, Carsten
2012-07-01
Electron spin dynamics in Kapitza-Dirac scattering from a standing laser wave of high frequency and high intensity is studied. We develop a fully relativistic quantum theory of the electron motion based on the time-dependent Dirac equation. Distinct spin dynamics, with Rabi oscillations and complete spin-flip transitions, is demonstrated for Kapitza-Dirac scattering involving three photons in a parameter regime accessible to future high-power x-ray laser sources. The Rabi frequency and, thus, the diffraction pattern is shown to depend crucially on the spin degree of freedom.
Characteristic Dirac Signature in Elastic Proton Scattering at Intermediate Energies
NASA Astrophysics Data System (ADS)
Hynes, M. V.; Picklesimer, A.; Tandy, P. C.; Thaler, R. M.
1984-03-01
Nonrelativistic nucleon-nucleus first-order multiple-scattering calculations are extended to include virtual (Dirac) negative energy states of just the projectile. This effect may be thought of as virtual NN¯ pair production and annihilation in the field of the nucleus. This extension leads to a parameter-free Dirac description of the projectile in elastic proton scattering which produces a characteristic effect in spin observables over a wide range of energies which is in agreement with experiment. This Dirac signature is extremely stable with respect to uncertainties in the microscopic input.
Dirac cone protected by non-symmorphic symmetry and three-dimensional Dirac line node in ZrSiS.
Schoop, Leslie M; Ali, Mazhar N; Straßer, Carola; Topp, Andreas; Varykhalov, Andrei; Marchenko, Dmitry; Duppel, Viola; Parkin, Stuart S P; Lotsch, Bettina V; Ast, Christian R
2016-05-31
Materials harbouring exotic quasiparticles, such as massless Dirac and Weyl fermions, have garnered much attention from physics and material science communities due to their exceptional physical properties such as ultra-high mobility and extremely large magnetoresistances. Here, we show that the highly stable, non-toxic and earth-abundant material, ZrSiS, has an electronic band structure that hosts several Dirac cones that form a Fermi surface with a diamond-shaped line of Dirac nodes. We also show that the square Si lattice in ZrSiS is an excellent template for realizing new types of two-dimensional Dirac cones recently predicted by Young and Kane. Finally, we find that the energy range of the linearly dispersed bands is as high as 2 eV above and below the Fermi level; much larger than of other known Dirac materials. This makes ZrSiS a very promising candidate to study Dirac electrons, as well as the properties of lines of Dirac nodes.
Dirac cone protected by non-symmorphic symmetry and three-dimensional Dirac line node in ZrSiS
Schoop, Leslie M.; Ali, Mazhar N.; Straßer, Carola; Topp, Andreas; Varykhalov, Andrei; Marchenko, Dmitry; Duppel, Viola; Parkin, Stuart S. P.; Lotsch, Bettina V.; Ast, Christian R.
2016-01-01
Materials harbouring exotic quasiparticles, such as massless Dirac and Weyl fermions, have garnered much attention from physics and material science communities due to their exceptional physical properties such as ultra-high mobility and extremely large magnetoresistances. Here, we show that the highly stable, non-toxic and earth-abundant material, ZrSiS, has an electronic band structure that hosts several Dirac cones that form a Fermi surface with a diamond-shaped line of Dirac nodes. We also show that the square Si lattice in ZrSiS is an excellent template for realizing new types of two-dimensional Dirac cones recently predicted by Young and Kane. Finally, we find that the energy range of the linearly dispersed bands is as high as 2 eV above and below the Fermi level; much larger than of other known Dirac materials. This makes ZrSiS a very promising candidate to study Dirac electrons, as well as the properties of lines of Dirac nodes. PMID:27241624
Dirac cone protected by non-symmorphic symmetry and three-dimensional Dirac line node in ZrSiS
NASA Astrophysics Data System (ADS)
Schoop, Leslie M.; Ali, Mazhar N.; Straßer, Carola; Topp, Andreas; Varykhalov, Andrei; Marchenko, Dmitry; Duppel, Viola; Parkin, Stuart S. P.; Lotsch, Bettina V.; Ast, Christian R.
2016-05-01
Materials harbouring exotic quasiparticles, such as massless Dirac and Weyl fermions, have garnered much attention from physics and material science communities due to their exceptional physical properties such as ultra-high mobility and extremely large magnetoresistances. Here, we show that the highly stable, non-toxic and earth-abundant material, ZrSiS, has an electronic band structure that hosts several Dirac cones that form a Fermi surface with a diamond-shaped line of Dirac nodes. We also show that the square Si lattice in ZrSiS is an excellent template for realizing new types of two-dimensional Dirac cones recently predicted by Young and Kane. Finally, we find that the energy range of the linearly dispersed bands is as high as 2 eV above and below the Fermi level; much larger than of other known Dirac materials. This makes ZrSiS a very promising candidate to study Dirac electrons, as well as the properties of lines of Dirac nodes.
Dirac fields in flat FLRW cosmology: Uniqueness of the Fock quantization
NASA Astrophysics Data System (ADS)
Cortez, Jerónimo; Elizaga Navascués, Beatriz; Martín-Benito, Mercedes; Mena Marugán, Guillermo A.; Velhinho, José M.
2017-01-01
We address the issue of the infinite ambiguity that affects the construction of a Fock quantization of a Dirac field propagating in a cosmological spacetime with flat compact sections. In particular, we discuss a physical criterion that restricts to a unique possibility (up to unitary equivalence) the infinite set of available vacua. We prove that this desired uniqueness is guaranteed, for any possible choice of spin structure on the spatial sections, if we impose two conditions. The first one is that the symmetries of the classical system must be implemented quantum mechanically, so that the vacuum is invariant under the symmetry transformations. The second and more important condition is that the constructed theory must have a quantum dynamics that is implementable as a (non-trivial) unitary operator in Fock space. Actually, this unitarity of the quantum dynamics leads us to identify as explicitly time dependent some very specific contributions of the Dirac field. In doing that, we essentially characterize the part of the dynamics governed by the Dirac equation that is unitarily implementable. The uniqueness of the Fock vacuum is attained then once a physically motivated convention for the concepts of particles and antiparticles is fixed.
A robust and tuneable mid-infrared optical switch enabled by bulk Dirac fermions
Zhu, Chunhui; Wang, Fengqiu; Meng, Yafei; Yuan, Xiang; Xiu, Faxian; Luo, Hongyu; Wang, Yazhou; Li, Jianfeng; Lv, Xinjie; He, Liang; Xu, Yongbing; Liu, Junfeng; Zhang, Chao; Shi, Yi; Zhang, Rong; Zhu, Shining
2017-01-01
Pulsed lasers operating in the mid-infrared (3–20 μm) are important for a wide range of applications in sensing, spectroscopy, imaging and communications. Despite recent advances with mid-infrared gain platforms, the lack of a capable pulse generation mechanism remains a significant technological challenge. Here we show that bulk Dirac fermions in molecular beam epitaxy grown crystalline Cd3As2, a three-dimensional topological Dirac semimetal, constitutes an exceptional ultrafast optical switching mechanism for the mid-infrared. Significantly, we show robust and effective tuning of the scattering channels of Dirac fermions via an element doping approach, where photocarrier relaxation times are found flexibly controlled over an order of magnitude (from 8 ps to 800 fs at 4.5 μm). Our findings reveal the strong impact of Cr doping on ultrafast optical properties in Cd3As2 and open up the long sought parameter space crucial for the development of compact and high-performance mid-infrared ultrafast sources. PMID:28106037
On Dirac equations for linear magnetoacoustic waves propagating in an isothermal atmosphere
NASA Technical Reports Server (NTRS)
Alicki, R.; Musielak, E. Z.; Sikorski, J.; Makowiec, D.
1994-01-01
A new analytical approach to study linear magnetoacoustic waves propagating in an isothermal, stratified, and uniformly magnetized atmosphere is presented. The approach is based on Dirac equations, and the theory of Sturm-Liouville operators is used to investigate spectral properties of the obtained Dirac Hamiltonians. Two cases are considered: (1) the background magnetic field is vertical, and the waves are separated into purely magnetic (transverse) and purely acoustic (longitudinal) modes; and (2) the field is tilted with respect to the vertical direction and the magnetic and acoustic modes become coupled giving magnetoacoustic waves. For the first case, the Dirac Hamiltonian possesses either a discrete spectrum, which corresponds to standing magnetic waves, or a continuous spectrum, which can be clearly identified with freely propagating acoustic waves. For the second case, the quantum mechanical perturbation calculus is used to study coupling and energy exchange between the magnetic and acoustic components of magnetoacoustic waves. It is shown that this coupling may efficiently prevent trapping of magnetoacoustic waves instellar atmospheres.
Mixed-state form factors of U(1) twist fields in the Dirac theory
NASA Astrophysics Data System (ADS)
Chen, Yixiong
2016-08-01
Using the ‘Liouville space’ (the space of operators) of the massive Dirac theory, we define mixed-state form factors of U(1) twist fields. We consider mixed states with density matrices diagonal in the asymptotic particle basis. This includes the thermal Gibbs state as well as all generalized Gibbs ensembles of the Dirac theory. When the mixed state is specialized to a thermal Gibbs state, using a Riemann-Hilbert problem and low-temperature expansion, we obtain finite-temperature form factors of U(1) twist fields. We then propose the expression for form factors of U(1) twist fields in general diagonal mixed states. We verify that these form factors satisfy a system of nonlinear functional differential equations, which is derived from the trace definition of mixed-state form factors. At last, under weak analytic conditions on the eigenvalues of the density matrix, we write down the large distance form factor expansions of two-point correlation functions of these twist fields. Using the relation between the Dirac and Ising models, this provides the large-distance expansion of the Rényi entropy (for integer Rényi parameter) in the Ising model in diagonal mixed states.
On Dirac equations for linear magnetoacoustic waves propagating in an isothermal atmosphere
NASA Technical Reports Server (NTRS)
Alicki, R.; Musielak, E. Z.; Sikorski, J.; Makowiec, D.
1994-01-01
A new analytical approach to study linear magnetoacoustic waves propagating in an isothermal, stratified, and uniformly magnetized atmosphere is presented. The approach is based on Dirac equations, and the theory of Sturm-Liouville operators is used to investigate spectral properties of the obtained Dirac Hamiltonians. Two cases are considered: (1) the background magnetic field is vertical, and the waves are separated into purely magnetic (transverse) and purely acoustic (longitudinal) modes; and (2) the field is tilted with respect to the vertical direction and the magnetic and acoustic modes become coupled giving magnetoacoustic waves. For the first case, the Dirac Hamiltonian possesses either a discrete spectrum, which corresponds to standing magnetic waves, or a continuous spectrum, which can be clearly identified with freely propagating acoustic waves. For the second case, the quantum mechanical perturbation calculus is used to study coupling and energy exchange between the magnetic and acoustic components of magnetoacoustic waves. It is shown that this coupling may efficiently prevent trapping of magnetoacoustic waves instellar atmospheres.
A robust and tuneable mid-infrared optical switch enabled by bulk Dirac fermions
NASA Astrophysics Data System (ADS)
Zhu, Chunhui; Wang, Fengqiu; Meng, Yafei; Yuan, Xiang; Xiu, Faxian; Luo, Hongyu; Wang, Yazhou; Li, Jianfeng; Lv, Xinjie; He, Liang; Xu, Yongbing; Liu, Junfeng; Zhang, Chao; Shi, Yi; Zhang, Rong; Zhu, Shining
2017-01-01
Pulsed lasers operating in the mid-infrared (3-20 μm) are important for a wide range of applications in sensing, spectroscopy, imaging and communications. Despite recent advances with mid-infrared gain platforms, the lack of a capable pulse generation mechanism remains a significant technological challenge. Here we show that bulk Dirac fermions in molecular beam epitaxy grown crystalline Cd3As2, a three-dimensional topological Dirac semimetal, constitutes an exceptional ultrafast optical switching mechanism for the mid-infrared. Significantly, we show robust and effective tuning of the scattering channels of Dirac fermions via an element doping approach, where photocarrier relaxation times are found flexibly controlled over an order of magnitude (from 8 ps to 800 fs at 4.5 μm). Our findings reveal the strong impact of Cr doping on ultrafast optical properties in Cd3As2 and open up the long sought parameter space crucial for the development of compact and high-performance mid-infrared ultrafast sources.
Global phase diagram of two-dimensional Dirac fermions in random potentials
NASA Astrophysics Data System (ADS)
Ryu, S.; Mudry, C.; Ludwig, A. W. W.; Furusaki, A.
2012-06-01
Anderson localization is studied for two flavors of massless Dirac fermions in two-dimensional space perturbed by static disorder that is invariant under a chiral symmetry (chS) and a time-reversal symmetry (TRS) operation which, when squared, is equal either to plus or minus the identity. The former TRS (symmetry class BDI) can, for example, be realized when the Dirac fermions emerge from spinless fermions hopping on a two-dimensional lattice with a linear energy dispersion such as the honeycomb lattice (graphene) or the square lattice with π flux per plaquette. The latter TRS is realized by the surface states of three-dimensional Z2-topological band insulators in symmetry class CII. In the phase diagram parametrized by the disorder strengths, there is an infrared stable line of critical points for both symmetry classes BDI and CII. Here we discuss a “global phase diagram” in which disordered Dirac fermion systems in all three chiral symmetry classes, AIII, CII, and BDI, occur in four quadrants, sharing one corner which represents the clean Dirac fermion limit. This phase diagram also includes symmetry classes AII [e.g., appearing at the surface of a disordered three-dimensional Z2-topological band insulator in the spin-orbit (symplectic) symmetry class] and D (e.g., the random bond Ising model in two dimensions) as boundaries separating regions of the phase diagram belonging to the three chS classes AIII, BDI, and CII. Moreover, we argue that physics of Anderson localization in the CII phase can be presented in terms of a non-linear-σ model (NLσM) with a Z2-topological term. We thereby complete the derivation of topological or Wess-Zumino-Novikov-Witten terms in the NLσM description of disordered fermionic models in all ten symmetry classes relevant to Anderson localization in two spatial dimensions.
Generalized Fermi-Dirac functions and derivatives: properties and evaluation
NASA Astrophysics Data System (ADS)
Gong, Z.; Zejda, L.; Däppen, W.; Aparicio, J. M.
2001-05-01
The generalized Fermi-Dirac functions and their derivatives are important in evaluating the thermodynamic quantities of partially degenerate electrons in hot dense stellar plasmas. New recursion relations of the generalized Fermi-Dirac functions have been found. An effective numerical method to evaluate the derivatives of the generalized Fermi-Dirac functions up to third order with respect to both degeneracy and temperature is then proposed, following Aparicio [Ap.J.S.S. 117 (1998) 627]. A Fortran program based on this method, together with a sample test case, is provided. Accuracy and domain of reliability of some other, popularly used analytic approximations of the generalized Fermi-Dirac functions for extreme conditions are investigated and compared with our results.
Pseudo-dirac neutrinos: a challenge for neutrino telescopes.
Beacom, John F; Bell, Nicole F; Hooper, Dan; Learned, John G; Pakvasa, Sandip; Weiler, Thomas J
2004-01-09
Neutrinos may be pseudo-Dirac states, such that each generation is actually composed of two maximally mixed Majorana neutrinos separated by a tiny mass difference. The usual active neutrino oscillation phenomenology would be unaltered if the pseudo-Dirac splittings are deltam(2) less, similar 10(-12) eV(2); in addition, neutrinoless double beta decay would be highly suppressed. However, it may be possible to distinguish pseudo-Dirac from Dirac neutrinos using high-energy astrophysical neutrinos. By measuring flavor ratios as a function of L/E, mass-squared differences down to deltam(2) approximately 10(-18) eV(2) can be reached. We comment on the possibility of probing cosmological parameters with neutrinos.
Does the Dirac cone of germanene exist on metal substrates?
Wang, Yangyang; Li, Jingzhen; Xiong, Junhua; Pan, Yuanyuan; Ye, Meng; Guo, Ying; Zhang, Han; Quhe, Ruge; Lu, Jing
2016-07-28
Germanene, a germanium analogue of graphene and silicene, has been synthesized on metal substrates. It is predicted that the intrinsic germanene has a Dirac cone in its band structure, just like graphene and silicene. Using first-principles calculations, we investigate the geometrical structures and electronic properties of germanene on the Ag, Au, Cu, Al, Pt and Ir substrates. The Dirac cone of germanene is destroyed on the Al, Pt and Ir substrates but preserved on the Ag and Au substrates with a slight band hybridization. The upper part of the Dirac cone is destroyed for germanene on the Cu substrate while the lower part remains preserved. By contrast, the Dirac cone is always destroyed for silicene on these metal substrates because of a strong band hybridization. Our study suggests that it is possible to extract the intrinsic properties of germanene on the Ag and Au substrates although it appears impossible for silicene on these two substrates.
Higher-order Dirac solitons in binary waveguide arrays
Tran, Truong X.; Duong, Dũng C.
2015-10-15
We study optical analogues of higher-order Dirac solitons (HODSs) in binary waveguide arrays. Like higher-order solitons obtained from the well-known nonlinear Schrödinger equation governing the pulse propagation in an optical fiber, these HODSs have amplitude profiles which are numerically shown to be periodic over large propagation distances. At the same time, HODSs possess some unique features. Firstly, the period of a HODS depends on its order parameter. Secondly, the discrete nature in binary waveguide arrays imposes the upper limit on the order parameter of HODSs. Thirdly, the order parameter of HODSs can vary continuously in a certain range. - Highlights: • Higher-order Dirac solitons in nonlinear binary waveguide arrays are numerically demonstrated. • Amplitude profiles of higher-order Dirac solitons are periodic during propagation. • The period of higher-order Dirac solitons decreases when the soliton order increases.
PT-Symmetric Real Dirac Fermions and Semimetals.
Zhao, Y X; Lu, Y
2017-02-03
Recently, Weyl fermions have attracted increasing interest in condensed matter physics due to their rich phenomenology originated from their nontrivial monopole charges. Here, we present a theory of real Dirac points that can be understood as real monopoles in momentum space, serving as a real generalization of Weyl fermions with the reality being endowed by the PT symmetry. The real counterparts of topological features of Weyl semimetals, such as Nielsen-Ninomiya no-go theorem, 2D subtopological insulators, and Fermi arcs, are studied in the PT symmetric Dirac semimetals and the underlying reality-dependent topological structures are discussed. In particular, we construct a minimal model of the real Dirac semimetals based on recently proposed cold atom experiments and quantum materials about PT symmetric Dirac nodal line semimetals.
Dirac Fermions in a Nanopatterned Two-Dimensional Electron Gas
NASA Astrophysics Data System (ADS)
Park, Cheol-Hwan
2013-03-01
If a lateral periodic potential with triangular (or honeycomb) lattice symmetry is applied to a conventional two-dimensional electron gas (2DEG), the charge carriers behave like massless Dirac ferions. A very interesting and useful point of these newly-generated massless Dirac fermions is that, unlike the case of graphene, their properties can be tuned through the external periodic potential. In this presentation, I will review the electronic properties of those newly-generated massless Dirac fermions in an artificial 2DEG superlattice system and will discuss how the elecctronic structure of those massless Dirac fermions changes depending on the external periodic potential. This work was partly supported by Research Settlement Fund for the new faculty of SNU.
Dirac cones in transition metal doped boron nitride
Feng, Min; Cao, Xuewei; Shao, Bin; Zuo, Xu
2015-05-07
The transition metal (TM) doped zinc blende boron nitride (c-BN) is studied by using the first principle calculation. TM atoms fill in the interstitials in c-BN and form two-dimensional honeycomb lattice. The generalized gradient approximation and projector augmented wave method are used. The calculated density of states and band structures show that d electrons of TM atoms form impurity bands in the gap of c-BN. When the TM-BN system is in ferromagnetic or non-magnetic state, Dirac cones emerge at the K point in Brillouin zone. When TM is Ti and Co, the Dirac cones are spin polarized and very close to the Fermi level, which makes them promising candidates of Dirac half-metal [H. Ishizuka and Y. Motome, Phys. Rev. Lett. 109, 237207 (2012)]. While TM is Ni and Cu, the system is non-magnetic and Dirac cones located above the Fermi level.
P T -Symmetric Real Dirac Fermions and Semimetals
NASA Astrophysics Data System (ADS)
Zhao, Y. X.; Lu, Y.
2017-02-01
Recently, Weyl fermions have attracted increasing interest in condensed matter physics due to their rich phenomenology originated from their nontrivial monopole charges. Here, we present a theory of real Dirac points that can be understood as real monopoles in momentum space, serving as a real generalization of Weyl fermions with the reality being endowed by the P T symmetry. The real counterparts of topological features of Weyl semimetals, such as Nielsen-Ninomiya no-go theorem, 2D subtopological insulators, and Fermi arcs, are studied in the P T symmetric Dirac semimetals and the underlying reality-dependent topological structures are discussed. In particular, we construct a minimal model of the real Dirac semimetals based on recently proposed cold atom experiments and quantum materials about P T symmetric Dirac nodal line semimetals.
The (weak) gravitational field of a Dirac monopole
NASA Astrophysics Data System (ADS)
Banyas, E.; Franklin, J.
