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Sample records for dunkl dirac operator

  1. 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.

  2. 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.

  3. Interacting particles on the line and Dunkl intertwining operator of type A: application to the freezing regime

    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.

  4. 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.

  5. Dunkl Hyperbolic Equations

    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.

  6. 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.

  7. 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.

  8. Microscopic Spectrum of the Wilson Dirac Operator

    SciTech Connect

    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.

  9. Spectrum of the Wilson Dirac operator at finite lattice spacings

    SciTech Connect

    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.

  10. 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.

  11. 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.

  12. 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.

  13. Spectral functionals, nonholonomic Dirac operators, and noncommutative Ricci flows

    SciTech Connect

    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.

  14. Dirac

    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.

  15. 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.

  16. Dirac operator zero-modes on a torus

    SciTech Connect

    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.

  17. Symmetry operators for Dirac's equation on two-dimensional spin manifolds

    SciTech Connect

    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.

  18. 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.

  19. Decomposition of the polynomial kernel of arbitrary higher spin Dirac operators

    SciTech Connect

    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.

  20. 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.

  1. 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.

  2. 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.

  3. On Painleve VI transcendents related to the Dirac operator on the hyperbolic disk

    SciTech Connect

    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.

  4. Spectral asymmetry of the massless Dirac operator on a 3-torus

    SciTech Connect

    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.

  5. 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.

  6. 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.

  7. 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.

  8. Overlap Dirac operator at nonzero chemical potential and random matrix theory.

    PubMed

    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.

  9. 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.

  10. Violation of chirality of the Möbius domain-wall Dirac operator from the eigenmodes

    NASA Astrophysics Data System (ADS)

    Cossu, Guido; Fukaya, Hidenori; Tomiya, Akio; Hashimoto, Shoji

    2016-02-01

    We investigate the effects of the violation of the Ginsparg-Wilson (GW) relation in the Möbius domain-wall fermion formulation on the lattice with finite fifth dimension. Using a decomposition in terms of the eigenmodes of its four-dimensional effective Dirac operator, we isolate the GW-violating terms for various physical quantities including the residual mass and the meson susceptibilities relevant for the effective restoration of the axial U(1) symmetry at finite temperature. Numerical result shows that the GW-violating effect is more significant, or even overwhelming, for the quantities that are dominated by the low-lying eigenmodes.

  11. 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).

  12. 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.

  13. Spectrum of the Dirac operator and multigrid algorithm with dynamical staggered fermions

    SciTech Connect

    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.

  14. 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 ) .

  15. Paul Dirac

    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.

  16. Paul Dirac

    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.

  17. 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.

  18. Spectral properties of a Dirac operator in the chiral quark soliton model

    SciTech Connect

    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.

  19. 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.

  20. Supersymmetric analysis of the Dirac-Weyl operator within PT symmetry

    SciTech Connect

    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.

  1. 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.

  2. 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

  3. 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.

  4. A numerical method to compute derivatives of functions of large complex matrices and its application to the overlap Dirac operator at finite chemical potential

    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.

  5. Paul Adrien Maurice Dirac

    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.

  6. FUN WITH DIRAC EIGENVALUES.

    SciTech Connect

    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.

  7. Photoconductivity in Dirac materials

    SciTech Connect

    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.

  8. Dirac point and transconductance of top-gated graphene field-effect transistors operating at elevated temperature

    SciTech Connect

    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.

  9. 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.

  10. 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.

  11. Dirac Fermions in Borophene

    NASA Astrophysics Data System (ADS)

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

    2017-03-01

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

  12. On nonautonomous Dirac equation

    SciTech Connect

    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.

  13. Dynamical supersymmetric Dirac Hamiltonians

    SciTech Connect

    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)

  14. Executor Framework for DIRAC

    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.

  15. Topological Superconductivity in Dirac Semimetals.

    PubMed

    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}.

  16. 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.

  17. Dirac equation for strings

    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.

  18. Separability of the Massive Dirac Equation and Hawking Radiation of Dirac Particles in the Charged AdS-KERR-TAUB-NUT Black Hole

    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.

  19. Dirac Semimetals in Two Dimensions.

    PubMed

    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.

  20. 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.

  1. 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.

  2. Optomechanical Dirac physics

    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.

  3. 'Parabolic' trapped modes and steered Dirac cones in platonic crystals.

    PubMed

    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.

  4. 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.

  5. Status of the DIRAC Project

    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.

  6. 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.

  7. 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.

  8. 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.