2017-10-01
We establish the gravitational detectability of a Dirac monopole using a weak-field limit of general relativity, which can be developed from the Newtonian gravitational potential by including energy as a source. The resulting potential matches (by construction) the weak-field limit of two different solutions to Einstein’s equations of general relativity: one associated with the magnetically monopolar spray of field lines emerging from the half-infinite solenoid that makes up the Dirac monopole, the other associated with the field-energetic source of the solenoid itself (the Dirac string). The string’s gravitational effect dominates, and we suggest that the primary strong-field contribution of the Dirac configuration is that of a half-infinite line of energy, whose GR solution is known.
Large optical conductivity of Dirac semimetal Fermi arc surface states
NASA Astrophysics Data System (ADS)
Shi, Li-kun; Song, Justin C. W.
2017-08-01
Fermi arc surface states, a hallmark of topological Dirac semimetals, can host carriers that exhibit unusual dynamics distinct from that of their parent bulk. Here we find that Fermi arc carriers in intrinsic Dirac semimetals possess a strong and anisotropic light-matter interaction. This is characterized by a large Fermi arc optical conductivity when light is polarized transverse to the Fermi arc; when light is polarized along the Fermi arc, Fermi arc optical conductivity is significantly muted. The large surface spectral weight is locked to the wide separation between Dirac nodes and persists as a large Drude weight of Fermi arc carriers when the system is doped. As a result, large and anisotropic Fermi arc conductivity provides a novel means of optically interrogating the topological surfaces states of Dirac semimetals.
Dirac directional emission in anisotropic zero refractive index photonic crystals.
He, Xin-Tao; Zhong, Yao-Nan; Zhou, You; Zhong, Zhi-Chao; Dong, Jian-Wen
2015-08-14
A certain class of photonic crystals with conical dispersion is known to behave as isotropic zero-refractive-index medium. However, the discrete building blocks in such photonic crystals are limited to construct multidirectional devices, even for high-symmetric photonic crystals. Here, we show multidirectional emission from low-symmetric photonic crystals with semi-Dirac dispersion at the zone center. We demonstrate that such low-symmetric photonic crystal can be considered as an effective anisotropic zero-refractive-index medium, as long as there is only one propagation mode near Dirac frequency. Four kinds of Dirac multidirectional emitters are achieved with the channel numbers of five, seven, eleven, and thirteen, respectively. Spatial power combination for such kind of Dirac directional emitter is also verified even when multiple sources are randomly placed in the anisotropic zero-refractive-index photonic crystal.
Tuning surface Dirac valleys by strain in topological crystalline insulators
NASA Astrophysics Data System (ADS)
Zhao, Lu; Wang, Jianfeng; Gu, Bing-Lin; Duan, Wenhui
2015-05-01
A topological crystalline insulator has an even number of Dirac cones (i.e., multiple valleys) in its surface band structure, thus potentially leading to valleytronic applications such as graphene. Using the density-functional-theory method, we systematically investigate the strain-induced evolution of topological surface states on the SnTe(111) surface. Our results show that compressive strain can shift the Dirac cones at the Γ ¯ and M ¯ valleys to different extents (even oppositely) in energy, while the tensile strain can induce different band gaps at the valleys due to the enhanced penetration depths of surface states. Exploiting a strain-induced nanostructure with well-defined edges on the (111) surface, we demonstrate strong valley-selective filtering for massless Dirac fermions by dynamically applying local external pressure. Our findings may pave the way for strain-engineered valley-resolved manipulation of Dirac fermions with high tunability and scalability.
Merging of the Dirac points in electronic artificial graphene
NASA Astrophysics Data System (ADS)
Feilhauer, J.; Apel, W.; Schweitzer, L.
2015-12-01
Theory predicts that graphene under uniaxial compressive strain in an armchair direction should undergo a topological phase transition from a semimetal into an insulator. Due to the change of the hopping integrals under compression, both Dirac points shift away from the corners of the Brillouin zone towards each other. For sufficiently large strain, the Dirac points merge and an energy gap appears. However, such a topological phase transition has not yet been observed in normal graphene (due to its large stiffness) neither in any other electronic system. We show numerically and analytically that such a merging of the Dirac points can be observed in electronic artificial graphene created from a two-dimensional electron gas by application of a triangular lattice of repulsive antidots. Here, the effect of strain is modeled by tuning the distance between the repulsive potentials along the armchair direction. Our results show that the merging of the Dirac points should be observable in a recent experiment with molecular graphene.
Monte Carlo study of Dirac semimetals phase diagram
NASA Astrophysics Data System (ADS)
Braguta, V. V.; Katsnelson, M. I.; Kotov, A. Yu.; Nikolaev, A. A.
2016-11-01
In this paper the phase diagram of Dirac semimetals is studied within a lattice Monte Carlo simulation. In particular, we concentrate on the dynamical chiral symmetry breaking which results in a semimetal-insulator transition. Using numerical simulation, we determine the values of the critical coupling constant of the semimetal-insulator transition for different values of the anisotropy of the Fermi velocity. This measurement allows us to draw a tentative phase diagram for Dirac semimetals. It turns out that within the Dirac model with Coulomb interaction both Na3Bi and Cd3As2 , known experimentally to be Dirac semimetals, would lie deep in the insulating region of the phase diagram. This result probably shows a decisive role of screening of the interelectron interaction in real materials, similar to the situation in graphene.
Dirac directional emission in anisotropic zero refractive index photonic crystals
He, Xin-Tao; Zhong, Yao-Nan; Zhou, You; Zhong, Zhi-Chao; Dong, Jian-Wen
2015-01-01
A certain class of photonic crystals with conical dispersion is known to behave as isotropic zero-refractive-index medium. However, the discrete building blocks in such photonic crystals are limited to construct multidirectional devices, even for high-symmetric photonic crystals. Here, we show multidirectional emission from low-symmetric photonic crystals with semi-Dirac dispersion at the zone center. We demonstrate that such low-symmetric photonic crystal can be considered as an effective anisotropic zero-refractive-index medium, as long as there is only one propagation mode near Dirac frequency. Four kinds of Dirac multidirectional emitters are achieved with the channel numbers of five, seven, eleven, and thirteen, respectively. Spatial power combination for such kind of Dirac directional emitter is also verified even when multiple sources are randomly placed in the anisotropic zero-refractive-index photonic crystal. PMID:26271208
Variational Integrators for Interconnected Lagrange-Dirac Systems
NASA Astrophysics Data System (ADS)
Parks, Helen; Leok, Melvin
2017-02-01
Interconnected systems are an important class of mathematical models, as they allow for the construction of complex, hierarchical, multiphysics, and multiscale models by the interconnection of simpler subsystems. Lagrange-Dirac mechanical systems provide a broad category of mathematical models that are closed under interconnection, and in this paper, we develop a framework for the interconnection of discrete Lagrange-Dirac mechanical systems, with a view toward constructing geometric structure-preserving discretizations of interconnected systems. This work builds on previous work on the interconnection of continuous Lagrange-Dirac systems (Jacobs and Yoshimura in J Geom Mech 6(1):67-98, 2014) and discrete Dirac variational integrators (Leok and Ohsawa in Found Comput Math 11(5), 529-562, 2011). We test our results by simulating some of the continuous examples given in Jacobs and Yoshimura (2014).
[P.A.M. Dirac and antimatter applied to medicine].
Kulenović, Fahrudin; Vobornik, Slavenka; Dalagija, Faruk
2003-01-01
Regarding to the hundredth anniversary of P. Dirac birth, it was made review on life and work of this genius in the history of physics and science generally. His ingenious scientific work, that significantly marked contemporary time, was presented in the simplest way with aim to approach more number of readers. Special accent was put on application of Dirac's ideas about antiparticles in medical practice.
The confluent supersymmetry algorithm for Dirac equations with pseudoscalar potentials
Contreras-Astorga, Alonso Schulze-Halberg, Axel E-mail: xbataxel@gmail.com
2014-10-15
We introduce the confluent version of the quantum-mechanical supersymmetry formalism for the Dirac equation with a pseudoscalar potential. Application of the formalism to spectral problems is discussed, regularity conditions for the transformed potentials are derived, and normalizability of the transformed solutions is established. Our findings extend and complement former results [L. M. Nieto, A. A. Pecheritsin, and B. F. Samsonov, “Intertwining technique for the one-dimensional stationary Dirac equation,” Ann. Phys. 305, 151–189 (2003)].
The confluent supersymmetry algorithm for Dirac equations with pseudoscalar potentials
NASA Astrophysics Data System (ADS)
Contreras-Astorga, Alonso; Schulze-Halberg, Axel
2014-10-01
We introduce the confluent version of the quantum-mechanical supersymmetry formalism for the Dirac equation with a pseudoscalar potential. Application of the formalism to spectral problems is discussed, regularity conditions for the transformed potentials are derived, and normalizability of the transformed solutions is established. Our findings extend and complement former results [L. M. Nieto, A. A. Pecheritsin, and B. F. Samsonov, "Intertwining technique for the one-dimensional stationary Dirac equation," Ann. Phys. 305, 151-189 (2003)].
Magnetotransport in Dirac metals: Chiral magnetic effect and quantum oscillations
Monteiro, Gustavo M.; Abanov, Alexander G.; Kharzeev, Dmitri E.
2015-10-08
Dirac metals are characterized by the linear dispersion of fermionic quasiparticles, with the Dirac point hidden inside a Fermi surface. We study the magnetotransport in these materials using chiral kinetic theory to describe within the same framework both the negative magnetoresistance caused by the chiral magnetic effect and quantum oscillations in the magnetoresistance due to the existence of the Fermi surface. Lastly, we discuss the relevance of obtained results to recent measurements on Cd3As2.
Magnetotransport in Dirac metals: Chiral magnetic effect and quantum oscillations
Monteiro, Gustavo M.; Abanov, Alexander G.; Kharzeev, Dmitri E.
2015-10-08
Dirac metals are characterized by the linear dispersion of fermionic quasiparticles, with the Dirac point hidden inside a Fermi surface. We study the magnetotransport in these materials using chiral kinetic theory to describe within the same framework both the negative magnetoresistance caused by the chiral magnetic effect and quantum oscillations in the magnetoresistance due to the existence of the Fermi surface. Lastly, we discuss the relevance of obtained results to recent measurements on Cd_{3}As_{2}.
Bimetric Weyl-Dirac theory and the gravitational constant
Rosen, N.
1983-03-01
The Weyl-Dirac theory of grativation and electromagnetism is modified by the introduction of a background metric characterized by a scale constant related to the size of the universe. One is led to a natural gauge giving G/G = -5.5 x 10/sup -12/y/sup -1/. This is smaller by about a factor of ten than the value obtained on the basis of Dirac's large number hypothesis.
Supersymmetry between Jackiw-Nair and Dirac-Majorana anyons
Horvathy, Peter A.; Valenzuela, Mauricio; Plyushchay, Mikhail S.
2010-06-15
The Jackiw-Nair description of anyons combines spin-1 topologically massive fields with the discrete series representation of the Lorentz algebra, which has fractional spin. In the Dirac-Majorana formulation the spin-1 part is replaced by the spin 1/2 planar Dirac equation. The two models are shown to belong to an N=1 supermultiplet, which carries a super-Poincare symmetry.
Dirac equation in low dimensions: The factorization method
Sánchez-Monroy, J.A.; Quimbay, C.J.
2014-11-15
We present a general approach to solve the (1+1) and (2+1)-dimensional Dirac equations in the presence of static scalar, pseudoscalar and gauge potentials, for the case in which the potentials have the same functional form and thus the factorization method can be applied. We show that the presence of electric potentials in the Dirac equation leads to two Klein–Gordon equations including an energy-dependent potential. We then generalize the factorization method for the case of energy-dependent Hamiltonians. Additionally, the shape invariance is generalized for a specific class of energy-dependent Hamiltonians. We also present a condition for the absence of the Klein paradox (stability of the Dirac sea), showing how Dirac particles in low dimensions can be confined for a wide family of potentials. - Highlights: • The low-dimensional Dirac equation in the presence of static potentials is solved. • The factorization method is generalized for energy-dependent Hamiltonians. • The shape invariance is generalized for energy-dependent Hamiltonians. • The stability of the Dirac sea is related to the existence of supersymmetric partner Hamiltonians.
Split Dirac Supersymmetry: An Ultraviolet Completion of Higgsino Dark Matter
Fox, Patrick J.; Kribs, Graham D.; Martin, Adam
2014-10-07
Motivated by the observation that the Higgs quartic coupling runs to zero at an intermediate scale, we propose a new framework for models of split supersymmetry, in which gauginos acquire intermediate scale Dirac masses of $\\sim 10^{8-11}$ GeV. Scalar masses arise from one-loop finite contributions as well as direct gravity-mediated contributions. Like split supersymmetry, one Higgs doublet is fine-tuned to be light. The scale at which the Dirac gauginos are introduced to make the Higgs quartic zero is the same as is necessary for gauge coupling unification. Thus, gauge coupling unification persists (nontrivially, due to adjoint multiplets), though with a somewhat higher unification scale $\\gtrsim 10^{17}$ GeV. The $\\mu$-term is naturally at the weak scale, and provides an opportunity for experimental verification. We present two manifestations of Split Dirac Supersymmetry. In the "Pure Dirac" model, the lightest Higgsino must decay through R-parity violating couplings, leading to an array of interesting signals in colliders. In the "Hypercharge Impure" model, the bino acquires a Majorana mass that is one-loop suppressed compared with the Dirac gluino and wino. This leads to weak scale Higgsino dark matter whose overall mass scale, as well as the mass splitting between the neutral components, is naturally generated from the same UV dynamics. We outline the challenges to discovering pseudo-Dirac Higgsino dark matter in collider and dark matter detection experiments.
Conjugated Molecules Described by a One-Dimensional Dirac Equation.
Ernzerhof, Matthias; Goyer, Francois
2010-06-08
Starting from the Hückel Hamiltonian of conjugated hydrocarbon chains (ethylene, allyl radical, butadiene, pentadienyl radical, hexatriene, etc.), we perform a simple unitary transformation and obtain a Dirac matrix Hamiltonian. Thus already small molecules are described exactly in terms of a discrete Dirac equation, the continuum limit of which yields a one-dimensional Dirac Hamiltonian. Augmenting this Hamiltonian with specially adapted boundary conditions, we find that all the orbitals of the unsaturated hydrocarbon chains are reproduced by the continuous Dirac equation. However, only orbital energies close to the highest occupied molecular orbital/lowest unoccupied molecular orbital energy are accurately predicted by the Dirac equation. Since it is known that a continuous Dirac equation describes the electronic structure of graphene around the Fermi energy, our findings answer the question to what extent this peculiar electronic structure is already developed in small molecules containing a delocalized π-electron system. We illustrate how the electronic structure of small polyenes carries over to a certain class of rectangular graphene sheets and eventually to graphene itself. Thus the peculiar electronic structure of graphene extends to a large degree to the smallest unsaturated molecule (ethylene).
Dirac Cone Protected by Non-Symmorphic Symmetry and highly dispersive 3D Dirac crossings in ZrSiS
NASA Astrophysics Data System (ADS)
Schoop, Leslie; Ali, Mazhar; Strasser, Carola; Duppel, Viola; Parkin, Stuart; Lotsch, Bettina; Ast, Christian
Materials harboring exotic quasiparticles, such as Dirac and Weyl fermions have garnered much attention from the physics and material science communities. Here, we show with angle resolved photoemission studies supported by ab initio calculations that the highly stable, non-toxic and earth-abundant material, ZrSiS, has an electronic band structure that hosts several Dirac cones which form a Fermi surface with a diamond-shaped line of Dirac nodes. We also experimentally show, for the first time, that the square Si lattice in ZrSiS is an excellent template for realizing the new types of 2D Dirac cones protected by non-symmophic symmetry and image an unforseen surface state that arises close to the 2D Dirac cone. Finally, we find that the energy range of the linearly dispersed bands is as high as 2 eV above and below the Fermi level; much larger than of any known Dirac material so far. We will discuss why these characteristics make ZrSiS very promising for future applications.
Weyl, Dirac and Maxwell Quantum Cellular Automata
NASA Astrophysics Data System (ADS)
Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo; Tosini, Alessandro
2015-10-01
Recent advances on quantum foundations achieved the derivation of free quantum field theory from general principles, without referring to mechanical notions and relativistic invariance. From the aforementioned principles a quantum cellular automata (QCA) theory follows, whose relativistic limit of small wave-vector provides the free dynamics of quantum field theory. The QCA theory can be regarded as an extended quantum field theory that describes in a unified way all scales ranging from an hypothetical discrete Planck scale up to the usual Fermi scale. The present paper reviews the automaton theory for the Weyl field, and the composite automata for Dirac and Maxwell fields. We then give a simple analysis of the dynamics in the momentum space in terms of a dispersive differential equation for narrowband wave-packets. We then review the phenomenology of the free-field automaton and consider possible visible effects arising from the discreteness of the framework. We conclude introducing the consequences of the automaton dispersion relation, leading to a deformed Lorentz covariance and to possible effects on the thermodynamics of ideal gases.
Dirac Green function for angular projection potentials.
Zeller, Rudolf
2015-11-25
The aim of this paper is twofold: first, it is shown that the angular dependence of the Dirac Green function can be described analytically for potentials with non-local dependence on the angular variables if they are chosen as projection potentials in angular momentum space. Because the local dependence on the radial variable can be treated to any precision with present computing capabilities, this means that the Green function can be calculated practically exactly. Second, it is shown that a result of this kind not only holds for a single angular projection potential but also more generally, for instance if space is divided into non-overlapping cells and a separate angular projection potential is used in each cell. This opens the way for relativistic density-functional calculations within a different perspective than the conventional one. Instead of trying to obtain the density for a given potential approximately as well as possible, the density is determined exactly for non-local potentials which can approximate arbitrary local potentials as well as desired.
Nonlinear propagation of light in Dirac matter.
Eliasson, Bengt; Shukla, P K
2011-09-01
The nonlinear interaction between intense laser light and a quantum plasma is modeled by a collective Dirac equation coupled with the Maxwell equations. The model is used to study the nonlinear propagation of relativistically intense laser light in a quantum plasma including the electron spin-1/2 effect. The relativistic effects due to the high-intensity laser light lead, in general, to a downshift of the laser frequency, similar to a classical plasma where the relativistic mass increase leads to self-induced transparency of laser light and other associated effects. The electron spin-1/2 effects lead to a frequency upshift or downshift of the electromagnetic (EM) wave, depending on the spin state of the plasma and the polarization of the EM wave. For laboratory solid density plasmas, the spin-1/2 effects on the propagation of light are small, but they may be significant in superdense plasma in the core of white dwarf stars. We also discuss extensions of the model to include kinetic effects of a distribution of the electrons on the nonlinear propagation of EM waves in a quantum plasma.
Planar Dirac electrons in magnetic quantum dots
NASA Astrophysics Data System (ADS)
Yang, Ning; Zhu, Jia-Lin
2012-05-01
In this paper, we explore the size- and mass-dependent energy spectra and the electronic correlation of two- and three-electron graphene magnetic quantum dots. It is found that only the magnetic dots with large size can well confine the electrons. For large graphene magnetic dots with massless (ultra-relativity) electrons, the energy level structures of two Dirac electrons and even the ground state spin and angular momentum of three electrons are quite different from those of the usual semiconductor quantum dots. Also we reveal that such differences are not due to the magnetic confinement but originate from the character of the Coulomb interaction of two-component electronic wavefunctions in graphene. We reveal that the increase of the mass leads to both the crossover of the energy spectrum structures from the ultra-relativity to non-relativity ones and the increasing of the crystallization. The results are helpful for the understanding of the mass and size effects and may be useful in controlling the few-electron states in graphene-based nanodevices.
DIRAC: reliable data management for LHCb
NASA Astrophysics Data System (ADS)
Smith, A. C.; Tsaregorodtsev, A.
2008-07-01
DIRAC, LHCb's Grid Workload and Data Management System, utilizes WLCG resources and middleware components to perform distributed computing tasks satisfying LHCb's Computing Model. The Data Management System (DMS) handles data transfer and data access within LHCb. Its scope ranges from the output of the LHCb Online system to Grid-enabled storage for all data types. It supports metadata for these files in replica and bookkeeping catalogues, allowing dataset selection and localization. The DMS controls the movement of files in a redundant fashion whilst providing utilities for accessing all metadata. To do these tasks effectively the DMS requires complete self integrity between its components and external physical storage. The DMS provides highly redundant management of all LHCb data to leverage available storage resources and to manage transient errors in underlying services. It provides data driven and reliable distribution of files as well as reliable job output upload, utilizing VO Boxes at LHCb Tier1 sites to prevent data loss. This paper presents several examples of mechanisms implemented in the DMS to increase reliability, availability and integrity, highlighting successful design choices and limitations discovered.
Two-dimensional Dirac signature of germanene
Zhang, L.; Bampoulis, P.; Houselt, A. van; Zandvliet, H. J. W.