  9. 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 }.

  10. Non-Abelian statistics of vortices with non-Abelian Dirac fermions.

    PubMed

    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.

  11. 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.

  12. Scalable implementation of spectral methods for the Dirac equation

    SciTech Connect

    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.

  13. Ground-state Dirac monopole

    SciTech Connect

    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.

  14. 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.

  15. Realization of Dirac Cones in Few Bilayer Sb(111) Films by Surface Modification.

    PubMed

    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.

  16. 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

  17. 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.

  18. Spawning rings of exceptional points out of Dirac cones.

    PubMed

    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.

  19. 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.

  20. Snapshots of Dirac fermions near the Dirac point in topological insulators.

    PubMed

    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.

  1. 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.

  2. 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.

  3. 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.

  4. Dirac fermions in nontrivial topology black hole backgrounds

    SciTech Connect

    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.

  5. 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.

  6. Mapping curved spacetimes into Dirac spinors

    PubMed Central

    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

  7. Mapping curved spacetimes into Dirac spinors.

    PubMed

    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.

  8. 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…

  9. Dirac tensor with heavy photon

    SciTech Connect

    Bytev, V. V.; Kuraev, E. A.; Scherbakova, E. S.

    2013-03-15

    For the large-angle hard-photon emission by initial leptons in the process of high-energy annihilation of e{sup +}e{sup -} to hadrons, the Dirac tensor is obtained by taking the lowest-order radiative corrections into account. The case of large-angle emission of two hard photons by initial leptons is considered. In the final result, the kinematic case of collinear emission of hard photons and soft virtual and real photons is included; it can be used for the construction of Monte-Carlo generators.

  10. Dirac's aether in curved spacetime.

    PubMed

    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.

  11. Dirac solutions for quaternionic potentials

    SciTech Connect

    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.

  12. Two dimensional Dirac carbon allotropes from graphene.

    PubMed

    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.

  13. 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…

  14. 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.

  15. Dirac-Kaehler Theory and Massless Fields

    SciTech Connect

    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.

  16. ‘Parabolic’ trapped modes and steered Dirac cones in platonic crystals

    PubMed Central

    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

  17. 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.

  18. Double Dirac Semimetals in Three Dimensions.

    PubMed

    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.

  19. 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.

  20. Highly Anisotropic Dirac Fermions in Square Graphynes.

    PubMed

    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.

  1. 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.

  2. Tunable Dirac fermion dynamics in topological insulators.

    PubMed

    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.

  3. Neutrino Masses from a Pseudo-Dirac Bino.

    PubMed

    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.

  4. Neutrino masses from a pseudo-Dirac bino

    DOE PAGES

    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

  5. Neutrino masses from a pseudo-Dirac bino

    SciTech Connect

    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.

  6. Magnetotransport properties near the Dirac point of Dirac semimetal Cd3As2 nanowires.

    PubMed

    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.

  7. 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.

  8. Dirac equation in Kerr-NUT-(A)dS spacetimes: Intrinsic characterization of separability in all dimensions

    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.

  9. 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.

  10. 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.

  11. The Dirac-Milne cosmology

    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.

  12. 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.

  13. 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.

  14. 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.

  15. Dirac cones and Dirac saddle points of bright excitons in monolayer transition metal dichalcogenides.

    PubMed

    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.

  16. 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.

  17. 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.

  18. The degeneracy of the free Dirac equation

    SciTech Connect

    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.

  19. 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.

  20. Phenomenology of Dirac Neutralino Dark Matter

    SciTech Connect

    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.

  1. The DIRAC Web Portal 2.0

    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.

  2. 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.

  3. Viability of Dirac phase leptogenesis

    SciTech Connect

    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.

  4. 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.

  5. 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.

  6. Dirac Sea and its Evolution

    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

  7. 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.

  8. 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.

  9. Strain engineering of Dirac cones in graphyne

    SciTech Connect

    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.

  10. Interlayer magnetoresistance in multilayer Dirac electron systems: motion and merging of Dirac cones.

    PubMed

    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.

  11. 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.

  12. Dirac neutrinos and SN 1987A

    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.

  13. 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.

  14. 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.

  15. Dirac particle tunneling from black rings

    SciTech Connect

    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.

  16. 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.

  17. Line of Dirac Nodes in Hyperhoneycomb Lattices.

    PubMed

    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.

  18. 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.

  19. 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.

  20. New routines for algebraic programming of the Dirac equation

    SciTech Connect

    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.