2015-09-14
The structural and electronic properties of germanene coated Ge{sub 2}Pt clusters have been determined by scanning tunneling microscopy and spectroscopy at room temperature. The interior of the germanene sheet exhibits a buckled honeycomb structure with a lattice constant of 4.3 Å and a buckling of 0.2 Å. The zigzag edges of germanene are reconstructed and display a 4× periodicity. The differential conductivity of the interior of the germanene sheet has a V-shape, which is reminiscent of the density of states of a two-dimensional Dirac system. The minimum of the differential conductivity is located close to the Fermi level and has a non-zero value, which we ascribe to the metallic character of the underlying Ge{sub 2}Pt substrate. Near the reconstructed germanene zigzag edges the shape of the differential conductivity changes from a V-shape to a more parabolic-like shape, revealing that the reconstructed germanene zigzag edges do not exhibit a pronounced metallic edge state.
Magnetic monopoles, electric currents, and dirac strings
NASA Astrophysics Data System (ADS)
Lipkin, Harry J.; Peshkin, Murray
1986-10-01
A magnetic charge interacting with an electric current is the simplest system containing both types of charges in which there is energy exchange between the kinetic energy of the motion of the charges and other degrees of freedom. In this system several energy paradoxes arise which prevent the definition of a hamiltonian for a magnetic charge moving in a static field of a stationary current. These paradoxes are simply exhibited in a toy model which treates the dynamics of the current and its sources and includes the limiting case of an externally fixed current. Hamiltonians and lagrangians exist, but the interaction of the current variable with the monopole is nonlocal. A local multivalued lagrangian and corresponding hamiltionian exist, which apparently introduce a kind of winding number as the monopole encircles the current. Requiring exp[(i/h) ƒ; Ldt] to be singlevalued even though L and H are not, gives the Dirac quantization condition, forcing the charge which has been introduced as a classical continuous variable to have a discrete spectrum. Permanent address: Argonne National Laboratory, Argonne, IL 60439-4843, USA.
Einstein-Yang-Mills-Dirac systems from the discretized Kaluza-Klein theory
NASA Astrophysics Data System (ADS)
Wali, Kameshwar; Viet, Nguyen Ali
2017-01-01
A unified theory of the non-Abelian gauge interactions with gravity in the framework of a discretized Kaluza-Klein theory is constructed with a modified Dirac operator and wedge product. All the couplings of chiral spinors to the non-Abelian gauge fields emerge naturally as components of the coupling of the chiral spinors in the generalized gravity together with some new interactions. In particular, the currently prevailing gravity-QCD quark and gravity-electroweak-quark and lepton models are shown to follow as special cases of the general framework.
LETTER TO THE EDITOR: Treating some solid state problems with the Dirac equation
NASA Astrophysics Data System (ADS)
Renan, R.; Pacheco, M. H.; Almeida, C. A. S.
2000-12-01
The ambiguity involved in the definition of effective-mass Hamiltonians for nonrelativistic models is resolved using the Dirac equation. The multistep approximation is extended for relativistic cases allowing the treatment of arbitrary potential and effective-mass profiles without ordering problems. On the other hand, if the Schrödinger equation is used, our relativistic approach demonstrates that the two results are coincident if the BenDaniel-Duke prescription for the kinetic-energy operator is implemented. Applications for semiconductor heterostructures are discussed.
Confinement of spin-orbit induced Dirac states in quantum point contacts
NASA Astrophysics Data System (ADS)
Li, Tommy
2015-08-01
The quantum transmission problem for a particle moving in a quantum point contact in the presence of a Rashba spin-orbit interaction and applied magnetic field is solved semiclassically. A strong Rashba interaction and parallel magnetic field form emergent Dirac states at the center of the constriction, leading to the appearance of resonances which carry spin current and become bound at high magnetic fields. These states can be controlled in situ by modulation of external electric and magnetic fields, and can be used to turn the channel into a spin pump which operates at zero bias. It is shown that this effect is currently experimentally accessible in p -type quantum point contacts.
Determination of the chiral condensate from QCD Dirac spectrum on the lattice
Fukaya, H.; Onogi, T.; Aoki, S.; Chiu, T. W.; Hashimoto, S.; Kaneko, T.; Yamada, N.; Noaki, J.
2011-04-01
We calculate the chiral condensate of QCD with 2, 2+1, and 3 flavors of sea quarks. Lattice QCD simulations are performed employing dynamical overlap fermions with up- and down-quark masses covering a range between 3 and 100 MeV. On L{approx}1.8-1.9 fm lattices at a lattice spacing {approx}0.11 fm, we calculate the eigenvalue spectrum of the overlap-Dirac operator. By matching the lattice data with the analytical prediction from chiral perturbation theory at the next-to-leading order, the chiral condensate in the massless limit of up and down quarks is determined.
Dirac matrices for Chern-Simons gravity
Izaurieta, Fernando; Ramirez, Ricardo; Rodriguez, Eduardo
2012-10-06
A genuine gauge theory for the Poincare, de Sitter or anti-de Sitter algebras can be constructed in (2n- 1)-dimensional spacetime by means of the Chern-Simons form, yielding a gravitational theory that differs from General Relativity but shares many of its properties, such as second order field equations for the metric. The particular form of the Lagrangian is determined by a rank n, symmetric tensor invariant under the relevant algebra. In practice, the calculation of this invariant tensor can be reduced to the computation of the trace of the symmetrized product of n Dirac Gamma matrices {Gamma}{sub ab} in 2n-dimensional spacetime. While straightforward in principle, this calculation can become extremely cumbersome in practice. For large enough n, existing computer algebra packages take an inordinate long time to produce the answer or plainly fail having used up all available memory. In this talk we show that the general formula for the trace of the symmetrized product of 2n Gamma matrices {Gamma}{sub ab} can be written as a certain sum over the integer partitions s of n, with every term being multiplied by a numerical cofficient {alpha}{sub s}. We then give a general algorithm that computes the {alpha}-coefficients as the solution of a linear system of equations generated by evaluating the general formula for different sets of tensors B{sup ab} with random numerical entries. A recurrence relation between different coefficients is shown to hold and is used in a second, 'minimal' algorithm to greatly speed up the computations. Runtime of the minimal algorithm stays below 1 min on a typical desktop computer for up to n = 25, which easily covers all foreseeable applications of the trace formula.
Dirac matrices for Chern-Simons gravity
NASA Astrophysics Data System (ADS)
Izaurieta, Fernando; Ramírez, Ricardo; Rodríguez, Eduardo
2012-10-01
A genuine gauge theory for the Poincaré, de Sitter or anti-de Sitter algebras can be constructed in (2n - 1)-dimensional spacetime by means of the Chern-Simons form, yielding a gravitational theory that differs from General Relativity but shares many of its properties, such as second order field equations for the metric. The particular form of the Lagrangian is determined by a rank n, symmetric tensor invariant under the relevant algebra. In practice, the calculation of this invariant tensor can be reduced to the computation of the trace of the symmetrized product of n Dirac Gamma matrices Γab in 2n-dimensional spacetime. While straightforward in principle, this calculation can become extremely cumbersome in practice. For large enough n, existing computer algebra packages take an inordinate long time to produce the answer or plainly fail having used up all available memory. In this talk we show that the general formula for the trace of the symmetrized product of 2n Gamma matrices Γab can be written as a certain sum over the integer partitions s of n, with every term being multiplied by a numerical cofficient αs. We then give a general algorithm that computes the α-coefficients as the solution of a linear system of equations generated by evaluating the general formula for different sets of tensors Bab with random numerical entries. A recurrence relation between different coefficients is shown to hold and is used in a second, "minimal" algorithm to greatly speed up the computations. Runtime of the minimal algorithm stays below 1 min on a typical desktop computer for up to n = 25, which easily covers all foreseeable applications of the trace formula.
Isometry generators in momentum representation of the Dirac theory on the de Sitter spacetime
NASA Astrophysics Data System (ADS)
Cotăescu, Ion I.; Băltăţeanu, Doru-Marcel
2015-11-01
In this paper, it is shown that the covariant representation (CR) transforming the Dirac field under de Sitter isometries is equivalent to a direct sum of two unitary irreducible representations (UIRs) of the Sp(2, 2) group transforming alike the particle and antiparticle field operators in momentum representation. Their basis generators and Casimir operators are written down for the first time finding that these representations are equivalent to an UIR from the principal series whose canonical labels are determined by the fermion mass and spin. The properties of the conserved observables (i.e. one-particle operators) associated to the de Sitter isometries via Noether theorem and of the corresponding Pauli-Lubanski type operator are also pointed out.
Designer Dirac fermions and topological phases in molecular graphene.
Gomes, Kenjiro K; Mar, Warren; Ko, Wonhee; Guinea, Francisco; Manoharan, Hari C
2012-03-14
The observation of massless Dirac fermions in monolayer graphene has generated a new area of science and technology seeking to harness charge carriers that behave relativistically within solid-state materials. Both massless and massive Dirac fermions have been studied and proposed in a growing class of Dirac materials that includes bilayer graphene, surface states of topological insulators and iron-based high-temperature superconductors. Because the accessibility of this physics is predicated on the synthesis of new materials, the quest for Dirac quasi-particles has expanded to artificial systems such as lattices comprising ultracold atoms. Here we report the emergence of Dirac fermions in a fully tunable condensed-matter system-molecular graphene-assembled by atomic manipulation of carbon monoxide molecules over a conventional two-dimensional electron system at a copper surface. Using low-temperature scanning tunnelling microscopy and spectroscopy, we embed the symmetries underlying the two-dimensional Dirac equation into electron lattices, and then visualize and shape the resulting ground states. These experiments show the existence within the system of linearly dispersing, massless quasi-particles accompanied by a density of states characteristic of graphene. We then tune the quantum tunnelling between lattice sites locally to adjust the phase accrual of propagating electrons. Spatial texturing of lattice distortions produces atomically sharp p-n and p-n-p junction devices with two-dimensional control of Dirac fermion density and the power to endow Dirac particles with mass. Moreover, we apply scalar and vector potentials locally and globally to engender topologically distinct ground states and, ultimately, embedded gauge fields, wherein Dirac electrons react to 'pseudo' electric and magnetic fields present in their reference frame but absent from the laboratory frame. We demonstrate that Landau levels created by these gauge fields can be taken to the
Theoretical prediction of a strongly correlated Dirac metal.
Mazin, I I; Jeschke, Harald O; Lechermann, Frank; Lee, Hunpyo; Fink, Mario; Thomale, Ronny; Valentí, Roser
2014-07-01
Recently, the most intensely studied objects in the electronic theory of solids have been strongly correlated systems and graphene. However, the fact that the Dirac bands in graphene are made up of sp(2) electrons, which are subject to neither strong Hubbard repulsion U nor strong Hund's rule coupling J, creates certain limitations in terms of novel, interaction-induced physics that could be derived from Dirac points. Here we propose GaCu3(OH)6Cl2 (Ga-substituted herbertsmithite) as a correlated Dirac-Kagome metal combining Dirac electrons, strong interactions and frustrated magnetic interactions. Using density functional theory, we calculate its crystallographic and electronic properties, and observe that it has symmetry-protected Dirac points at the Fermi level. Its many-body physics is diverse, with possible charge, magnetic and superconducting instabilities. Through a combination of various many-body methods we study possible symmetry-lowering phase transitions such as Mott-Hubbard, charge or magnetic ordering, and unconventional superconductivity, which in this compound assumes an f-wave symmetry.
Relativistic space-charge-limited current for massive Dirac fermions
NASA Astrophysics Data System (ADS)
Ang, Y. S.; Zubair, M.; Ang, L. K.
2017-04-01
A theory of relativistic space-charge-limited current (SCLC) is formulated to determine the SCLC scaling, J ∝Vα/Lβ , for a finite band-gap Dirac material of length L biased under a voltage V . In one-dimensional (1D) bulk geometry, our model allows (α ,β ) to vary from (2,3) for the nonrelativistic model in traditional solids to (3/2,2) for the ultrarelativistic model of massless Dirac fermions. For 2D thin-film geometry we obtain α =β , which varies between 2 and 3/2, respectively, at the nonrelativistic and ultrarelativistic limits. We further provide rigorous proof based on a Green's-function approach that for a uniform SCLC model described by carrier-density-dependent mobility, the scaling relations of the 1D bulk model can be directly mapped into the case of 2D thin film for any contact geometries. Our simplified approach provides a convenient tool to obtain the 2D thin-film SCLC scaling relations without the need of explicitly solving the complicated 2D problems. Finally, this work clarifies the inconsistency in using the traditional SCLC models to explain the experimental measurement of a 2D Dirac semiconductor. We conclude that the voltage scaling 3 /2 <α <2 is a distinct signature of massive Dirac fermions in a Dirac semiconductor and is in agreement with experimental SCLC measurements in MoS2.
Observation of Dirac monopoles in a synthetic magnetic field
NASA Astrophysics Data System (ADS)
Ray, M. W.; Ruokokoski, E.; Kandel, S.; Möttönen, M.; Hall, D. S.
2014-01-01
Magnetic monopoles--particles that behave as isolated north or south magnetic poles--have been the subject of speculation since the first detailed observations of magnetism several hundred years ago. Numerous theoretical investigations and hitherto unsuccessful experimental searches have followed Dirac's 1931 development of a theory of monopoles consistent with both quantum mechanics and the gauge invariance of the electromagnetic field. The existence of even a single Dirac magnetic monopole would have far-reaching physical consequences, most famously explaining the quantization of electric charge. Although analogues of magnetic monopoles have been found in exotic spin ices and other systems, there has been no direct experimental observation of Dirac monopoles within a medium described by a quantum field, such as superfluid helium-3 (refs 10, 11, 12, 13). Here we demonstrate the controlled creation of Dirac monopoles in the synthetic magnetic field produced by a spinor Bose-Einstein condensate. Monopoles are identified, in both experiments and matching numerical simulations, at the termini of vortex lines within the condensate. By directly imaging such a vortex line, the presence of a monopole may be discerned from the experimental data alone. These real-space images provide conclusive and long-awaited experimental evidence of the existence of Dirac monopoles. Our result provides an unprecedented opportunity to observe and manipulate these quantum mechanical entities in a controlled environment.
Observation of Dirac monopoles in a synthetic magnetic field.
Ray, M W; Ruokokoski, E; Kandel, S; Möttönen, M; Hall, D S
2014-01-30
Magnetic monopoles--particles that behave as isolated north or south magnetic poles--have been the subject of speculation since the first detailed observations of magnetism several hundred years ago. Numerous theoretical investigations and hitherto unsuccessful experimental searches have followed Dirac's 1931 development of a theory of monopoles consistent with both quantum mechanics and the gauge invariance of the electromagnetic field. The existence of even a single Dirac magnetic monopole would have far-reaching physical consequences, most famously explaining the quantization of electric charge. Although analogues of magnetic monopoles have been found in exotic spin ices and other systems, there has been no direct experimental observation of Dirac monopoles within a medium described by a quantum field, such as superfluid helium-3 (refs 10-13). Here we demonstrate the controlled creation of Dirac monopoles in the synthetic magnetic field produced by a spinor Bose-Einstein condensate. Monopoles are identified, in both experiments and matching numerical simulations, at the termini of vortex lines within the condensate. By directly imaging such a vortex line, the presence of a monopole may be discerned from the experimental data alone. These real-space images provide conclusive and long-awaited experimental evidence of the existence of Dirac monopoles. Our result provides an unprecedented opportunity to observe and manipulate these quantum mechanical entities in a controlled environment.
NASA Astrophysics Data System (ADS)
McConnell, Sean; Fritzsche, Stephan; Surzhykov, Andrey
2010-03-01
During recent years, the DIRAC package has proved to be an efficient tool for studying the structural properties and dynamic behavior of hydrogen-like ions. Originally designed as a set of MAPLE procedures, this package provides interactive access to the wave and Green's functions in the non-relativistic and relativistic frameworks and supports analytical evaluation of a large number of radial integrals that are required for the construction of transition amplitudes and interaction cross sections. We provide here a new version of the DIRAC program which is developed within the framework of MATHEMATICA (version 6.0). This new version aims to cater to a wider community of researchers that use the MATHEMATICA platform and to take advantage of the generally faster processing times therein. Moreover, the addition of new procedures, a more convenient and detailed help system, as well as source code revisions to overcome identified shortcomings should ensure expanded use of the new DIRAC program over its predecessor. New version program summaryProgram title: DIRAC Catalogue identifier: ADUQ_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUQ_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 45 073 No. of bytes in distributed program, including test data, etc.: 285 828 Distribution format: tar.gz Programming language: Mathematica 6.0 or higher Computer: All computers with a license for the computer algebra package Mathematica (version 6.0 or higher) Operating system: Mathematica is O/S independent Classification: 2.1 Catalogue identifier of previous version: ADUQ_v1_0 Journal reference of previous version: Comput. Phys. Comm. 165 (2005) 139 Does the new version supersede the previous version?: Yes Nature of problem: Since the early days of quantum mechanics, the
Nonlinear modes of the tensor Dirac equation and CPT violation
NASA Technical Reports Server (NTRS)
Reifler, Frank J.; Morris, Randall D.
1993-01-01
Recently, it has been shown that Dirac's bispinor equation can be expressed, in an equivalent tensor form, as a constrained Yang-Mills equation in the limit of an infinitely large coupling constant. It was also shown that the free tensor Dirac equation is a completely integrable Hamiltonian system with Lie algebra type Poisson brackets, from which Fermi quantization can be derived directly without using bispinors. The Yang-Mills equation for a finite coupling constant is investigated. It is shown that the nonlinear Yang-Mills equation has exact plane wave solutions in one-to-one correspondence with the plane wave solutions of Dirac's bispinor equation. The theory of nonlinear dispersive waves is applied to establish the existence of wave packets. The CPT violation of these nonlinear wave packets, which could lead to new observable effects consistent with current experimental bounds, is investigated.
Dirac Cones in two-dimensional conjugated polymer networks
NASA Astrophysics Data System (ADS)
Adjizian, Jean-Joseph; Briddon, Patrick; Humbert, Bernard; Duvail, Jean-Luc; Wagner, Philipp; Adda, Coline; Ewels, Christopher
2014-12-01
Linear electronic band dispersion and the associated Dirac physics has to date been limited to special-case materials, notably graphene and the surfaces of three-dimensional (3D) topological insulators. Here we report that it is possible to create two-dimensional fully conjugated polymer networks with corresponding conical valence and conduction bands and linear energy dispersion at the Fermi level. This is possible for a wide range of polymer types and connectors, resulting in a versatile new family of experimentally realisable materials with unique tuneable electronic properties. We demonstrate their stability on substrates and possibilities for doping and Dirac cone distortion. Notably, the cones can be maintained in 3D-layered crystals. Resembling covalent organic frameworks, these materials represent a potentially exciting new field combining the unique Dirac physics of graphene with the structural flexibility and design opportunities of organic-conjugated polymer chemistry.
Spin-1 Dirac-Weyl fermions protected by bipartite symmetry
Lin, Zeren; Liu, Zhirong
2015-12-07
We propose that bipartite symmetry allows spin-1 Dirac-Weyl points, a generalization of the spin-1/2 Dirac points in graphene, to appear as topologically protected at the Fermi level. In this spirit, we provide methodology to construct spin-1 Dirac-Weyl points of this kind in a given 2D space group and get the classification of the known spin-1 systems in the literature. We also apply the workflow to predict two new systems, P3m1-9 and P31m-15, to possess spin-1 at K/K′ in the Brillouin zone of hexagonal lattice. Their stability under various strains is investigated and compared with that of T{sub 3}, an extensively studied model of ultracold atoms trapped in optical lattice with spin-1 also at K/K′.
Shot noise in systems with semi-Dirac points
Zhai, Feng; Wang, Juan
2014-08-14
We calculate the ballistic conductance and shot noise of electrons through a two-dimensional stripe system (width W ≫ length L) with semi-Dirac band-touching points. We find that the ratio between zero-temperature noise power and mean current (the Fano factor) is highly anisotropic. When the transport is along the linear-dispersion direction and the Fermi energy is fixed at the semi-Dirac point, the Fano factor has a universal value F = 0.179 while a minimum conductivity exists and scales with L{sup 1∕2}. Along the parabolic dispersion direction, the Fano factor at the semi-Dirac point has a contact-independent limit exceeding 0.9, which varies weakly with L due to the common-path interference of evanescent waves. Our findings suggest a way to discern the type of band-touching points.
Dirac charge dynamics in graphene by infrared spectroscopy
Martin, Michael C; Li, Z.Q.; Henriksen, E.A.; Jiang, Z.; Hao, Z.; Martin, Michael C; Kim, P.; Stormer, H.L.; Basov, Dimitri N.
2008-04-29
A remarkable manifestation of the quantum character of electrons in matter is offered by graphene, a single atomic layer of graphite. Unlike conventional solids where electrons are described with the Schrödinger equation, electronic excitations in graphene are governed by the Dirac hamiltonian. Some of the intriguing electronic properties of graphene, such as massless Dirac quasiparticles with linear energy-momentum dispersion, have been confirmed by recent observations. Here, we report an infrared spectromicroscopy study of charge dynamics in graphene integrated in gated devices. Our measurements verify the expected characteristics of graphene and, owing to the previously unattainable accuracy of infrared experiments, also uncover significant departures of the quasiparticle dynamics from predictions made for Dirac fermions in idealized, free-standing graphene. Several observations reported here indicate the relevance of many-body interactions to the electromagnetic response of graphene.
Spin precession of Dirac particles in Kerr geometry
NASA Astrophysics Data System (ADS)
Farooqui, Anusar
2017-01-01
We isolate and study the transformation of the intrinsic spin of Dirac particles as they propagate along timelike geodesics in Kerr geometry. Reference frames play a crucial role in the definition and measurement of the intrinsic spin of test particles. We show how observers located in the outer geometry of Kerr black holes may exploit the symmetries of the geometry to set up reference frames using purely geometric, locally-available information. Armed with these geometrically-defined reference frames, we obtain a closed-form expression for the geometrically-induced spin precession of Dirac particles in the outer geometry of Kerr black holes. We show that the spin of Dirac particles does not precess on the equatorial place of Kerr geometry; and hence, in Schwarzschild geometry.
Photocontrol of Dirac electrons in a bulk Rashba semiconductor
NASA Astrophysics Data System (ADS)
Ogawa, N.; Bahramy, M. S.; Kaneko, Y.; Tokura, Y.
2014-09-01
We demonstrate the generation of circularly polarized light induced current of bulk Dirac electrons at room temperature by exploiting a giant Rashba effect in a bulk semiconductor. The photocurrent is spin polarized due to the spin-momentum locking of the electronic states, which is manifested by a sign reversal upon flipping either the photon helicity or the sign of the Rashba parameter, without any stray current. The action spectra revealed the photon energy range, where the photocurrent is carried by the Dirac electrons at the inner Fermi surface. This photogalvanic control is enabled by the sizable spin splittings both at the valence and conduction bands with the same helicity, and also by a number of optical transition pathways compared to those in the two-dimensional Rashba systems. An efficient coupling between the photon field and large spin-orbit interaction is accordingly proposed to allow the universal control of Dirac electrons.
Electronic structure of a graphene superlattice with massive Dirac fermions
Lima, Jonas R. F.
2015-02-28
We study the electronic and transport properties of a graphene-based superlattice theoretically by using an effective Dirac equation. The superlattice consists of a periodic potential applied on a single-layer graphene deposited on a substrate that opens an energy gap of 2Δ in its electronic structure. We find that extra Dirac points appear in the electronic band structure under certain conditions, so it is possible to close the gap between the conduction and valence minibands. We show that the energy gap E{sub g} can be tuned in the range 0 ≤ E{sub g} ≤ 2Δ by changing the periodic potential. We analyze the low energy electronic structure around the contact points and find that the effective Fermi velocity in very anisotropic and depends on the energy gap. We show that the extra Dirac points obtained here behave differently compared to previously studied systems.
Classification of stable three-dimensional Dirac semimetals with nontrivial topology.
Yang, Bohm-Jung; Nagaosa, Naoto
2014-09-15
A three-dimensional (3D) Dirac semimetal (SM) is the 3D analogue of graphene having linear energy dispersion around Fermi points. Owing to the nontrivial topology of electronic wave functions, the 3D Dirac SM shows nontrivial physical properties and hosts various exotic quantum states such as Weyl SMs and topological insulators under proper external conditions. There are several kinds of Dirac SMs proposed theoretically and partly confirmed experimentally, but its unified picture is still missing. Here we propose a general framework to classify stable 3D Dirac SMs in systems having the time-reversal, inversion and uniaxial rotational symmetries. We show that there are two distinct classes of 3D Dirac SMs. In one class, the Dirac SM possesses a single Dirac point (DP) at a time-reversal invariant momentum on the rotation axis. Whereas the other class of Dirac SMs have a pair of DPs created by band inversion, and carry a quantized topological invariant.
PREFACE: International Workshop on Dirac Electrons in Solids 2015
NASA Astrophysics Data System (ADS)
Ogata, M.; Suzumura, Y.; Fuseya, Y.; Matsuura, H.
2015-04-01
It is our pleasure to publish the Proceedings of the International Workshop on Dirac Electrons in Solids held in University of Tokyo, Japan, for January 14-15, 2015. The workshop was organized by the entitled project which lasted from April 2012 to March 2015 with 10 theorists. It has been supported by a Grand-in-Aid for Scientific Research (A) from the Ministry of Education, Culture, Sports, Science, and Technology, Japan. The subjects discussed in the workshop include bismuth, organic conductors, graphene, topological insulators, new materials including Ca3PbO, and new directions in theory (superconductivity, orbital susceptibility, etc). The number of participants was about 70 and the papers presented in the workshop include four invited talks, 16 oral presentations, and 23 poster presentations. Dirac electron systems appear in various systems, such as graphene, quasi-two-dimensional organic conductors, bismuth, surface states in topological insulators, new materials like Ca3PbO. In these systems, characteristic transport properties caused by the linear dispersion of Dirac electrons and topological properties, have been extensively discussed. In addition to these, there are many interesting research fields such as Spin-Hall effect, orbital diamagnetism due to interband effects, Landau levels characteristic to Dirac dispersion, anomalous interlayer transport phenomena and magnetoresistance, the effects of spin-orbit interaction, and electron correlation. The workshop focused on recent developments of theory and experiment of Dirac electron systems in the above materials. We note that all papers published in this volume of Journal of Physics: Conference Series were peer reviewed. Reviews were performed by expert referees with professional knowledge and high scientific standards in this field. Editors made efforts so that the papers may satisfy the criterion of a proceedings journal published by IOP Publishing. We hope that all the participants of the workshop
Chemistry at the dirac point of graphene
NASA Astrophysics Data System (ADS)
Sarkar, Santanu
device mobility. To this end, we find that the organometallic hexahapto metal complexation chemistry of graphene, in which the graphene pi-band constructively hybridizes with the vacant d-orbitals of transition metals, allows the fabrication of field effect devices which retain a high degree of the mobility with enhanced on-off ratio. In summary, we find that the singular electronic structure of graphene at the Dirac point governs the chemical reactivity of graphene and this chemistry will play a vital role in propelling graphene to assume its role as the next generation electronic material beyond silicon.
SuperB evaluation of DIRAC Distributed Infrastructure
NASA Astrophysics Data System (ADS)
Fella, A.; Donvito, G.; Santeramo, B.; Gianoli, A.; Luppi, E.; Manzali, M.; Tomassetti, L.; Rama, M.; Russo, G.; Pardi, S.; Del Prete, D.; Stroili, R.; Corvo, M.; Longo, S.; Perez, A.; Di Simone, A.; Bianchi, F.; Luitz, S.; Giacomini, F.; Ciaschini, V.
2012-12-01
The SuperB asymmetric energy e+e- collider and detector to be built at the newly founded Nicola Cabibbo Lab will provide a uniquely sensitive probe of New Physics in the flavour sector of the Standard Model. SuperB distributed computing group performed a detailed evaluation of DIRAC Distributed Infrastructure for use in the SuperB experiment based on the two use cases: End User Analysis and Monte Carlo Production. Test aims to evaluate DIRAC capabilities to manage both gLite and OSG sites, File Catalog management, job and data management features in SuperB realistic use cases.
Effective Dirac dynamics of ultracold atoms in bichromatic optical lattices
Witthaut, D.; Salger, T.; Kling, S.; Grossert, C.; Weitz, M.
2011-09-15
We study the dynamics of ultracold atoms in tailored bichromatic optical lattices. By tuning the lattice parameters, one can readily engineer the band structure and realize a Dirac point, i.e., a true crossing of two Bloch bands. The dynamics in the vicinity of such a crossing is described by the one-dimensional Dirac equation, which is rigorously shown beyond the tight-binding approximation. Within this framework we analyze the effects of an external potential and demonstrate numerically that it is possible to demonstrate Klein tunneling with current experimental setups.
Three-dimensional gauge theory in Dirac formalism
NASA Astrophysics Data System (ADS)
Kamimura, Kiyoshi
1986-08-01
The Hagen model [C. R. Hagen, Ann. Phys. (NY) 157, 342 (1984); Phys. Rev. D 31, 331 (1985)] is studied using the method of constrained Hamiltonian formalism developed by Dirac [P. A. M. Dirac, Can. J. Math. 2, 129 (1950); Lectures on Quantum Mechanics (Yeshiva U. P., New York, 1964)]. The results recently obtained by Burnel and Van Der Rest-Jaspers [A. Burnel and M. Van Der Rest-Jaspers, J. Math. Phys. 26, 3155 (1985)] are reexamined and modified. There appear two second-class constraints and their choice is not crucial. The equivalence of different gauges is proved without referring to the current conservation law.
Relativistic Lagrangians for the Lorentz–Dirac equation
Deguchi, Shinichi; Nakano, Kunihiko; Suzuki, Takafumi
2015-09-15
We present two types of relativistic Lagrangians for the Lorentz–Dirac equation written in terms of an arbitrary world-line parameter. One of the Lagrangians contains an exponential damping function of the proper time and explicitly depends on the world-line parameter. Another Lagrangian includes additional cross-terms consisting of auxiliary dynamical variables and does not depend explicitly on the world-line parameter. We demonstrate that both the Lagrangians actually yield the Lorentz–Dirac equation with a source-like term.
Dirac oscillator in perpendicular magnetic and transverse electric fields
Nath, D.; Roy, P.
2014-12-15
We study (2+1) dimensional massless Dirac oscillator in the presence of perpendicular magnetic and transverse electric fields. Exact solutions are obtained and it is shown that there exists a critical magnetic field B{sub c} such that the spectrum is different in the two regions B>B{sub c} and BDirac Oscillator with magnetic as well as electric field. • Exact solutions are found. • Critical cases have been examined.
Microwave collimation based on zero index metamaterials with Dirac point.
Fang, Kai; Zhang, Yewen; Li, Fangfei; Jiang, Haitao; Li, Yunhui; Wang, Wusong; Chen, Hong
2012-11-15
The microwave zero index metamaterials (ZIMs) can be realized by loading lumped elements into two-dimensional transmission lines (TLs) with Dirac cones whose linear dispersion can appear around the center of the Brillouin zone. Based on Snell's law, the refracted angle of waves nearly equals zero when a point source radiates from the ZIM TL into the double positive (DPS) one in the ZIM-DPS TL structure. Experimental results demonstrate that at Dirac point the curved wavefronts in the ZIM region are transformed into planar ones in DPS region.
Chiral anomaly in Dirac semimetals due to dislocations
NASA Astrophysics Data System (ADS)
Chernodub, M. N.; Zubkov, M. A.
2017-03-01
The dislocation in Dirac semimetal carries an emergent magnetic flux parallel to the dislocation axis. We show that due to the emergent magnetic field, the dislocation accommodates a single fermion massless mode of the corresponding low-energy one-particle Hamiltonian. The mode is propagating along the dislocation with its spin directed parallel to the dislocation axis. In agreement with the chiral anomaly observed in Dirac semimetals, an external electric field results in the spectral flow of the one-particle Hamiltonian, in pumping of the fermionic quasiparticles out from vacuum, and in creating a nonzero axial (chiral) charge in the vicinity of the dislocation.
Does the Dirac Cone Exist in Silicene on Metal Substrates?
Quhe, Ruge; Yuan, Yakun; Zheng, Jiaxin; Wang, Yangyang; Ni, Zeyuan; Shi, Junjie; Yu, Dapeng; Yang, Jinbo; Lu, Jing
2014-01-01
Absence of the Dirac cone due to a strong band hybridization is revealed to be a common feature for epitaxial silicene on metal substrates according to our first-principles calculations for silicene on Ir, Cu, Mg, Au, Pt, Al, and Ag substrates. The destroyed Dirac cone of silicene, however, can be effectively restored with linear or parabolic dispersion by intercalating alkali metal atoms between silicene and the metal substrates, offering an opportunity to study the intriguing properties of silicene without further transfer of silicene from the metal substrates. PMID:24969493
Twisting dirac fermions: circular dichroism in bilayer graphene
NASA Astrophysics Data System (ADS)
Suárez Morell, E.; Chico, Leonor; Brey, Luis
2017-09-01
Twisted bilayer graphene is a chiral system which has been recently shown to present circular dichroism. In this work we show that the origin of this optical activity is the rotation of the Dirac fermions’ helicities in the top and bottom layer. Starting from the Kubo formula, we obtain a compact expression for the Hall conductivity that takes into account the dephasing of the electromagnetic field between the top and bottom layers and gathers all the symmetries of the system. Our results are based in both a continuum and a tight-binding model, and they can be generalized to any two-dimensional Dirac material with a chiral stacking between layers.
Radiative heat transfer in 2D Dirac materials.
Rodriguez-López, Pablo; Tse, Wang-Kong; Dalvit, Diego A R
2015-06-03
We compute the radiative heat transfer between two sheets of 2D Dirac materials, including topological Chern insulators and graphene, within the framework of the local approximation for the optical response of these materials. In this approximation, which neglects spatial dispersion, we derive both numerically and analytically the short-distance asymptotic of the near-field heat transfer in these systems, and show that it scales as the inverse of the distance between the two sheets. Finally, we discuss the limitations to the validity of this scaling law imposed by spatial dispersion in 2D Dirac materials.
Plasmonics in Dirac systems: from graphene to topological insulators.
Stauber, Tobias
2014-03-26
Recent developments in the emerging field of plasmonics in graphene and other Dirac systems are reviewed and a comprehensive introduction to the standard models and techniques is given. In particular, we discuss intrinsic plasmon excitation of single and bilayer graphene via hydrodynamic equations and the random phase approximation, but also comment on double and multilayer structures. Additionally, we address Dirac systems in the retardation limit and also with large spin–orbit coupling including topological insulators. Finally, we summarize basic properties of the charge, current and photon linear response functions in an appendix.
Anisotropic magnetotransport in Dirac-Weyl magnetic junctions
NASA Astrophysics Data System (ADS)
Ominato, Yuya; Kobayashi, Koji; Nomura, Kentaro
2017-02-01
We theoretically study the anisotropic magnetotransport in Dirac-Weyl magnetic junctions where a doped ferromagnetic Weyl semimetal is sandwiched between doped Dirac semimetals. We calculate the conductance using the Landauer formula and find that the system exhibits extraordinarily large anisotropic magnetoresistance (AMR). The AMR depends on the ratio of the Fermi energy to the strength of the exchange interaction. The origin of the AMR is the shift of the Fermi surface in the Weyl semimetal, and the mechanism is completely different from the conventional AMR originating from the spin dependent scattering and the spin-orbit interaction.
Radiative heat transfer in 2D Dirac materials
Rodriguez-López, Pablo; Tse, Wang -Kong; Dalvit, Diego A. R.
2015-05-12
We compute the radiative heat transfer between two sheets of 2D Dirac materials, including topological Chern insulators and graphene, within the framework of the local approximation for the optical response of these materials. In this approximation, which neglects spatial dispersion, we derive both numerically and analytically the short-distance asymptotic of the near-field heat transfer in these systems, and show that it scales as the inverse of the distance between the two sheets. In conclusion, we discuss the limitations to the validity of this scaling law imposed by spatial dispersion in 2D Dirac materials.
Gordon Decomposition of Dirac Spinors in Gravitational Background
NASA Astrophysics Data System (ADS)
Parashar, D.
The scheme outlined earlier is continued here to investigate the structure of Dirac spinors in the background of a gravitational field within the context of cosmological Robertson-Walker metric where the treatment is based on general considerations of spatially curved (non-flat) hypersurfaces embracing open as well as closed versions of the Universe. A Gordon decomposition of the generalized Dirac current is then carried out in terms of the polarization and the magnetization densities. We also take a look at the Klein-Gordon equation in the curved space formalism.
Dirac particles tunneling from black holes with topological defects
NASA Astrophysics Data System (ADS)
Jusufi, Kimet
2016-08-01
We study Hawking radiation of Dirac particles with spin-1 / 2 as a tunneling process from Schwarzschild-de Sitter and Reissner-Nordström-de Sitter black holes in background spacetimes with a spinning cosmic string and a global monopole. Solving Dirac's equation by employing the Hamilton-Jacobi method and WKB approximation we find the corresponding tunneling probabilities and the Hawking temperature. Furthermore, we show that the Hawking temperature of those black holes remains unchanged in presence of topological defects in both cases.
Two-dimensional Fourier transform of scaled Dirac delta curves
NASA Astrophysics Data System (ADS)
Guizar-Sicairos, Manuel; Gutiérrez-Vega, Julio C.
2004-09-01
We obtain a Fourier transform scaling relation to find analytically, numerically, or experimentally the spectrum of an arbitrary scaled two-dimensional Dirac delta curve from the spectrum of the nonscaled curve. An amplitude factor is derived and given explicitly in terms of the scaling factors and the angle of the forward tangent at each point of the curve about the positive x axis. With the scaling relation we determine the spectrum of an elliptic curve by a circular geometry instead of an elliptical one. The generalization to N-dimensional Dirac delta curves is also included.
Topological transport in Dirac electronic systems: A concise review
NASA Astrophysics Data System (ADS)
Song, Hua-Ding; Sheng, Dian; Wang, An-Qi; Li, Jin-Guang; Yu, Da-Peng; Liao, Zhi-Min
2017-03-01
Various novel physical properties have emerged in Dirac electronic systems, especially the topological characters protected by symmetry. Current studies on these systems have been greatly promoted by the intuitive concepts of Berry phase and Berry curvature, which provide precise definitions of the topological orders. In this topical review, transport properties of topological insulator (Bi2Se3), topological Dirac semimetal (Cd3As2) and topological insulator-graphene heterojunction are presented and discussed. Perspectives about transport properties of two-dimensional topological nontrivial systems, including topological edge transport, topological valley transport and topological Weyl semimetals, are provided.
Radiative heat transfer in 2D Dirac materials
Rodriguez-López, Pablo; Tse, Wang -Kong; Dalvit, Diego A. R.
2015-05-12
We compute the radiative heat transfer between two sheets of 2D Dirac materials, including topological Chern insulators and graphene, within the framework of the local approximation for the optical response of these materials. In this approximation, which neglects spatial dispersion, we derive both numerically and analytically the short-distance asymptotic of the near-field heat transfer in these systems, and show that it scales as the inverse of the distance between the two sheets. In conclusion, we discuss the limitations to the validity of this scaling law imposed by spatial dispersion in 2D Dirac materials.
Levinson theorem for the Dirac equation in D+1 dimensions
Gu Xiaoyan; Ma Zhongqi; Dong Shihai
2003-06-01
In terms of the generalized Sturm-Liouville theorem, the Levinson theorem for the Dirac equation with a spherically symmetric potential in D+1 dimensions is uniformly established as a relation between the total number of bound states and the sum of the phase shifts of the scattering states at E={+-}M with a given angular momentum. The critical case, where the Dirac equation has a half bound state, is analyzed in detail. A half bound state is a zero-momentum solution if its wave function is finite but does not decay fast enough at infinity to be square integrable.
Noncommutative Dirac quantization condition using the Seiberg-Witten map
NASA Astrophysics Data System (ADS)
Maceda, Marco; Martínez-Carbajal, Daniel
2016-11-01
The Dirac quantization condition (DQC) for magnetic monopoles in noncommutative space-time is analyzed. For this a noncommutative generalization of the method introduced by Wu and Yang is considered; the effects of noncommutativity are analyzed using the Seiberg-Witten map and the corresponding deformed Maxwell's equations are discussed. By using a perturbation expansion in the noncommutativity parameter θ , we show first that the DQC remains unmodified up to the first and second order. This result is then generalized to all orders in the expansion parameter for a class of noncommutative electric currents induced by the Seiberg-Witten map; these currents reduce to the Dirac delta function in the commutative limit.
Dirac equation on coordinate dependent noncommutative space-time
NASA Astrophysics Data System (ADS)
Kupriyanov, V. G.
2014-05-01
In this paper we discuss classical aspects of spinor field theory on the coordinate dependent noncommutative space-time. The noncommutative Dirac equation describing spinning particle in an external vector field and the corresponding action principle are proposed. The specific choice of a star product allows us to derive a conserved noncommutative probability current and to obtain the energy-momentum tensor for free noncommutative spinor field. Finally, we consider a free noncommutative Dirac fermion and show that if the Poisson structure is Lorentz-covariant, the standard energy-momentum dispersion relation remains valid.
Job monitoring on DIRAC for Belle II distributed computing
NASA Astrophysics Data System (ADS)
Kato, Yuji; Hayasaka, Kiyoshi; Hara, Takanori; Miyake, Hideki; Ueda, Ikuo
2015-12-01
We developed a monitoring system for Belle II distributed computing, which consists of active and passive methods. In this paper we describe the passive monitoring system, where information stored in the DIRAC database is processed and visualized. We divide the DIRAC workload management flow into steps and store characteristic variables which indicate issues. These variables are chosen carefully based on our experiences, then visualized. As a result, we are able to effectively detect issues. Finally, we discuss the future development for automating log analysis, notification of issues, and disabling problematic sites.
NASA Astrophysics Data System (ADS)
Gonçalves, Bruno; Ribeiro, Baltazar J.; Pereira, Dante D.; Dias, Mário M.