  1. Tuning Dirac points by strain in MoX2 nanoribbons (X = S, Se, Te) with a 1T' structure.

    PubMed

    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.

  2. 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.

  3. 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…

  4. 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.

  5. 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…

  6. Single-layer and bilayer graphene superlattices: collimation, additional Dirac points and Dirac lines.

    PubMed

    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.

  7. Identifying Dirac cones in carbon allotropes with square symmetry.

    PubMed

    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.

  8. Dirac node arcs in PtSn4

    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.

  9. 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

  10. 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.

  11. Plexciton Dirac points and topological modes

    PubMed Central

    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

  12. 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.

  13. Plexciton Dirac points and topological modes

    DOE PAGES

    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

  14. Plexciton Dirac points and topological modes

    SciTech Connect

    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.

  15. 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.

  16. 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.

  17. Quantum transport through 3D Dirac materials

    SciTech Connect

    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.

  18. 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.

  19. Manipulation of Dirac Cones in Mechanical Graphene

    PubMed Central

    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

  20. Manipulation of Dirac Cones in Mechanical Graphene.

    PubMed

    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.

  1. 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

  2. Near-room-temperature Chern insulator and Dirac spin-gapless semiconductor: nickel chloride monolayer.

    PubMed

    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.

  3. Pseudo-Dirac dark matter leaves a trace.

    PubMed

    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.

  4. 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.

  5. 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.

  6. 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.

  7. Klein tunneling and Dirac potentials in trapped ions

    SciTech Connect

    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.

  8. 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.

  9. Quasiparticle dynamics in reshaped helical Dirac cone of topological insulators.

    PubMed

    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.

  10. Quasiparticle dynamics in reshaped helical Dirac cone of topological insulators

    PubMed Central

    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

  11. 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.

  12. Prototype of a production system for Cherenkov Telescope Array with DIRAC

    NASA Astrophysics Data System (ADS)

    Arrabito, L.; Bregeon, J.; Haupt, A.; Graciani Diaz, R.; Stagni, F.; Tsaregorodtsev, A.

    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

  13. Hawking radiation for Dirac spinors on the RP{sup 3} geon

    SciTech Connect

    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.

  14. 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.

  15. 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.

  16. 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.

  17. Dirac oscillator interacting with a topological defect

    SciTech Connect

    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.

  18. Incomplete Dirac reduction of constrained Hamiltonian systems

    SciTech Connect

    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.

  19. Self-adjoint extensions of the Dirac Hamiltonian in the magnetic-solenoid field and related exact solutions

    SciTech Connect

    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.

  20. Dirac point movement and topological phase transition in patterned graphene.

    PubMed

    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.

  1. 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.…

  2. Dirac oscillator and nonrelativistic Snyder-de Sitter algebra

    SciTech Connect

    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.

  3. Strong topological metal material with multiple Dirac cones

    DOE PAGES

    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

  4. Strong topological metal material with multiple Dirac cones

    SciTech Connect

    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, 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 Zr2Te2P 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.

  5. 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.

  6. Lorentz-Dirac equation and circularly moving charges

    NASA Astrophysics Data System (ADS)

    Comay, E.

    1987-09-01

    The Lorentz-Dirac equation of radiation reaction is tested in a system of circularly moving changes. It is shown that this equation together with the Lienard-Wiechert retarded fields is consistent with energy conservation. Therefore, in this particular experiment, any alternative expression of radiation reaction must agree with the Lorentz-Dirac equation.

  7. 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.

  8. Strain-induced nonsymmorphic symmetry breaking and removal of Dirac semimetallic nodal line in an orthoperovskite iridate

    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.

  9. 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.

  10. 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.

  11. Z_{2} and Chiral Anomalies in Topological Dirac Semimetals.

    PubMed

    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.

  12. 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.

  13. 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.

  14. Optical analogue of relativistic Dirac solitons in binary waveguide arrays

    SciTech Connect

    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.

  15. 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].

  16. 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.

  17. 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.

  18. The Dirac point electron in zero-gravity Kerr–Newman spacetime

    SciTech Connect

    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.

  19. The Dirac Equation in Two Dimensions: Dispersive Estimates and Classification of Threshold Obstructions

    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.

  20. 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.

  1. Dirac node arcs in PtSn4

    SciTech Connect

    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 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 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.

  2. Dirac node arcs in PtSn4

    DOE PAGES

    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

  3. Operations

    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,…

  4. 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.

  5. Absorbing layers for the Dirac equation

    SciTech Connect

    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.