2016-05-01
In this paper, we focus our attention in the inconsistency that appears when the semi-exact Foldy-Wouthuysen transformation for the Dirac field interacting with space-time torsion field is performed. In order to solve this problem, we present a new involution operator that makes possible to perform the exact transformation when torsion field is present. Such operator has a structure, well known in the literature, composed of the product of an operator that acts in the matrices space and another one that acts in the function space. We also present the bound state of this theory and discuss the possible experimental analysis.
From Rational Numbers to Dirac's Bra and Ket: Symbolic Representation of Physical Laws
NASA Astrophysics Data System (ADS)
D'Agostino, Salvo
2002-05-01
Beginning at least in the nineteenth century, symbols used by physicists in their equations interacted with their physical concepts. In the 1850s, Wilhelm Eduard Weber introduced a more rational order into symbolization by adopting an absolute system of units, and thus expressing electrodynamic laws in the form of algebraic equations instead of proportionality relationships, the formerly accepted representation of physical laws. In the 1860s, James Clerk Maxwell made a further advance by using dimensional quantities, and more complex symbolic forms such as gradient, convergence, rotor, and the like, in his electromagnetic and kinetic theories. In the twentieth century, Werner Heisenberg, Max Born, Erwin Schrödinger, and others introduced new symbols for complex numbers, operators, and matrices, thus passing from the representation of metrical properties of physical systems to higher-level mathematical objects. This process was enhanced in modern theoretical physics through the introduction of matrices, creation and destruction operators, Paul A. M. Dirac's q and c numbers, and so on. In the 1930s, Dirac radicalized this transformation of symbols, being aware of the profound modification in the method and scope of the mathematical-physical relationship it entailed.
The asymptotics of an eigenfunction-correlation determinant for Dirac-δ perturbations
NASA Astrophysics Data System (ADS)
Gebert, Martin
2015-07-01
We prove the exact asymptotics of the scalar product of the ground states of two non-interacting Fermi gases confined to a 3-dimensional ball BL of radius L in the thermodynamic limit, where the underlying one-particle operators differ by a Dirac-δ perturbation. More precisely, we show the algebraic decay of the correlation determinant |det|(< φ)j L, ψk L > j , k = 1 , … , N 2 = L - ζ ( E ) + o ( 1 ) , as N, L → ∞ and N / |B L| → ρ > 0 , where φj L and ψk L denote the lowest-energy eigenfunctions of the finite-volume one-particle Schrödinger operators. The decay exponent is given in terms of the s-wave scattering phase shift ζ ( E ) ≔ /1 π 2 δ 2 ( √{ E } ) . For an attractive Dirac-δ perturbation, we conclude that the decay exponent /1 π 2 ↑arcsin↑ |T ( E ) / 2| HS 2 found in the work of Gebert et al. [J. Spect. Theory (to be published); e-print arXiv:1407.2512] does not provide a sharp upper bound on the decay of the correlation determinant.
NASA Astrophysics Data System (ADS)
Roy, Bitan; Yang, Kun
2013-12-01
The effective theory for bilayer graphene (BLG), subject to parallel/in-plane magnetic fields, is derived. With a sizable magnetic field the trigonal warping becomes irrelevant, and one ends up with two Dirac points in the vicinity of each valley in the low-energy limit, similar to the twisted BLG. Combining twisting and parallel field thus gives rise to a Dirac system with tunable Fermi velocity and cutoff. If the interactions are sufficiently strong, several fully gapped states can be realized in these systems, in addition to the ones in a pristine setup. Transformations of the order parameters under various symmetry operations are analyzed. The quantum critical behavior of various phase transitions driven by the twisting and the magnetic field is reported. The effects of an additional perpendicular field and possible ways to realize the new massive phases are highlighted.
Realizing double Dirac particles in the presence of electronic interactions
NASA Astrophysics Data System (ADS)
Di Sante, Domenico; Hausoel, Andreas; Barone, Paolo; Tomczak, Jan M.; Sangiovanni, Giorgio; Thomale, Ronny
2017-09-01
Double Dirac fermions have recently been identified as possible quasiparticles hosted by three-dimensional crystals with particular nonsymmorphic point-group symmetries. Applying a combined approach of a b initio methods and dynamical mean-field theory, we investigate how interactions and double Dirac band topology conspire to form the electronic quantum state of Bi2CuO4 . We derive a downfolded eight-band model of the pristine material at low energies around the Fermi level. By tuning the model parameters from the free band structure to the realistic strongly correlated regime, we find a persistence of the double Dirac dispersion until its constituting time-reversal symmetry is broken due to the onset of magnetic ordering at the Mott transition. Our calculations suggest that the double Dirac fermions in Bi2CuO4 can be restored by experimentally accessible hydrostatic pressures. In light of the growing attention to the topological quantum chemistry approach, our results on Bi2CuO4 show how many-body effects must be included beyond the static mean-field level for reliable predictions on new materials.
Hydrogenated arsenenes as planar magnet and Dirac material
Zhang, Shengli; Cai, Bo; Zeng, Haibo E-mail: zeng.haibo@njust.edu.cn; Hu, Yonghong; Hu, Ziyu E-mail: zeng.haibo@njust.edu.cn
2015-07-13
Arsenene and antimonene are predicted to have 2.49 and 2.28 eV band gaps, which have aroused intense interest in the two-dimensional (2D) semiconductors for nanoelectronic and optoelectronic devices. Here, the hydrogenated arsenenes are reported to be planar magnet and 2D Dirac materials based on comprehensive first-principles calculations. The semi-hydrogenated (SH) arsenene is found to be a quasi-planar magnet, while the fully hydrogenated (FH) arsenene is a planar Dirac material. The buckling height of pristine arsenene is greatly decreased by the hydrogenation, resulting in a planar and relatively low-mass-density sheet. The electronic structures of arsenene are also evidently altered after hydrogenating from wide-band-gap semiconductor to metallic material for SH arsenene, and then to Dirac material for FH arsenene. The SH arsenene has an obvious magnetism, mainly contributed by the p orbital of the unsaturated As atom. Such magnetic and Dirac materials modified by hydrogenation of arsenene may have potential applications in future optoelectronic and spintronic devices.
Geometrization of the Dirac theory of the electron
NASA Technical Reports Server (NTRS)
Fock, V.
1977-01-01
Using the concept of parallel displacement of a half vector, the Dirac equations are generally written in invariant form. The energy tensor is formed and both the macroscopic and quantum mechanic equations of motion are set up. The former have the usual form: divergence of the energy tensor equals the Lorentz force and the latter are essentially identical with those of the geodesic line.
Dirac cones in the spectrum of bond-decorated graphenes
Van den Heuvel, Willem Soncini, Alessandro
2014-06-21
We present a two-band model based on periodic Hückel theory, which is capable of predicting the existence and position of Dirac cones in the first Brillouin zone of an infinite class of two-dimensional periodic carbon networks, obtained by systematic perturbation of the graphene connectivity by bond decoration, that is by inclusion of arbitrary π-electron Hückel networks into each of the three carbon–carbon π-bonds within the graphene unit cell. The bond decoration process can fundamentally modify the graphene unit cell and honeycomb connectivity, representing a simple and general way to describe many cases of graphene chemical functionalization of experimental interest, such as graphyne, janusgraphenes, and chlorographenes. Exact mathematical conditions for the presence of Dirac cones in the spectrum of the resulting two-dimensional π-networks are formulated in terms of the spectral properties of the decorating graphs. Our method predicts the existence of Dirac cones in experimentally characterized janusgraphenes and chlorographenes, recently speculated on the basis of density functional theory calculations. For these cases, our approach provides a proof of the existence of Dirac cones, and can be carried out at the cost of a back of the envelope calculation, bypassing any diagonalization step, even within Hückel theory.
De-Mystifying the Dirac [delta]-Function
ERIC Educational Resources Information Center
Lutzer, Carl V.
2007-01-01
In this article, we discuss an alternative method of teaching students about the Dirac [delta]-function. The method provides students with the mechanical tools they need in order to work with the [delta]-function in practice, while also fostering a sense of cohesion in the calculus curriculum by presenting the [delta]-function as an evolution of…
Path Integral for Dirac oscillator with generalized uncertainty principle
Benzair, H.; Boudjedaa, T.; Merad, M.
2012-12-15
The propagator for Dirac oscillator in (1+1) dimension, with deformed commutation relation of the Heisenberg principle, is calculated using path integral in quadri-momentum representation. As the mass is related to momentum, we then adapt the space-time transformation method to evaluate quantum corrections and this latter is dependent from the point discretization interval.
Strain-Mediated Modification of Phagraphene Dirac Cones
Lopez-Bezanilla, Alejandro
2016-07-07
We present a first-principles study on the electronic and dynamical properties of phagraphene [Nano Lett., 2015, 15 (9), pp 6182]. This carbon allotrope exhibits a square unit cell, Dirac cones, and robustness against uniaxial deformation. By analyzing the contribution of each carbon atom orbital in the formation of the electronic states, we conclude that only the pz orbitals of eight out of the twenty atoms in the square unit cell are responsible of the formation of the nano-structure Dirac cones. Spatial symmetry breaking of the underlying honeycomb-like network upon shear stress application leads to a band gap opening. The analysismore » of the phonon spectra demonstrates that the dynamical stability of phagraphene is guaranteed for small distortion angles. Phagraphene is identified here as the first all-C graphitic monolayer with Dirac cones modifiable by a small and realistic physical deformation. The analysis and conclusions of this study can be applied to other monolayered materials exhibiting Dirac cones in square lattices.« less
P3/2 state in New Dirac Equation
NASA Astrophysics Data System (ADS)
Maker, David
2006-03-01
In this talk I explain the very interesting properties of the most probable excited state of a new type of Dirac equation and singularity when applied to a single type of charge 'e'. Notably this first excited state psi*psi P3/2 (state lobes) shape is a trifolium, three lobed. Thus for each lobe there is a (1/3)e average charge given the charge 'e' spends on average 1/3 of the time in each lobe. Thus combinations of lobes have average charge, e/3, 2e/3 (FRACTIONAL CHARGE) or e. The lobes can't leave (ASSYMPTOTIC FREEDOM) or move so are NONRELATIVISTIC. The singularity of this Dirac equation results in containment at about .6 Fermi, the TOTAL CHARGE is still `e'(explaining away the need for COLOR), etc. Most importantly the Frobenius series solution to this new Dirac equation also gives accurate hadron eigenvalues. You quickly see that you are getting here all the properties of quarks (identified here as individual lobes) obtained in a very simple way from the movement of a single unit charge `e' using this new Dirac equation. There appears no simpler way to explain all these many quark properties.
Common origin of neutrino mass, dark matter and Dirac leptogenesis
NASA Astrophysics Data System (ADS)
Borah, Debasish; Dasgupta, Arnab
2016-12-01
We study the possibility of generating tiny Dirac neutrino masses at one loop level through the scotogenic mechanism such that one of the particles going inside the loop can be a stable cold dark matter (DM) candidate. Majorana mass terms of singlet fermions as well as tree level Dirac neutrino masses are prevented by incorporating the presence of additional discrete symmetries in a minimal fashion, which also guarantee the stability of the dark matter candidate. Due to the absence of total lepton number violation, the observed baryon asymmetry of the Universe is generated through the mechanism of Dirac leptogenesis where an equal and opposite amount of leptonic asymmetry is generated in the left and right handed sectors which are prevented from equilibration due to tiny Dirac Yukawa couplings. Dark matter relic abundance is generated through its usual freeze-out at a temperature much below the scale of leptogenesis. We constrain the relevant parameter space from neutrino mass, baryon asymmetry, Planck bound on dark matter relic abundance, and latest LUX bound on spin independent DM-nucleon scattering cross section. We also discuss the charged lepton flavour violation (μ → e γ) and electric dipole moment of electron in this model in the light of the latest experimental data and constrain the parameter space of the model.
Chiral tunnelling of Dirac electrons in strained graphene
NASA Astrophysics Data System (ADS)
Garcia-Saravia, A.; Cordourier-Maruri, G.; Cifuentes-Quintal, M. E.; Martinez-Guerra, E.; de Coss, R.
2009-03-01
The behavior of the electrons in graphene is like massless Dirac fermions, which is a consequence of the characteristic energy spectrum of this material (E˜k). Perfect chiral tunnelling is expected when Dirac electrons pass through a step barrier (Klein paradox). However, in a two-dimensional system like graphene, the perfect tunneling is obtained only in a small range of incident angles. In the present work, we have studied the uniaxial deformation as a method of tunning the electronic transmittance in graphene. The effect of the armchair and zigzag strain on graphene was studied by means of first principles calculations, using the Density Functional Theory. For the calculations we used the pseudopotential-LCAO method. We found that the uniaxial deformations, induce an ellipsoidal distortion of the Dirac cones and isotropy breaking of the Fermi velocity. Finally, we used the Dirac--like equation to find the electronic transmittance as a function of the incident angle. We obtain that the strain induces a strong changes in the transmittance when the deformation is perpendicular to the incident axis.
Dirac model of electronic transport in graphene antidot barriers.
Thomsen, M R; Brun, S J; Pedersen, T G
2014-08-20
In order to use graphene for semiconductor applications, such as transistors with high on/off ratios, a band gap must be introduced into this otherwise semimetallic material. A promising method of achieving a band gap is by introducing nanoscale perforations (antidots) in a periodic pattern, known as a graphene antidot lattice (GAL). A graphene antidot barrier (GAB) can be made by introducing a 1D GAL strip in an otherwise pristine sheet of graphene. In this paper, we will use the Dirac equation (DE) with a spatially varying mass term to calculate the electronic transport through such structures. Our approach is much more general than previous attempts to use the Dirac equation to calculate scattering of Dirac electrons on antidots. The advantage of using the DE is that the computational time is scale invariant and our method may therefore be used to calculate properties of arbitrarily large structures. We show that the results of our Dirac model are in quantitative agreement with tight-binding for hexagonal antidots with armchair edges. Furthermore, for a wide range of structures, we verify that a relatively narrow GAB, with only a few antidots in the unit cell, is sufficient to give rise to a transport gap.
Dirac-like plasmons in honeycomb lattices of metallic nanoparticles.
Weick, Guillaume; Woollacott, Claire; Barnes, William L; Hess, Ortwin; Mariani, Eros
2013-03-08
We consider a two-dimensional honeycomb lattice of metallic nanoparticles, each supporting a localized surface plasmon, and study the quantum properties of the collective plasmons resulting from the near-field dipolar interaction between the nanoparticles. We analytically investigate the dispersion, the effective Hamiltonian, and the eigenstates of the collective plasmons for an arbitrary orientation of the individual dipole moments. When the polarization points close to the normal to the plane, the spectrum presents Dirac cones, similar to those present in the electronic band structure of graphene. We derive the effective Dirac Hamiltonian for the collective plasmons and show that the corresponding spinor eigenstates represent Dirac-like massless bosonic excitations that present similar effects to electrons in graphene, such as a nontrivial Berry phase and the absence of backscattering off smooth inhomogeneities. We further discuss how one can manipulate the Dirac points in the Brillouin zone and open a gap in the collective plasmon dispersion by modifying the polarization of the localized surface plasmons, paving the way for a fully tunable plasmonic analogue of graphene.
Dirac's HdCdTe semimetals grown by MBE technology
NASA Astrophysics Data System (ADS)
Grendysa, Jakub; Becker, Charles R.; Trzyna, Malgorzata; Wojnarowska-Nowak, Renata; Bobko, Ewa; Sheregii, Eugen M.
2016-12-01
Peculiarities of the MBE growth technology for the Dirac's semimetal based on the Hg1-xCdxTe alloys have been presented. Composition of layers was controlled by ToF-SIMS, FTIR measurements, and by the E1+Δ1 maximum position of optical reflectivity in visible reason. The surface morphology has by determined via atomic force and electron microscopy.
Different models of gravitating Dirac fermions in optical lattices
NASA Astrophysics Data System (ADS)
Celi, Alessio
2017-07-01
In this paper I construct the naive lattice Dirac Hamiltonian describing the propagation of fermions in a generic 2D optical metric for different lattice and flux-lattice geometries. First, I apply a top-down constructive approach that we first proposed in [Boada et al., New J. Phys. 13, 035002 (2011)] to the honeycomb and to the brickwall lattices. I carefully discuss how gauge transformations that generalize momentum (and Dirac cone) shifts in the Brillouin zone in the Minkowski homogeneous case can be used in order to change the phases of the hopping. In particular, I show that lattice Dirac Hamiltonian for Rindler spacetime in the honeycomb and brickwall lattices can be realized by considering real and isotropic (but properly position dependent) tunneling terms. For completeness, I also discuss a suitable formulation of Rindler Dirac Hamiltonian in semi-synthetic brickwall and π-flux square lattices (where one of the dimension is implemented by using internal spin states of atoms as we originally proposed in [Boada et al., Phys. Rev. Lett. 108, 133001 (2012)] and [Celi et al., Phys. Rev. Lett. 112, 043001 (2014)]).
De-Mystifying the Dirac [delta]-Function
ERIC Educational Resources Information Center
Lutzer, Carl V.
2007-01-01
In this article, we discuss an alternative method of teaching students about the Dirac [delta]-function. The method provides students with the mechanical tools they need in order to work with the [delta]-function in practice, while also fostering a sense of cohesion in the calculus curriculum by presenting the [delta]-function as an evolution of…
Type-II Dirac surface states in topological crystalline insulators
NASA Astrophysics Data System (ADS)
Chiu, Ching-Kai; Chan, Y.-H.; Li, Xiao; Nohara, Y.; Schnyder, A. P.
2017-01-01
Recently, it has been realized that topological Weyl semimetals come in two different varieties: (i) with standard Weyl cones with pointlike Fermi surfaces (type I) and (ii) with tilted Weyl cones that appear at the contact of electron and hole pockets (type II). These two types of Weyl semimetals have very different physical properties, in particular, in their thermodynamics and magnetotransport. Here, we show that Dirac cone surface states of topological crystalline insulators can be distinguished in a similar way. We demonstrate this in terms of a general surface theory and then apply this knowledge to a family of antiperovskites of the form A3E O , where A denotes an alkaline earth metal, while E stands for Pb or Sn. Using ab initio DFT calculations, we investigate the bulk and surface topology of these antiperovskites and show that they exhibit type-I as well as type-II Dirac surface states protected by reflection symmetry. We find that the type-II Dirac states, as opposed to the type-I Dirac states, exhibit characteristic van Hove singularities in their dispersion, which lead to different thermodynamic properties, and which can serve as an experimental fingerprint of type-II surface states. The different magnetotransport characteristics between type-I and type-II surface states are discussed. In addition, we show that both type-I and type-II surface states exhibit an unusual helical spin polarization, which could lead to topological surface superconductivity.
750 GeV diphotons from supersymmetry with Dirac gauginos
NASA Astrophysics Data System (ADS)
Cohen, Timothy; Kribs, Graham D.; Nelson, Ann E.; Ostdiek, Bryan
2016-07-01
Motivated by the recent excess in the diphoton invariant mass near 750 GeV, we explore a supersymmetric extension of the Standard Model that includes the minimal set of superpartners as well as additional Dirac partner chiral superfields in the adjoint representation for each gauge group. The bino partner pseudoscalar is identified as the 750 GeV resonance, while superpotential interactions between it and the gluino (wino) partners yield production via gluon fusion (decay to photon pairs) at one-loop. The gauginos and these additional adjoint superpartners are married by a Dirac mass and must also have Majorana masses. While a large wino partner Majorana mass is necessary to explain the excess, the gluino can be approximately Dirac-like, providing benefits consistent with being both "supersoft" (loop corrections to the scalar masses from Dirac gauginos are free of logarithmic enhancements) and "supersafe" (the experimental limits on the squark/gluino masses can be relaxed due to the reduced production rate). Consistency with the measured Standard Model-like Higgs boson mass is imposed, and a numerical exploration of the parameter space is provided. Models that can account for the diphoton excess are additionally characterized by having couplings that can remain perturbative up to very high scales, while remaining consistent with experimental constraints, the Higgs boson mass, and an electroweak scale which is not excessively fine-tuned.
Strain-Mediated Modification of Phagraphene Dirac Cones
Lopez-Bezanilla, Alejandro
2016-07-07
We present a first-principles study on the electronic and dynamical properties of phagraphene [Nano Lett., 2015, 15 (9), pp 6182]. This carbon allotrope exhibits a square unit cell, Dirac cones, and robustness against uniaxial deformation. By analyzing the contribution of each carbon atom orbital in the formation of the electronic states, we conclude that only the pz orbitals of eight out of the twenty atoms in the square unit cell are responsible of the formation of the nano-structure Dirac cones. Spatial symmetry breaking of the underlying honeycomb-like network upon shear stress application leads to a band gap opening. The analysis of the phonon spectra demonstrates that the dynamical stability of phagraphene is guaranteed for small distortion angles. Phagraphene is identified here as the first all-C graphitic monolayer with Dirac cones modifiable by a small and realistic physical deformation. The analysis and conclusions of this study can be applied to other monolayered materials exhibiting Dirac cones in square lattices.
Distinguishing between Dirac and Majorana neutrinos withtwo-particle interferometry
Gutierrez, Thomas D.
2006-03-02
Two-particle interferometry, a second-order interferenceeffect, is explored as another possible tool to distinguish betweenmassive Dirac and Majorana neutrinos. A simple theoretical framework isdiscussed in the context of several gedanken experiments. The method canin principle provide both the mass scale and the quantum nature of theneutrino for a certain class of incoherent left-handed sourcecurrents.
Dirac Magnon Nodal Loops in Quasi-2D Quantum Magnets.
Owerre, S A
2017-07-31
In this report, we propose a new concept of one-dimensional (1D) closed lines of Dirac magnon nodes in two-dimensional (2D) momentum space of quasi-2D quantum magnetic systems. They are termed "2D Dirac magnon nodal-line loops". We utilize the bilayer honeycomb ferromagnets with intralayer coupling J and interlayer coupling J L , which is realizable in the honeycomb chromium compounds CrX3 (X ≡ Br, Cl, and I). However, our results can also exist in other layered quasi-2D quantum magnetic systems. Here, we show that the magnon bands of the bilayer honeycomb ferromagnets overlap for J L ≠ 0 and form 1D closed lines of Dirac magnon nodes in 2D momentum space. The 2D Dirac magnon nodal-line loops are topologically protected by inversion and time-reversal symmetry. Furthermore, we show that they are robust against weak Dzyaloshinskii-Moriya interaction Δ DM < J L and possess chiral magnon edge modes.
Some Characterizations of Dirac Type Singularity of Monopoles
NASA Astrophysics Data System (ADS)
Mochizuki, Takuro; Yoshino, Masaki
2017-08-01
We study singular monopoles on open subsets in the 3-dimensional Euclidean space. We give two characterizations of Dirac type singularities. One is given in terms of the growth order of the norms of sections which are invariant by the scattering map. The other is given in terms of the growth order of the norms of the Higgs fields.
Dirac Fermions in heterostructures for designer topological phases
NASA Astrophysics Data System (ADS)
Feng, Ji
2014-03-01
Massless Dirac Fermions are found in graphene and on the surfaces of topological insulators, which are quasiparticles moving at a constant speed independent of its energy as governed by relativistic quantum mechanics. In this talk, I will show, via interfacial orbital design of Dirac states, emergent topological phases can be engineered in artificial heterostructures. As a first example, I will show that a novel class of half semi-metallic Dirac electronic phase emerges at the interface CrO2 with TiO2 in both thin film and superlattice configurations. With four spin-polarized Dirac points in the band structure, this system with simple, non-topological oxides displays spontaneous quantum anomalous Hall effect. In a second example, I will show that the superlattice valley engineering, starting with the SnTe topological mirror insulator, leads to designer topological phases with a remarkably rich phase diagram. JF acknowledges financial support by NSFC Project 11174009, and China 973 Program Projects 2013CB921900 and 2011CBA00109.
Tilted Dirac cone on W(110) protected by mirror symmetry
NASA Astrophysics Data System (ADS)
Varykhalov, A.; Marchenko, D.; Sánchez-Barriga, J.; Golias, E.; Rader, O.; Bihlmayer, G.
2017-06-01
Topologically nontrivial states reveal themselves in strongly spin-orbit coupled systems by Dirac cones. However, their appearance is not a sufficient criterion for a topological phase. In topological insulators, where these states protect surface metallicity, they are straightforwardly assigned based on bulk-boundary correspondence. On metals, where these states are suspected to have tremendous impact as well, e.g., in catalysis, their topological protection is difficult to assess due to the lacking band gap and the frequent assignment to topological properties appears unjustified. Here, we discover by angle-resolved photoemission a state with the dispersion of a Dirac cone at a low-symmetry point of W(110). Our ab initio calculations predict this feature with a linear band crossing and high spin polarization. However, instead of being born by topology, the states arise from Rashba split bands and do not fundamentally depend on the opening of a spin-orbit gap. On the other hand, we find that the [001] mirror plane protects the band crossing point and renormalizes the dispersion towards a Dirac-cone shape. In this sense, the discovered state is the metal counterpart of the surface state of a topological crystalline insulator. The Dirac cone is tilted due to its origin in an accidental band crossing away from high symmetry points. Tilted Dirac cones have recently been predicted for two- and three-dimensional materials and were observed in three-dimensional Weyl semimetals. Accordingly, the protection and renormalization by mirror symmetry uncovered here are a potentially much wider spread phenomenon which does not require topological properties. Our results also indicate why the massive gapless crossing predicted for topological crystalline insulators has never been observed.
Phonon-drag thermopower in 3D Dirac semimetals.
Kubakaddi, S S
2015-11-18
A theory of low-temperature phonon-drag thermopower S(g) in three-dimensional (3D) Dirac semimetals has been developed considering screened electron-phonon deformation potential coupling. Numerical investigations of S(g), in the boundary scattering regime for phonons, are made in 3D Dirac semimetal Cd3As2, as a function of temperature T and electron concentration n e. S(g) is found to increase rapidly for about T < 1 K and nearly levels off for higher T. It is also seen that S(g) increases (decreases) with decreasing n e at lower (higher) T (<2 K). A screening effect is found to be very significant, strongly affecting T and n e dependence for about <1 K and becoming negligible at higher temperature. In the Bloch-Gruneisen (BG) regime the power laws S(g) ~ T(8) (T(4)) and S(g) ~ n(e)(-5/3)(n(e)(-1/3) with (without) screening are obtained. These laws with respect to T and n e are, respectively, characteristics of 3D phonons and Dirac 3D electrons. Comparison with diffusion thermopower S(d) shows that S (g) dominates (and is much greater than) S(d) for about T > 0.2 K. Herring's law S(g) μ p ~ T (-1), relating phonon limited mobility μ p and S(g) in the BG regime, is shown to be valid in 3D Dirac semimetals. The results obtained here are compared with those in 3D semiconductors, low-dimensional semiconductor heterojunctions and graphene. We conclude that n e-dependent measurements, rather than T-dependent ones, provide a clearer signature of the 3D Dirac semimetal phase.
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.
Analysis of DIRAC's behavior using model checking with process algebra
NASA Astrophysics Data System (ADS)
Remenska, Daniela; Templon, Jeff; Willemse, Tim; Bal, Henri; Verstoep, Kees; Fokkink, Wan; Charpentier, Philippe; Graciani Diaz, Ricardo; Lanciotti, Elisa; Roiser, Stefan; Ciba, Krzysztof
2012-12-01
DIRAC is the grid solution developed to support LHCb production activities as well as user data analysis. It consists of distributed services and agents delivering the workload to the grid resources. Services maintain database back-ends to store dynamic state information of entities such as jobs, queues, staging requests, etc. Agents use polling to check and possibly react to changes in the system state. Each agent's logic is relatively simple; the main complexity lies in their cooperation. Agents run concurrently, and collaborate using the databases as shared memory. The databases can be accessed directly by the agents if running locally or through a DIRAC service interface if necessary. This shared-memory model causes entities to occasionally get into inconsistent states. Tracing and fixing such problems becomes formidable due to the inherent parallelism present. We propose more rigorous methods to cope with this. Model checking is one such technique for analysis of an abstract model of a system. Unlike conventional testing, it allows full control over the parallel processes execution, and supports exhaustive state-space exploration. We used the mCRL2 language and toolset to model the behavior of two related DIRAC subsystems: the workload and storage management system. Based on process algebra, mCRL2 allows defining custom data types as well as functions over these. This makes it suitable for modeling the data manipulations made by DIRAC's agents. By visualizing the state space and replaying scenarios with the toolkit's simulator, we have detected race-conditions and deadlocks in these systems, which, in several cases, were confirmed to occur in the reality. Several properties of interest were formulated and verified with the tool. Our future direction is automating the translation from DIRAC to a formal model.
Phonon-drag thermopower in 3D Dirac semimetals
NASA Astrophysics Data System (ADS)
Kubakaddi, S. S.
2015-11-01
A theory of low-temperature phonon-drag thermopower S g in three-dimensional (3D) Dirac semimetals has been developed considering screened electron-phonon deformation potential coupling. Numerical investigations of S g, in the boundary scattering regime for phonons, are made in 3D Dirac semimetal Cd3As2, as a function of temperature T and electron concentration n e. S g is found to increase rapidly for about T < 1 K and nearly levels off for higher T. It is also seen that S g increases (decreases) with decreasing n e at lower (higher) T (<2 K). A screening effect is found to be very significant, strongly affecting T and n e dependence for about <1 K and becoming negligible at higher temperature. In the Bloch-Gruneisen (BG) regime the power laws S g ~ T 8 (T 4) and S g ~ n\\text{e}-5/3 (n\\text{e}-1/3) with (without) screening are obtained. These laws with respect to T and n e are, respectively, characteristics of 3D phonons and Dirac 3D electrons. Comparison with diffusion thermopower S d shows that S g dominates (and is much greater than) S d for about T > 0.2 K. Herring’s law S g μ p ~ T -1, relating phonon limited mobility μ p and S g in the BG regime, is shown to be valid in 3D Dirac semimetals. The results obtained here are compared with those in 3D semiconductors, low-dimensional semiconductor heterojunctions and graphene. We conclude that n e-dependent measurements, rather than T-dependent ones, provide a clearer signature of the 3D Dirac semimetal phase.
Phenomenology of a semi-Dirac semi-Weyl semimetal
NASA Astrophysics Data System (ADS)
Banerjee, S.; Pickett, W. E.
2012-08-01
We extend the semiclassical study of fermionic particle-hole symmetric semi-Dirac (more appropriately, semi-Dirac semi-Weyl) dispersion of quasiparticles, ɛK=±(kx2/2m)2+(vky)2)=±ɛ0Kx4+Ky2 in dimensionless units, discovered computationally in oxide heterostructures by Pardo and collaborators. This unique system is a highly anisotropic sister phase of both (symmetric) graphene and what has become known as a Weyl semimetal, having
NASA Astrophysics Data System (ADS)
Lu, Wei; Ge, Shaofeng; Liu, Xuefeng; Lu, Hong; Li, Caizhen; Lai, Jiawei; Zhao, Chuan; Liao, Zhimin; Jia, Shuang; Sun, Dong
2017-01-01
Three-dimensional (3D) Dirac semimetals that can be seen as 3D analogues of graphene have attracted enormous interest in research recently. In order to apply these ultra-high-mobility materials in future electronic/optoelectronic devices, it is crucial to understand the relaxation dynamics of photoexcited carriers and their coupling with lattice. In this paper, we report ultrafast transient reflection measurements of the photoexcited carrier dynamics in cadmium arsenide (C d3A s2 ), which is one of the most stable Dirac semimetals that have been confirmed experimentally. By using the low-energy probe photon of 0.3 eV, we probed the dynamics of the photoexcited carriers that are Dirac-Fermi-like approaching the Dirac point. We systematically studied the transient reflection on bulk and nanoplate samples that have different doping intensities by tuning the probe wavelength, pump power, and lattice temperature and find that the dynamical evolution of carrier distributions can be retrieved qualitatively by using a two-temperature model. This result is very similar to that of graphene, but the carrier cooling through the optical phonon couplings is slower and lasts over larger electron temperature range because the optical phonon energies in C d3A s2 are much lower than those in graphene.
Precise identification of Dirac-like point through a finite photonic crystal square matrix.
Dong, Guoyan; Zhou, Ji; Yang, Xiulun; Meng, Xiangfeng
2016-11-18
The phenomena of the minimum transmittance spectrum or the maximum reflection spectrum located around the Dirac frequency have been observed to demonstrate the 1/L scaling law near the Dirac-like point through the finite ribbon structure. However, so far there is no effective way to identify the Dirac-like point accurately. In this work we provide an effective measurement method to identify the Dirac-like point accurately through a finite photonic crystal square matrix. Based on the Dirac-like dispersion achieved by the accidental degeneracy at the centre of the Brillouin zone of dielectric photonic crystal, both the simulated and experimental results demonstrate that the transmittance spectra through a finite photonic crystal square matrix not only provide the clear evidence for the existence of Dirac-like point but also can be used to identify the precise location of Dirac-like point by the characteristics of sharp cusps embedded in the extremum spectra surrounding the conical singularity.
Consistency of multi-time Dirac equations with general interaction potentials
Deckert, Dirk-André Nickel, Lukas
2016-07-15
In 1932, Dirac proposed a formulation in terms of multi-time wave functions as candidate for relativistic many-particle quantum mechanics. A well-known consistency condition that is necessary for existence of solutions strongly restricts the possible interaction types between the particles. It was conjectured by Petrat and Tumulka that interactions described by multiplication operators are generally excluded by this condition, and they gave a proof of this claim for potentials without spin-coupling. Under suitable assumptions on the differentiability of possible solutions, we show that there are potentials which are admissible, give an explicit example, however, show that none of them fulfills the physically desirable Poincaré invariance. We conclude that in this sense, Dirac’s multi-time formalism does not allow to model interaction by multiplication operators, and briefly point out several promising approaches to interacting models one can instead pursue.
Thermal and thermoelectric response from Keldysh formalism with application to gapped Dirac fermions
NASA Astrophysics Data System (ADS)
Zhu, Guo-Bao; Yang, Hui-Min; Yang, Sheng-Yuan
2015-04-01
Based on the Keldysh Green’s functions theory, we present a general formula of the thermal and thermoelectric transport. In the clean limit, our formula recovers the previous results obtained from the semiclassical transport theory. In our approach, we propose an appropriate energy current operator and electric current operator, and the unphysical divergence from the direct application of the Kubo formula is eliminated. As an application, we study the thermal and the thermoelectric Hall conductivities of a gapped Dirac fermion model in the presence of impurity scattering. Project supported by the Special Funds of the National Natural Science Foundation of China (Grant No. 11447145) and the Doctoral Program of Heze University, Shandong Province, China (Grant No. XY14B002).
Strong disorder effects of a Dirac fermion with a random vector field
NASA Astrophysics Data System (ADS)
Fukui, Takahiro
2003-10-01
We study a Dirac fermion model with a random vector field, especially paying attention to the strong disorder regime. Applying Bosonization techniques, we first derive an equivalent sine-Gordon model, and next average over the random vector field using the replica approach. The operator product expansion based on the replica action leads to scaling equations of the coupling constants (“fugacities”) with nonlinear terms, if we take into account the fusion of the vertex operators. These equations are converted into a nonlinear diffusion equation known as the Kolmogorov-Petrovsky-Piscounov (KPP) equation. Using the asymptotic solution of the equation, we calculate the spatial correlations of the generalized inverse participation ratios. The scaling exponent thus obtained reproduces the recent numerical calculations of the density correlation function. This implies that the freezing transition has actually revealed itself in such calculations.
Integration of the gUSE/WS-PGRADE and InSilicoLab portals with DIRAC
NASA Astrophysics Data System (ADS)
Navarro, A. Puig; Viana Casals, D.; Graciani Díaz, R.; Casajús Ramo, A.; Balaskó, Á.; Kacksuk, P.; Kocot, J.; Harezlak, D.
2012-12-01
The gUSE (Grid User Support Environment) framework allows to create, store and distribute application workflows. This workflow architecture includes a wide variety of payload execution operations, such as loops, conditional execution of jobs and combination of output. These complex multi-job workflows can easily be created and modified by application developers through the WS-PGRADE portal. The portal also allows end users to download and use existing workflows, as well as executing them. The DIRAC framework for distributed computing, a complete Grid solution for a community of users needing access to distributed computing resources, has been integrated into the gUSE/WS-PGRADE system. This integration allows the execution of gUSE workflows in a distributed computing environment, thus greatly expanding the capability of the portal to several Grids and Cloud Computing facilities. The main features and possibilities of the gUSE/WS-PGRADE-DIRAC system, as well as the benefits for users, will be outlined and discussed.
Dynamic zero modes of Dirac fermions and competing singlet phases of antiferromagnetic order
NASA Astrophysics Data System (ADS)
Goswami, Pallab; Si, Qimiao
2017-06-01
In quantum spin systems, singlet phases often develop in the vicinity of an antiferromagnetic order. Typical settings for such problems arise when itinerant fermions are also present. In this paper, we develop a theoretical framework for addressing such competing orders in an itinerant system, described by Dirac fermions strongly coupled to an O(3) nonlinear sigma model. We focus on two spatial dimensions, where upon disordering the antiferromagnetic order by quantum fluctuations the singular tunneling events also known as (anti)hedgehogs can nucleate competing singlet orders in the paramagnetic phase. In the presence of an isolated hedgehog configuration of the nonlinear sigma model field, we show that the fermion determinant vanishes as the dynamic Euclidean Dirac operator supports fermion zero modes of definite chirality. This provides a topological mechanism for suppressing the tunneling events. Using the methodology of quantum chromodynamics, we evaluate the fermion determinant in the close proximity of magnetic quantum phase transition, when the antiferromagnetic order-parameter field can be described by a dilute gas of hedgehogs and antihedgehogs. We show how the precise nature of emergent singlet order is determined by the overlap between dynamic fermion zero modes of opposite chirality, localized on the hedgehogs and antihedgehogs. For a Kondo-Heisenberg model on the honeycomb lattice, we demonstrate the competition between spin Peierls order and Kondo singlet formation, thereby elucidating its global phase diagram. We also discuss other physical problems that can be addressed within this general framework.
Uniqueness of the Fock quantization of Dirac fields in 2 +1 dimensions
NASA Astrophysics Data System (ADS)
Cortez, Jerónimo; Navascués, Beatriz Elizaga; Martín-Benito, Mercedes; Mena Marugán, Guillermo A.; Velhinho, José M.
2017-07-01
We study the Fock quantization of a free Dirac field in 2 +1 -dimensional backgrounds which are conformally ultrastatic, with a time-dependent conformal factor. As it is typical for field theories, there is an infinite ambiguity in the Fock representation of the canonical anticommutation relations. Different choices may lead to unitarily inequivalent theories that describe different physics. To remove this ambiguity one usually requires that the vacuum be invariant under the unitary transformations that implement the symmetries of the equations of motion. However, in nonstationary backgrounds, where time translation is not a symmetry transformation, the requirement of vacuum invariance is in general not enough to fix completely the Fock representation. We show that this problem is overcome in the considered scenario by demanding, in addition, a unitarily implementable nontrivial quantum dynamics. The combined imposition of these conditions selects a unique family of equivalent Fock representations. Moreover, one also obtains an essentially unique splitting of the time variation of the Dirac field into an explicit dependence on the background scale factor and a quantum evolution of the corresponding creation and annihilation operators.
Ultrafast Broadband Photodetectors Based on Three-Dimensional Dirac Semimetal Cd3As2.
Wang, Qinsheng; Li, Cai-Zhen; Ge, Shaofeng; Li, Jin-Guang; Lu, Wei; Lai, Jiawei; Liu, Xuefeng; Ma, Junchao; Yu, Da-Peng; Liao, Zhi-Min; Sun, Dong
2017-02-08
Photodetection with extreme performances in terms of ultrafast response time, broad detection wavelength range, and high sensitivity has a wide range of optoelectronic and photonic applications, such as optical communications, interconnects, imaging, and remote sensing. Graphene, a typical two-dimensional Dirac semimetal, has shown excellent potential toward a high-performance photodetector with high operation speed, broadband response, and efficient carrier multiplications benefiting from its linear dispersion band structure with a high carrier mobility and zero bandgap. As the three-dimensional analogues of graphene, Dirac semimetal Cd3As2 processes all advantages of graphene as a photosensitive material but potentially has stronger interaction with light as a bulk material and thus enhanced responsivity. In this work, we report the realization of an ultrafast broadband photodetector based on Cd3As2. The prototype metal-Cd3As2-metal photodetector exhibits a responsivity of 5.9 mA/W with a response time of about 6.9 ps without any special device optimization. Broadband responses from 532 nm to 10.6 μm are achieved with a potential detection range extendable to far-infrared and terahertz. Systematical studies indicate that the photothermoelectric effect plays an important role in photocurrent generation. Our results suggest this emerging class of exotic quantum materials can be harnessed for photodetection with a high sensitivity and high speed (∼145 GHz) over a broad wavelength range.
An Exact Separation of the Spin-Free and Spin-Dependent Terms of the Dirac-Coulomb-Breit Hamiltonian
NASA Technical Reports Server (NTRS)
Dyall, Kenneth G.
1994-01-01
The Dirac Hamiltonian is transformed by extracting the operator (sigma x p)/2mc from the small component of the wave function and applying it to the operators of the original Hamiltonian. The resultant operators contain products of Paull matrices that can be rearranged to give spin-free and spin-dependent operators. These operators are the ones encountered in the Breit-Pauli Hamiltonian, as well as some of higher order in alpha(sup 2). However, since the transformation of the original Dirac Hamiltonian is exact, the new Hamiltonian can be used in variational calculations, with or without the spin-dependent terms. The new small component functions have the same symmetry properties as the large component. Use of only the spin-free terms of the new Hamiltonian permits the same factorization over spin variables as in nonrelativistic theory, and therefore all the post-Self-Consistent Field (SCF) machinery of nonrelativistic calculations can be applied. However, the single-particle functions are two-component orbitals having a large and small component, and the SCF methods must be modified accordingly. Numerical examples are presented, and comparisons are made with the spin-free second-order Douglas-Kroll transformed Hamiltonian of Hess.