  6. 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.

  7. Supersymmetric model with Dirac neutrino masses

    SciTech Connect

    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.

  8. 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.

  9. 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.

  10. Dirac cone protected by non-symmorphic symmetry and three-dimensional Dirac line node in ZrSiS.

    PubMed

    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.

  11. Dirac cone protected by non-symmorphic symmetry and three-dimensional Dirac line node in ZrSiS

    PubMed Central

    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

  12. 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.

  13. 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.

  14. 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.

  15. A robust and tuneable mid-infrared optical switch enabled by bulk Dirac fermions

    PubMed Central

    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

  16. 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.

  17. 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.

  18. Does the Dirac cone of germanene exist on metal substrates?

    PubMed

    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.

  19. Dirac directional emission in anisotropic zero refractive index photonic crystals.

    PubMed

    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.

  20. 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.

  1. PT-Symmetric Real Dirac Fermions and Semimetals.

    PubMed

    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.

  2. 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.

  3. 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.

  4. Higher-order Dirac solitons in binary waveguide arrays

    SciTech Connect

    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.

  5. 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).

  6. 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.

  7. Pseudo-dirac neutrinos: a challenge for neutrino telescopes.

    PubMed

    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.

  8. Dirac cones in transition metal doped boron nitride

    SciTech Connect

    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.

  9. 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.

  10. 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.

  11. Supersymmetry between Jackiw-Nair and Dirac-Majorana anyons

    SciTech Connect

    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.

  12. Magnetotransport in Dirac metals: Chiral magnetic effect and quantum oscillations

    DOE PAGES

    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.

  13. Magnetotransport in Dirac metals: Chiral magnetic effect and quantum oscillations

    SciTech Connect

    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.

  14. Letter: On the Solutions of the Lorentz-Dirac Equation

    NASA Astrophysics Data System (ADS)

    Vogt, D.; Letelier, P. S.

    2003-12-01

    We discuss the unstable character of the solutions of the Lorentz-Dirac equation and stress the need of methods like order reduction to derive a physically acceptable equation of motion. The discussion is illustrated with the paradigmatic example of the non-relativistic harmonic oscillator with radiation reaction. We also illustrate the removal of the noncausal pre-acceleration with the introduction of a small correction in the Lorentz-Dirac equation.

  15. 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)].

  16. The confluent supersymmetry algorithm for Dirac equations with pseudoscalar potentials

    SciTech Connect

    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)].

  17. Split Dirac Supersymmetry: An Ultraviolet Completion of Higgsino Dark Matter

    SciTech Connect

    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.

  18. Conjugated Molecules Described by a One-Dimensional Dirac Equation.

    PubMed

    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).

  19. Two-dimensional Dirac signature of germanene

    SciTech Connect

    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.

  20. Nonlinear propagation of light in Dirac matter.

    PubMed

    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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. Determination of the chiral condensate from QCD Dirac spectrum on the lattice

    SciTech Connect

    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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. Designer Dirac fermions and topological phases in molecular graphene.

    PubMed

    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

  11. Theoretical prediction of a strongly correlated Dirac metal.

    PubMed

    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.

  12. Observation of Dirac monopoles in a synthetic magnetic field.

    PubMed

    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.

  13. 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.

  14. DIRAC: A new version of computer algebra tools for studying the properties and behavior of hydrogen-like ions

    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

  15. Dirac charge dynamics in graphene by infrared spectroscopy

    SciTech Connect

    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.

  16. Spin-1 Dirac-Weyl fermions protected by bipartite symmetry

    SciTech Connect

    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′.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. Electronic structure of a graphene superlattice with massive Dirac fermions

    SciTech Connect

    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.

  2. Classification of stable three-dimensional Dirac semimetals with nontrivial topology.

    PubMed

    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.

  3. 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

  4. 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.

  5. 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.

  6. Dirac oscillator in perpendicular magnetic and transverse electric fields

    SciTech Connect

    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.

  7. Radiative heat transfer in 2D Dirac materials.

    PubMed

    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.

  8. 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.

  9. Relativistic Lagrangians for the Lorentz–Dirac equation

    SciTech Connect

    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.

  10. Plasmonics in Dirac systems: from graphene to topological insulators.

    PubMed

    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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. Effective Dirac dynamics of ultracold atoms in bichromatic optical lattices

    SciTech Connect

    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.

  17. Radiative heat transfer in 2D Dirac materials

    DOE PAGES

    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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. The space-time torsion in the context of the exact Foldy-Wouthuysen transformation for a Dirac fermion

    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.