An Exact Separation of the Spin-Free and Spin-Dependent Terms of the Dirac-Coulomb-Breit Hamiltonian
NASA Technical Reports Server (NTRS)
Dyall, Kenneth G.
1994-01-01
The Dirac Hamiltonian is transformed by extracting the operator (sigma x p)/2mc from the small component of the wave function and applying it to the operators of the original Hamiltonian. The resultant operators contain products of Paull matrices that can be rearranged to give spin-free and spin-dependent operators. These operators are the ones encountered in the Breit-Pauli Hamiltonian, as well as some of higher order in alpha(sup 2). However, since the transformation of the original Dirac Hamiltonian is exact, the new Hamiltonian can be used in variational calculations, with or without the spin-dependent terms. The new small component functions have the same symmetry properties as the large component. Use of only the spin-free terms of the new Hamiltonian permits the same factorization over spin variables as in nonrelativistic theory, and therefore all the post-Self-Consistent Field (SCF) machinery of nonrelativistic calculations can be applied. However, the single-particle functions are two-component orbitals having a large and small component, and the SCF methods must be modified accordingly. Numerical examples are presented, and comparisons are made with the spin-free second-order Douglas-Kroll transformed Hamiltonian of Hess.
Fractional Dirac bracket and quantization for constrained systems
NASA Astrophysics Data System (ADS)
Abreu, Everton M. C.; Godinho, Cresus F. L.
2011-08-01
So far, it is not well known how to deal with dissipative systems. There are many paths of investigation in the literature and none of them present a systematic and general procedure to tackle the problem. On the other hand, it is well known that the fractional formalism is a powerful alternative when treating dissipative problems. In this paper, we propose a detailed way of attacking the issue using fractional calculus to construct an extension of the Dirac brackets in order to carry out the quantization of nonconservative theories through the standard canonical way. We believe that, by using the extended Dirac bracket definition, it will be possible to analyze more deeply gauge theories starting with second-class systems.
Stability of Dirac Liquids with Strong Coulomb Interaction
NASA Astrophysics Data System (ADS)
Tupitsyn, Igor S.; Prokof'ev, Nikolay V.
2017-01-01
We develop and apply the diagrammatic Monte Carlo technique to address the problem of the stability of the Dirac liquid state (in a graphene-type system) against the strong long-range part of the Coulomb interaction. So far, all attempts to deal with this problem in the field-theoretical framework were limited either to perturbative or random phase approximation and functional renormalization group treatments, with diametrically opposite conclusions. Our calculations aim at the approximation-free solution with controlled accuracy by computing vertex corrections from higher-order skeleton diagrams and establishing the renormalization group flow of the effective Coulomb coupling constant. We unambiguously show that with increasing the system size L (up to ln (L )˜40 ), the coupling constant always flows towards zero; i.e., the two-dimensional Dirac liquid is an asymptotically free T =0 state with divergent Fermi velocity.
Peccei-Quinn symmetry for Dirac seesaw and leptogenesis
Gu, Pei-Hong
2016-07-04
We extend the DFSZ invisible axion model to simultaneously explain small Dirac neutrino masses and cosmic matter-antimatter asymmetry. After the Peccei-Quinn and electroweak symmetry breaking, the effective Yukawa couplings of the Dirac neutrinos to the standard model Higgs scalar can be highly suppressed by the ratio of the vacuum expectation value of an iso-triplet Higgs scalar over the masses of some heavy gauge-singlet fermions, iso-doublet Higgs scalars or iso-triplet fermions. The iso-triplet fields can carry a zero or nonzero hypercharge. Through the decays of the heavy gauge-singlet fermions, iso-doublet scalars or iso-triplet fermions, we can obtain a lepton asymmetry in the left-handed leptons and an opposite lepton asymmetry in the right-handed neutrinos. Since the right-handed neutrinos do not participate in the sphaleron processes, the left-handed lepton asymmetry can be partially converted to a baryon asymmetry.
Thermoelectric transport in junctions of Majorana and Dirac channels
NASA Astrophysics Data System (ADS)
Shapiro, Dmitriy S.; Feldman, D. E.; Mirlin, Alexander D.; Shnirman, Alexander
2017-05-01
We investigate the thermoelectric current and heat conductance in a chiral Josephson contact on a surface of a three-dimensional topological insulator, covered with superconducting and magnetic insulator films. The contact consists of two junctions of Majorana and Dirac channels next to two superconductors. Geometric asymmetry results in a supercurrent without a phase bias. The interference of Dirac fermions causes oscillations of the electric and heat currents with an unconventional period 2 Φ0=h /e as functions of the Aharonov-Bohm flux. Due to the gapless character of Majorana modes, there is no threshold for the thermoelectric effect, and the current-flux relationship is nonsinusoidal. Depending on the magnetic flux, the direction of the electric current can be both from the hot to the cold lead and vice versa.
Pairing symmetry and vortex zero mode for superconducting Dirac fermions
Lu, C.-K.; Herbut, Igor F.
2010-10-01
We study vortex zero-energy bound states in presence of pairing between low-energy Dirac fermions on the surface of a topological insulator. The pairing symmetries considered include the s-wave, p-wave, and, in particular, the mixed-parity symmetry, which arises in absence of the inversion symmetry on the surface. The zero mode is analyzed within the generalized Jackiw-Rossi-Dirac Hamiltonian that contains a momentum-dependent mass term, and includes the effects of the electromagnetic gauge field and the Zeeman coupling as well. At a finite chemical potential, as long as the spectrum without the vortex is fully gapped, the presence of a single Fermi surface with a definite helicity always leads to one Majorana zero mode, in which both electron's spin projections participate. In particular, the critical effects of the Zeeman coupling on the zero mode are discussed.
Manipulation of Dirac cones in intercalated epitaxial graphene
Kim, Minsung; Tringides, Michael C.; Hershberger, Matthew T.; ...
2017-07-12
Graphene is an intriguing material in view of its unique Dirac quasi-particles, and the manipulation of its electronic structure is important in material design and applications. Here, we theoretically investigate the electronic band structure of epitaxial graphene on SiC with intercalation of rare earth metal ions (e.g., Yb and Dy) using first-principles calculations. We can use the intercalation to control the coupling of the constituent components (buffer layer, graphene, and substrate), resulting in strong modification of the graphene band structure. We also demonstrate that the metal-intercalated epitaxial graphene has tunable band structures by controlling the energies of Dirac cones asmore » well as the linear and quadratic band dispersion depending on the intercalation layer and density. Thus, the metal intercalation is a viable method to manipulate the electronic band structure of the epitaxial graphene, which can enhance the functional utility and controllability of the material.« less
Three-dimensional periodic dielectric structures having photonic Dirac points
Bravo-Abad, Jorge; Joannopoulos, John D.; Soljacic, Marin
2015-06-02
The dielectric, three-dimensional photonic materials disclosed herein feature Dirac-like dispersion in quasi-two-dimensional systems. Embodiments include a face-centered cubic (fcc) structure formed by alternating layers of dielectric rods and dielectric slabs patterned with holes on respective triangular lattices. This fcc structure also includes a defect layer, which may comprise either dielectric rods or a dielectric slab with patterned with holes. This defect layer introduces Dirac cone dispersion into the fcc structure's photonic band structure. Examples of these fcc structures enable enhancement of the spontaneous emission coupling efficiency (the .beta.-factor) over large areas, contrary to the conventional wisdom that the .beta.-factor degrades as the system's size increases. These results enable large-area, low-threshold lasers; single-photon sources; quantum information processing devices; and energy harvesting systems.
Dirac semimetal phase in hexagonal LiZnBi
NASA Astrophysics Data System (ADS)
Cao, Wendong; Tang, Peizhe; Xu, Yong; Wu, Jian; Gu, Bing-Lin; Duan, Wenhui
2017-09-01
Based on first-principles calculations, we find that LiZnBi, a metallic hexagonal A B C compound, has a pair of three-dimensional Dirac nodes and exhibits nontrivial topological properties under proper strain configurations. The nontrivial topological nature of the strained LiZnBi is directly demonstrated by calculating its Z2 index and the surface states. The low-energy states are shown to be sensitive to strain configurations, and we propose that these nontrivial topological properties can be observed under compressive in-plane strain in experiments. The finding of the Dirac semimetal phase in LiZnBi may intrigue further research on the topological properties of hexagonal A B C materials and promote new practical applications.
Torsion and noninertial effects on a nonrelativistic Dirac particle
Bakke, K.
2014-07-15
We investigate torsion and noninertial effects on a spin-1/2 quantum particle in the nonrelativistic limit of the Dirac equation. We consider the cosmic dislocation spacetime as a background and show that a rotating system of reference can be used out to distances which depend on the parameter related to the torsion of the defect. Therefore, we analyse torsion effects on the spectrum of energy of a nonrelativistic Dirac particle confined to a hard-wall potential in a Fermi–Walker reference frame. -- Highlights: •Torsion effects on a spin- 1/2 particle in a noninertial reference frame. •Fermi–Walker reference frame in the cosmic dislocation spacetime background. •Torsion and noninertial effects on the confinement to a hard-wall confining potential.
Peccei-Quinn symmetry for Dirac seesaw and leptogenesis
NASA Astrophysics Data System (ADS)
Gu, Pei-Hong
2016-07-01
We extend the DFSZ invisible axion model to simultaneously explain small Dirac neutrino masses and cosmic matter-antimatter asymmetry. After the Peccei-Quinn and electroweak symmetry breaking, the effective Yukawa couplings of the Dirac neutrinos to the standard model Higgs scalar can be highly suppressed by the ratio of the vacuum expectation value of an iso-triplet Higgs scalar over the masses of some heavy gauge-singlet fermions, iso-doublet Higgs scalars or iso-triplet fermions. The iso-triplet fields can carry a zero or nonzero hypercharge. Through the decays of the heavy gauge-singlet fermions, iso-doublet scalars or iso-triplet fermions, we can obtain a lepton asymmetry in the left-handed leptons and an opposite lepton asymmetry in the right-handed neutrinos. Since the right-handed neutrinos do not participate in the sphaleron processes, the left-handed lepton asymmetry can be partially converted to a baryon asymmetry.
Gate-tunable graphene quantum dot and Dirac oscillator
NASA Astrophysics Data System (ADS)
Belouad, Abdelhadi; Jellal, Ahmed; Zahidi, Youness
2016-02-01
We obtain the solution of the Dirac equation in (2 + 1) dimensions in the presence of a constant magnetic field normal to the plane together with a two-dimensional Dirac-oscillator potential coupling. We study the energy spectrum of graphene quantum dot (QD) defined by electrostatic gates. We give discussions of our results based on different physical settings, whether the cyclotron frequency is similar or larger/smaller compared to the oscillator frequency. This defines an effective magnetic field that produces the effective quantized Landau levels. We study analytically such field in gate-tunable graphene QD and show that our structure allows us to control the valley degeneracy. Finally, we compare our results with already published work and also discuss the possible applications of such QD.
Composite Dirac liquids: parent states of symmetric surface topological orders
NASA Astrophysics Data System (ADS)
Essin, Andrew; Mross, David; Alicea, Jason
2015-03-01
In the absence of interactions, topological insulators surfaces must be gapless or break symmetry. With the addition of strong interactions at the surface, a third possibility is a gapped, symmetric surface that supports anyons, as has been recognized in a number of recent developments. The composite Dirac liquid (CDL) provides a natural stepping stone to identifying such states. The CDL consists of neutral, fractional Dirac fermions coupled to gapped charges, and the addition of pairing to the neutral sector produces a gap for all excitations without breaking any symmetry. The quasi-1d technology we have used in the study of the CDL also allows us to construct and characterize such gapped surface phases, and generalizes naturally to (bosonic) symmetry protected topological phases as well. This work was supported by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation through Grant GBMF1250
Interplay of Dirac fermions and heavy quasiparticles in solids.
Höppner, M; Seiro, S; Chikina, A; Fedorov, A; Güttler, M; Danzenbächer, S; Generalov, A; Kummer, K; Patil, S; Molodtsov, S L; Kucherenko, Y; Geibel, C; Strocov, V N; Shi, M; Radovic, M; Schmitt, T; Laubschat, C; Vyalikh, D V
2013-01-01
Many-body interactions in crystalline solids can be conveniently described in terms of quasiparticles with strongly renormalized masses as compared with those of non-interacting particles. Examples of extreme mass renormalization are on the one hand graphene, where the charge carriers obey the linear dispersion relation of massless Dirac fermions, and on the other hand heavy-fermion materials where the effective electron mass approaches the mass of a proton. Here we show that both extremes, Dirac fermions, like they are found in graphene and extremely heavy quasiparticles characteristic for Kondo materials, may not only coexist in a solid but can also undergo strong mutual interactions. Using the example of EuRh₂Si₂, we explicitly demonstrate that these interactions can take place at the surface and in the bulk. The presence of the linear dispersion is imposed solely by the crystal symmetry, whereas the existence of heavy quasiparticles is caused by the localized nature of the 4f states.
Confined Dirac fermions in a constant magnetic field
Jellal, Ahmed; Alhaidari, Abdulaziz D.; Bahlouli, Hocine
2009-07-15
We obtain an exact solution of the Dirac equation in (2+1) dimensions in the presence of a constant magnetic field normal to the plane together with a two-dimensional Dirac-oscillator potential coupling. The solution space consists of positive- and negative-energy solutions, each of which splits into two disconnected subspaces depending on the sign of an azimuthal quantum number k=0,{+-}1,{+-}2,... and whether the cyclotron frequency is larger or smaller than the oscillator frequency. The spinor wave function is written in terms of the associated Laguerre polynomials. For negative k, the relativistic energy spectrum is infinitely degenerate due to the fact that it is independent of k. We compare our results with already published work and point out the relevance of these findings to a systematic formulation of the relativistic quantum Hall effect in a confining potential.
Solutions of the multiconfiguration Dirac-Fock equations
NASA Astrophysics Data System (ADS)
Levitt, Antoine
2014-08-01
The multiconfiguration Dirac-Fock (MCDF) model uses a linear combination of Slater determinants to approximate the electronic N-body wave function of a relativistic molecular system, resulting in a coupled system of nonlinear eigenvalue equations, the MCDF equations. In this paper, we prove the existence of solutions of these equations in the weakly relativistic regime. First, using a new variational principle as well as the results of Lewin on the multiconfiguration non-relativistic model, and Esteban and Séré on the single-configuration relativistic model, we prove the existence of critical points for the associated energy functional, under the constraint that the occupation numbers are not too small. Then, this constraint can be removed in the weakly relativistic regime, and we obtain non-constrained critical points, i.e. solutions of the multiconfiguration Dirac-Fock equations.
Unusual microwave response of dirac quasiparticles in graphene.
Gusynin, V P; Sharapov, S G; Carbotte, J P
2006-06-30
Recent experiments have proven that the quasiparticles in graphene obey a Dirac equation. Here we show that microwaves are an excellent probe of their unusual dynamics. When the chemical potential is small, the intraband response can exhibit a cusp around zero frequency Omega and this unusual line shape changes to Drude-like by increasing the chemical potential |mu|, with width linear in mu. The interband contribution at T=0 is a constant independent of Omega with a lower cutoff at 2mu. Distinctly different behavior occurs if interaction-induced phenomena in graphene cause an opening of a gap Delta. At a large magnetic field B, the diagonal and Hall conductivities at small Omega become independent of B but remain nonzero and show a structure associated with the lowest Landau level. This occurs because in the Dirac theory the energy of this level, E0 = +/-Delta, is field independent in sharp contrast to the conventional case.
Lamb shift of the Dirac cone of graphene
NASA Astrophysics Data System (ADS)
de Melo, Pedro Miguel M. C.; Marini, Andrea
2016-11-01
The fluctuations of the electromagnetic vacuum are one of the most powerful manifestations of the quantum structure of nature. Their effect on the Dirac electrons of graphene is known to induce some spectacular and purely quantistic phenomena, like the Casimir and the Aharanov-Bohm effects. In this work we demonstrate, by using a first-principles approach, that the Dirac cone of graphene is also affected by a sizeable Lamb shift. We show that the microscopic electronic currents flowing on the graphene plane are strongly coupled with the vacuum fluctuations causing a renormalisation of the electronic levels (as large as 4 meV). This shift is one order of magnitude larger than the value predicted for an isolated carbon atom, which imposes a reinterpretation of the Lamb shift as a collective effect.
Dirac bound states of anharmonic oscillator in external fields
Hamzavi, Majid; Ikhdair, Sameer M.; Falaye, Babatunde J.
2014-02-15
We explore the effect of the external magnetic and Aharonov–Bohm (AB) flux fields on the energy levels of Dirac particle subjects to mixed scalar and vector anharmonic oscillator field in the two-dimensional (2D) space. We calculate the exact energy eigenvalues and the corresponding un-normalized two-spinor-components wave functions in terms of the chemical potential parameter, magnetic field strength, AB flux field and magnetic quantum number by using the Nikiforov–Uvarov (NU) method. -- Highlights: • Effect of the external fields on the energy levels of Dirac particle with the anharmonic oscillator is investigated. • The solutions are discussed in view of spin and pseudospin symmetries limits. • The energy levels and wave function are presented by the Nikiforov–Uvarov method.
Spinor Slow-Light and Dirac Particles with Variable Mass
Unanyan, R. G.; Otterbach, J.; Fleischhauer, M.; Ruseckas, J.; Kudriasov, V.; Juzeliunas, G.
2010-10-22
We consider the interaction of two weak probe fields of light with an atomic ensemble coherently driven by two pairs of standing wave laser fields in a tripod-type linkage scheme. The system is shown to exhibit a Dirac-like spectrum for light-matter quasiparticles with multiple dark states, termed spinor slow-light polaritons. They posses an 'effective speed of light' given by the group velocity of slow light, and can be made massive by inducing a small two-photon detuning. Control of the two-photon detuning can be used to locally vary the mass including a sign flip. Particularly, this allows the implementation of the random-mass Dirac model for which localized zero-energy (midgap) states exist with unusual long-range correlations.
A spatially homogeneous and isotropic Einstein-Dirac cosmology
NASA Astrophysics Data System (ADS)
Finster, Felix; Hainzl, Christian
2011-04-01
We consider a spatially homogeneous and isotropic cosmological model where Dirac spinors are coupled to classical gravity. For the Dirac spinors we choose a Hartree-Fock ansatz where all one-particle wave functions are coherent and have the same momentum. If the scale function is large, the universe behaves like the classical Friedmann dust solution. If however the scale function is small, quantum effects lead to oscillations of the energy-momentum tensor. It is shown numerically and proven analytically that these quantum oscillations can prevent the formation of a big bang or big crunch singularity. The energy conditions are analyzed. We prove the existence of time-periodic solutions which go through an infinite number of expansion and contraction cycles.
Flavor and chiral oscillations with Dirac wave packets
Bernardini, A.E.; Leo, S. de
2005-04-01
We report about recent results on Dirac wave packets in the treatment of neutrino flavor oscillation where the initial localization of a spinor state implies an interference between positive and negative energy components of mass-eigenstate wave packets. A satisfactory description of fermionic particles requires the use of the Dirac equation as evolution equation for the mass eigenstates. In this context, a new flavor conversion formula can be obtained when the effects of chiral oscillation are taken into account. Our study leads to the conclusion that the fermionic nature of the particles, where chiral oscillations and the interference between positive and negative frequency components of mass-eigenstate wave packets are implicitly assumed, modifies the standard oscillation probability. Nevertheless, for ultrarelativistic particles and sharply peaked momentum distributions, we can analytically demonstrate that these modifications introduce correction factors proportional to m{sub 1,2}{sup 2}/p{sub 0}{sup 2} which are practically undetectable by any experimental analysis.
Phase-integral solution of the radial Dirac equation
Linnaeus, Staffan
2010-03-15
A phase-integral (WKB) solution of the radial Dirac equation is constructed, retaining perfect symmetry between the two components of the wave function and introducing no singularities except at the classical transition points. The potential is allowed to be the time component of a four-vector, a Lorentz scalar, a pseudoscalar, or any combination of these. The key point in the construction is the transformation from two coupled first-order equations constituting the radial Dirac equation to a single second-order Schroedinger-type equation. This transformation can be carried out in infinitely many ways, giving rise to different second-order equations but with the same spectrum. A unique transformation is found that produces a particularly simple second-order equation and correspondingly simple and well-behaved phase-integral solutions. The resulting phase-integral formulas are applied to unbound and bound states of the Coulomb potential. For bound states, the exact energy levels are reproduced.
Multiple Virtual Tunneling of Dirac Fermions in Granular Graphene
Pachoud, Alexandre; Jaiswal, Manu; Wang, Yu; Hong, Byung-Hee; Ahn, Jong-Hyun; Loh, Kian Ping; Özyilmaz, Barbaros
2013-01-01
Graphene charge carriers behave as massless Dirac fermions, opening the exciting possibility to observe long-range virtual tunneling of electrons in a solid. In granular metals, electron hops arising from series of virtual transitions are predicted to yield observable currents at low-enough temperatures, but to date experimental evidence is lacking. We report on electron transport in granular graphene films self-assembled by hydrogenation of suspended graphene. While the log-conductance shows a characteristic T−1/2 temperature dependence, cooling the samples below 10 K drives a triple crossover: a slope break in log-conductance, simultaneous to a substantial increase in magneto-conductance and onset of large mesoscopic conductance fluctuations. These phenomena are signatures of virtual transitions of electrons between distant localized states, and conductance statistics reveal that the high crossover-temperature is due to the Dirac nature of granular graphene charge carriers. PMID:24296942
Johnson noise thermometry reveals the Dirac fluid in graphene
NASA Astrophysics Data System (ADS)
Crossno, Jesse; Shi, Jing; Wang, Ke; Liu, Xiaomeng; Harzheim, Achim; Lucas, Andrew; Sachdev, Subir; Kim, Philip; Taniguchi, Takashi; Watanabe, Kenji; Ohki, Thomas; Fong, Kin Chung
Near the charge neutrality point in graphene, the Fermi surface vanishes leading to the formation of a strongly-interacting quasi-relativistic electron-hole plasma, known as a Dirac fluid. These non-Fermi liquids share many features with quantum critical systems including a fast electron-electron scattering rate which makes them well suited to hydrodynamic descriptions. A number of exotic properties have been predicted including a diverging thermal conductivity resulting in the breakdown of the Wiedemann-Franz (WF) law. I will discuss the experimental technique--based on Johnson noise thermometry--used to measure the electronic thermal conductivity of graphene and probe the unique transport dynamics of the Dirac fluid.
Dirac Calculations for Proton Inelastic Scattering at Intermediate Energies
NASA Astrophysics Data System (ADS)
El-Nohy, N. A.; El-Hammamy, M. N.; Aly, N. E.; Abdel-Moneim, A. M.; Hamza, A. F.
2016-12-01
Relativistic proton inelastic scattering from different targets (16O, 24Mg, 28Si, 40Ca, 54Fe, 58Ni, 90Zr, 154Sm, 176Yb, and 208Pb) at intermediate energies is analyzed in the framework of phenomenological optical potentials based on the Dirac formalism. Parameters of the Dirac phenomenological potential with Woods Saxon (WS) shape are obtained. The first order vibrational collective model with one phonon is used to calculate the transition optical potentials to the first low-lying excited state (2+) of the investigated target nuclei. Also, the variation of deformation length ( δ) with energy and mass number is studied. It is noticed that the deformation length increases slightly with energy at intermediate range.
Dirac-orthogonality in the space of tempered distributions
NASA Astrophysics Data System (ADS)
Carfì, David
2003-04-01
The main goal of this paper is the realization that some formal basic results and definitions of the mathematical formalism of the quantum mechanics have a solid mathematical basis. In particular, we justify the so-called "delta" normalization in the continuous case introduced by Dirac (P.A.M. Dirac, The principles of Quantum Mechanics, Clarendon Press, Oxford, 1930, pp. 66-68), works that are of fundamental importance in the foundation of the modern quantum physics. This formal mathematical tool had not, until now, a rigorous counterpart, neither in the area of the rigged Hilbert spaces theory. It is possible to find a systematic application of the above mentioned formal tool in (W. Pauli, Wellenmechanik, 1958), (R. Shankar, Principles of Quantum Mechanics, Plenum Press, New York, 1994) and others.
General spin and pseudospin symmetries of the Dirac equation
NASA Astrophysics Data System (ADS)
Alberto, P.; Malheiro, M.; Frederico, T.; de Castro, A.
2015-12-01
In the 1970s Smith and Tassie [G. B. Smith and L. J. Tassie, Ann. Phys. (NY) 65, 352 (1971), 10.1016/0003-4916(71)90172-2] and Bell and Ruegg [J. S. Bell and H. Ruegg, Nucl. Phys. B 98, 151 (1975), 10.1016/0550-3213(75)90206-0; J. S. Bell and H. Ruegg, Nucl. Phys. B 104, 546 (1976), 10.1016/0550-3213(76)90035-3] independently found SU(2) symmetries of the Dirac equation with scalar and vector potentials. These symmetries, known as pseudospin and spin symmetries, have been extensively researched and applied to several physical systems. Twenty years after, in 1997, the pseudospin symmetry was revealed by Ginocchio [J. N. Ginocchio, Phys. Rev. Lett. 78, 436 (1997), 10.1103/PhysRevLett.78.436] as a relativistic symmetry of the atomic nuclei when it is described by relativistic mean-field hadronic models. The main feature of these symmetries is the suppression of the spin-orbit coupling either in the upper or lower components of the Dirac spinor, thereby turning the respective second-order equations into Schrödinger-like equations, i.e, without a matrix structure. In this paper we propose a generalization of these SU(2) symmetries for potentials in the Dirac equation with several Lorentz structures, which also allow for the suppression of the matrix structure of the second-order equation of either the upper or lower components of the Dirac spinor. We derive the general properties of those potentials and list some possible candidates, which include the usual spin-pseudospin potentials, and also two- and one-dimensional potentials. An application for a particular physical system in two dimensions, electrons in graphene, is suggested.
Relativistic Photoionization Computations with the Time Dependent Dirac Equation
2016-10-12
The Dirac equation describes the motion of a spin one-half particle in an external electromagnetic field. The stationary states in both Coulomb...5, the peaks of the time dependent spectrum neatly line up with the dashed lines, which denote the discrete energies predicted by the time...near a null of a particular eigenfunction, the associated energy eigenvalue may not appear in the numerical spectrum . In Fig. 5, the diagnostic point
Dirac Oscillator in a Galilean Covariant Non-commutative Space
NASA Astrophysics Data System (ADS)
de Melo, G. R.; de Montigny, M.; Pompeia, P. J.; Santos, E. S.
2013-02-01
We study the Galilean Dirac oscillator in a non-commutative situation, with space-space and momentum-momentum non-commutativity. The wave equation is obtained via a `Galilean covariant' approach, which consists in projecting the covariant equations from a (4,1)-dimensional manifold with light-cone coordinates, to a (3,1)-dimensional Galilean space-time. We obtain the exact wave functions and their energy levels for the plane and discuss the effects of non-commutativity.
2D Hybrid Nanostructured Dirac Materials for Broadband Transparent Electrodes.
Guo, Yunfan; Lin, Li; Zhao, Shuli; Deng, Bing; Chen, Hongliang; Ma, Bangjun; Wu, Jinxiong; Yin, Jianbo; Liu, Zhongfan; Peng, Hailin
2015-08-05
Broadband transparent electrodes based on 2D hybrid nanostructured Dirac materials between Bi2 Se3 and graphene are synthesized using a chemical vapor deposition (CVD) method. Bi2 Se3 nanoplates are preferentially grown along graphene grain boundaries as "smart" conductive patches to bridge the graphene boundary. These hybrid films increase by one- to threefold in conductivity while remaining highly transparent over broadband wavelength. They also display outstanding chemical stability and mechanical flexibility.
Semi-Classical Dirac Vacuum Polarisation in a Scalar Field
NASA Astrophysics Data System (ADS)
Lampart, Jonas; Lewin, Mathieu
2016-08-01
We study vacuum polarisation effects of a Dirac field coupled to an external scalar field and derive a semi-classical expansion of the regu-larised vacuum energy. The leading order of this expansion is given by a classical formula due to Chin, Lee-Wick and Walecka, for which our result provides the first rigorous proof. We then discuss applications to the non-relativistic large-coupling limit of an interacting system, and to the stability of homogeneous systems.
Hawking radiation of Dirac particles from black strings
Ahmed, Jamil; Saifullah, K. E-mail: saifullah@qau.edu.pk
2011-08-01
Hawking radiation has been studied as a phenomenon of quantum tunneling in different black holes. In this paper we extend this semi-classical approach to cylindrically symmetric black holes. Using the Hamilton-Jacobi method and WKB approximation we calculate the tunneling probabilities of incoming and outgoing Dirac particles from the event horizon and find the Hawking temperature of these black holes. We obtain results both for uncharged as well as charged particles.
Dirac-graphene quasiparticles in strong slow-light pulse
NASA Astrophysics Data System (ADS)
Golovinski, P. A.; Astapenko, V. A.; Yakovets, A. V.
2017-02-01
An analytical Volkov's solution of the massless Dirac equation for graphene in the field of slow-light pulse with arbitrary time dependence is obtained. Exact solutions are presented for special cases of monochromatic field and a single-cycle pulse. Following the Fock-Schwinger proper time method, the Green's function for quasiparticles is derived with the account of the influence an external classical electromagnetic wave field.
Existence of stationary states for nonlinear Dirac equations
NASA Astrophysics Data System (ADS)
Merle, F.
We generalize the previous result of Cazenave and Vasquez on the existence of stationary states for nonlinear Dirac equations of the form i∑ μ3 = 0 γμ∂μΨ - mΨ + L( ΨΨ) Ψ = 0. We seek solutions which are separable in spherical coordinates and we then make use of a shooting method to solve the associated problem for ordinary differential equations.
Cawley's Counterexample to Dirac's Conjecture as a Curved Spacetime
NASA Astrophysics Data System (ADS)
Carmeli, M.
1987-01-01
Cawley's counterexample Lagrangian to Dirac's conjecture on dynamical systems is modified to a line element in curved spacetime, and the energy-momentum tensor corresponding to such a spacetime is found. The spacetime obtained satisfies the Einstein field equations and describes a three-dimensional matterfilled universe. It is further shown that such a universe cannot be filled up with other sources, such as a perfect fluid, a scalar field, or an electromagnetic field, without violating the Einstein field equations.
Dirac equation in four time and four space dimensions
NASA Astrophysics Data System (ADS)
Nieto, J. A.; Espinoza, M.
2017-10-01
The Dirac equation in four time and four space dimensions (or (4 + 4)-dimensions) is considered. Step by step, we show that such an equation admits Majorana and Weyl solutions. In order to obtain the Majorana or Weyl spinors, we used a method based on the construction of Clifford algebra in terms of 2 × 2-matrices. We argue that our approach can be useful in supergravity, superstrings and qubit theory.
Dirac Points in Two-Dimensional Inverse Opals
NASA Astrophysics Data System (ADS)
Mahan, G. D.
2013-10-01
The electron energy states and energy bands are calculated for a two-dimensional inverse opal structure. Assume that the opal structure is closed-packed circles, the inverse opal has the honeycomb lattice. The honeycomb lattice in two dimensions has a Dirac point. Its properties can be manipulated by altering the structure of the inverse opal: the radius of the circle, and the small gap between circles.
Thermal bath of Dirac field in non-inertial frames
NASA Astrophysics Data System (ADS)
Zhang, Anwei
2016-07-01
The properties of inertial Dirac thermal bath viewed from the perspective of a uniformly accelerated observer is investigated. Using the single-mode approximation, we obtain the expression of the thermal reduced density matrix, which is constructed by the effective partition function in another way compared with the case of scalar field. We deduce the spectrum of particles and antiparticles seen by Rob and antiRob, respectively. It is found that the fermionic thermal bath will suppress the appearance of Unruh particles.
Dirac fermions on an anti-de Sitter background
Ambruş, Victor E. Winstanley, Elizabeth
2014-11-24
Using an exact expression for the bi-spinor of parallel transport, we construct the Feynman propagator for Dirac fermions in the vacuum state on anti-de Sitter space-time. We compute the vacuum expectation value of the stress-energy tensor by removing coincidence-limit divergences using the Hadamard method. We then use the vacuum Feynman propagator to compute thermal expectation values at finite temperature. We end with a discussion of rigidly rotating thermal states.
Topological Dirac semimetal phase in Pd and Pt oxides
NASA Astrophysics Data System (ADS)
Li, Gang; Yan, Binghai; Wang, Zhijun; Held, Karsten
2017-01-01
Topological Dirac semimetals (DSMs) exhibit nodal points through which energy bands disperse linearly in three-dimensional (3D) momentum space, a 3D analog of graphene. The first experimentally confirmed DSMs with a pair of Dirac points (DPs), Na3Bi and Cd3As2 , show topological surface Fermi arc states and exotic magnetotransport properties, boosting the interest in the search for stable and nontoxic DSM materials. Based on density-functional theory and dynamical mean-field theory calculations, we predict a family of palladium and platinum oxides to be robust 3D DSMs with three pairs of Dirac points that are well separated from bulk bands. The Fermi arcs at the surface display a Lifshitz transition upon a continuous change of the chemical potential. Corresponding oxides are already available as high-quality single crystals, an excellent precondition for the verification of our predictions by photoemission and magnetotransport experiments, extending DSMs to the versatile family of transition-metal oxides.
MPI support in the DIRAC Pilot Job Workload Management System
NASA Astrophysics Data System (ADS)
Tsaregorodtsev, A.; Hamar, V.
2012-12-01
Parallel job execution in the grid environment using MPI technology presents a number of challenges for the sites providing this support. Multiple flavors of the MPI libraries, shared working directories required by certain applications, special settings for the batch systems make the MPI support difficult for the site managers. On the other hand the workload management systems with Pilot Jobs became ubiquitous although the support for the MPI applications in the Pilot frameworks was not available. This support was recently added in the DIRAC Project in the context of the GISELA Latin American Grid Initiative. Special services for dynamic allocation of virtual computer pools on the grid sites were developed in order to deploy MPI rings corresponding to the requirements of the jobs in the central task queue of the DIRAC Workload Management System. Pilot Jobs using user space file system techniques install the required MPI software automatically. The same technique is used to emulate shared working directories for the parallel MPI processes. This makes it possible to execute MPI jobs even on the sites not supporting them officially. Reusing so constructed MPI rings for execution of a series of parallel jobs increases dramatically their efficiency and turnaround. In this contribution we describe the design and implementation of the DIRAC MPI Service as well as its support for various types of MPI libraries. Advantages of coupling the MPI support with the Pilot frameworks are outlined and examples of usage with real applications are presented.
Critical exact solutions for self-gravitating Dirac fields
NASA Astrophysics Data System (ADS)
Cianci, Roberto; Fabbri, Luca; Vignolo, Stefano
2016-11-01
We consider the Einstein-Dirac field equations describing a self-gravitating massive neutrino, looking for axially symmetric exact solutions; in the search of general solutions, we find some that are specific and which have critical features, such as the fact that the space-time curvature turns out to be flat and the spinor field gives rise to a vanishing bi-linear scalar overline{ψ }ψ =0 with non-vanishing bi-linear pseudo-scalar ioverline{ψ }γ ^5ψ not =0: because in quantum-field theory general computational methods are built on plane-wave solutions, for which the bi-linear pseudo-scalar vanishes while the bi-linear scalar does not vanish, then the solutions we found cannot be treated with the usual machinery of quantum-field theory. This means that for the Einstein-Dirac system there exist admissible solutions which nevertheless cannot be quantized with the common prescriptions; we regard this situation as yet another issue of tension between Einstein gravity and quantum principles. Possible ways to quench this tension can be seen either in enlarging the validity of quantum-field theory or by restricting the space of the solutions of the Einstein-Dirac system of field equations.
Imaging electrostatically confined Dirac fermions in graphene quantum dots
NASA Astrophysics Data System (ADS)
Lee, Juwon; Wong, Dillon; Velasco, Jairo, Jr.; Rodriguez-Nieva, Joaquin F.; Kahn, Salman; Tsai, Hsin-Zon; Taniguchi, Takashi; Watanabe, Kenji; Zettl, Alex; Wang, Feng; Levitov, Leonid S.; Crommie, Michael F.
2016-11-01
Electrostatic confinement of charge carriers in graphene is governed by Klein tunnelling, a relativistic quantum process in which particle-hole transmutation leads to unusual anisotropic transmission at p-n junction boundaries. Reflection and transmission at these boundaries affect the quantum interference of electronic waves, enabling the formation of novel quasi-bound states. Here we report the use of scanning tunnelling microscopy to map the electronic structure of Dirac fermions confined in quantum dots defined by circular graphene p-n junctions. The quantum dots were fabricated using a technique involving local manipulation of defect charge within the insulating substrate beneath a graphene monolayer. Inside such graphene quantum dots we observe resonances due to quasi-bound states and directly visualize the quantum interference patterns arising from these states. Outside the quantum dots Dirac fermions exhibit Friedel oscillation-like behaviour. Bolstered by a theoretical model describing relativistic particles in a harmonic oscillator potential, our findings yield insights into the spatial behaviour of electrostatically confined Dirac fermions.
Are the surface Fermi arcs in Dirac semimetals topologically protected?
Kargarian, Mehdi; Randeria, Mohit; Lu, Yuan-Ming
2016-08-02
Motivated by recent experiments probing anomalous surface states of Dirac semimetals (DSMs) Na3Bi and Cd3As2, we raise the question posed in the title. We find that, in marked contrast to Weyl semimetals, the gapless surface states of DSMs are not topologically protected in general, except on time-reversal-invariant planes of surface Brillouin zone. We first demonstrate this finding in a minimal four-band model with a pair of Dirac nodes at [Formula: see text] where gapless states on the side surfaces are protected only near [Formula: see text] We then validate our conclusions about the absence of a topological invariant protecting double Fermi arcs in DSMs, using a K-theory analysis for space groups of Na3Bi and Cd3As2 Generically, the arcs deform into a Fermi pocket, similar to the surface states of a topological insulator, and this pocket can merge into the projection of bulk Dirac Fermi surfaces as the chemical potential is varied. We make sharp predictions for the doping dependence of the surface states of a DSM that can be tested by angle-resolved photoemission spectroscopy and quantum oscillation experiments.
Are the surface Fermi arcs in Dirac semimetals topologically protected?
Kargarian, Mehdi; Randeria, Mohit
2016-01-01
Motivated by recent experiments probing anomalous surface states of Dirac semimetals (DSMs) Na3Bi and Cd3As2, we raise the question posed in the title. We find that, in marked contrast to Weyl semimetals, the gapless surface states of DSMs are not topologically protected in general, except on time-reversal-invariant planes of surface Brillouin zone. We first demonstrate this finding in a minimal four-band model with a pair of Dirac nodes at k=(0,0,±Q), where gapless states on the side surfaces are protected only near kz=0. We then validate our conclusions about the absence of a topological invariant protecting double Fermi arcs in DSMs, using a K-theory analysis for space groups of Na3Bi and Cd3As2. Generically, the arcs deform into a Fermi pocket, similar to the surface states of a topological insulator, and this pocket can merge into the projection of bulk Dirac Fermi surfaces as the chemical potential is varied. We make sharp predictions for the doping dependence of the surface states of a DSM that can be tested by angle-resolved photoemission spectroscopy and quantum oscillation experiments. PMID:27436895
Transport properties of Dirac semimetal Cd3As2
NASA Astrophysics Data System (ADS)
Liang, Tian; Gibson, Quinn; Xiong, Jun; Liu, Minhao; Hirschberger, Maximilian; Cava, Robert; Ong, Nai Phuan
2014-03-01
The semimetal Cd3As2 has emerged as an attractive candidate for a Dirac semimetal. A recent LDA calculation reveals that, at the Fermi energy, it has two bulk Dirac nodes which straddle the Γ point along the kz axis. The Dirac nodes were recently observed by ARPES. We have made extensive transport measurements of Cd3As2. Because of possible Cd vacancy disorder in the very large unit cell (160 atoms), the SdH oscillations reveal a quantum lifetime that is moderately damped. Despite the disorder, the observed resistivity ρ in some crystals displays a RRR of 1000. At 4 K, the residual resistivity is anomalously low (30 n Ω cm). We estimate that the mobility exceeds 106 cm2V-1s-1. A magnetic field H strongly increases ρ by factors of 100 to 1000 at 10 Tesla. This giant magnetoresistance (MR) is highly anisotropic. The MR is largest when H is perpendicular to the axis (110) and minimal when H is ∥(110). We will discuss possible origins of this unusual anisotropic giant MR. We also discuss the possibility of detecting an enhanced longitudinal MR associated with charge pumping between Weyl nodes (the chiral anomaly). Supported by Army Research Office (ARO W911NF-11-1-0379) and NSF-MRSEC Grant DMR 0819860.
Upper-division student difficulties with the Dirac delta function
NASA Astrophysics Data System (ADS)
Wilcox, Bethany R.; Pollock, Steven J.
2015-06-01
The Dirac delta function is a standard mathematical tool that appears repeatedly in the undergraduate physics curriculum in multiple topical areas including electrostatics, and quantum mechanics. While Dirac delta functions are often introduced in order to simplify a problem mathematically, students still struggle to manipulate and interpret them. To characterize student difficulties with the delta function at the upper-division level, we examined students' responses to traditional exam questions and a standardized conceptual assessment, and conducted think-aloud interviews. Our analysis was guided by an analytical framework that focuses on how students activate, construct, execute, and reflect on the Dirac delta function in the context of problem solving in physics. Here, we focus on student difficulties using the delta function to express charge distributions in the context of junior-level electrostatics. Common challenges included invoking the delta function spontaneously, translating a description of a charge distribution into a mathematical expression using delta functions, integrating 3D or non-Cartesian delta function expressions, and recognizing that the delta function can have units. We also briefly discuss implications of these difficulties for instruction.