  3. 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.

  4. Bilayer graphene with parallel magnetic field and twisting: Phases and phase transitions in a highly tunable Dirac system

    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.

  5. 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…

  6. Dirac cones in the spectrum of bond-decorated graphenes

    SciTech Connect

    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.

  7. 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.

  8. Distinguishing between Dirac and Majorana neutrinos withtwo-particle interferometry

    SciTech Connect

    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.

  9. 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.

  10. 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.

  11. Path Integral for Dirac oscillator with generalized uncertainty principle

    SciTech Connect

    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.

  12. Dirac-like plasmons in honeycomb lattices of metallic nanoparticles.

    PubMed

    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.

  13. 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.

  14. 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.

  15. 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.

  16. Generalization of the Lorentz-Dirac equation to include spin

    NASA Astrophysics Data System (ADS)

    Barut, A. O.; Unal, Nuri

    1989-11-01

    For the classical point electron with Zitterbewegung (hence spin) we derive, after regularization, the radiation reaction force and covariant equations for the dynamical variables (xμ, πμ, vμ, and Sμν), which reduce to the Lorentz-Dirac equation in the spinless limit.

  17. 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.

  18. Hydrogenated arsenenes as planar magnet and Dirac material

    SciTech Connect

    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.

  19. Dirac model of electronic transport in graphene antidot barriers.

    PubMed

    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.

  20. 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.

  1. Phonon-drag thermopower in 3D Dirac semimetals.

    PubMed

    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.

  2. 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.

  3. 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 1/2≈v independent of energy, and 1/2∝m-1/2ɛ being very strongly dependent on energy (ɛ) and depending only on the effective mass m. Each of these systems is distinguished by bands crossing (sometimes referred to as touching) at a point Fermi surface, with one consequence being that for this semi-Dirac system the ratio |χorb/χsp| of orbital to spin susceptibilities diverges at low doping. We extend the study of the low-energy behavior of the semi-Dirac system, finding the plasmon frequency to be highly anisotropic while the Hall coefficient scales with carrier density in the usual manner. The Faraday rotation behavior is also reported. For Klein tunneling at normal incidence on an arbitrarily oriented barrier, the kinetic energy mixes both linear (massless) and quadratic (massive) contributions depending on orientation. Analogous to graphene, perfect transmission occurs under resonant conditions, except for the specific orientation that eliminates massless dispersion. Comparisons of the semi-Dirac system are made throughout with both other types of point Fermi surface systems.

  4. Ultrafast relaxation dynamics of photoexcited Dirac fermions in the three-dimensional Dirac semimetal C d3A s2

    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.

  5. Precise identification of Dirac-like point through a finite photonic crystal square matrix.

    PubMed

    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.

  6. Anderson localization in high temperature QCD: background configuration properties and Dirac eigenmodes

    NASA Astrophysics Data System (ADS)

    Cossu, Guido; Hashimoto, Shoji

    2016-06-01

    We investigate the properties of the background gauge field configurations that act as disorder for the Anderson localization mechanism in the Dirac spectrum of QCD at high temperatures. We compute the eigenmodes of the Möbius domain-wall fermion operator on configurations generated for the SU(3) gauge theory with two flavors of fermions, in the temperature range [0.9, 1.9]T c . We identify the source of localization of the eigenmodes with gauge configurations that are self-dual and support negative fluctuations of the Polyakov loop P L , in the high temperature sea of P L ˜ 1. The dependence of these observations on the boundary conditions of the valence operator is studied. We also investigate the spatial overlap of the left-handed and right-handed projected eigenmodes in correlation with the localization and the corresponding eigenvalue. We discuss an interpretation of the results in terms of monopole-instanton structures.

  7. 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.

  8. 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).

  9. 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.

  10. Ultrafast Broadband Photodetectors Based on Three-Dimensional Dirac Semimetal Cd3As2.

    PubMed

    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.

  11. 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.

  12. Phase-integral solution of the radial Dirac equation

    SciTech Connect

    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.

  13. 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.

  14. 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.

  15. 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.

  16. Unusual microwave response of dirac quasiparticles in graphene.

    PubMed

    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.

  17. 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.

  18. Torsion and noninertial effects on a nonrelativistic Dirac particle

    SciTech Connect

    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.

  19. Multiple Virtual Tunneling of Dirac Fermions in Granular Graphene

    PubMed Central

    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

  20. 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

  1. 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.

  2. 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.

  3. Confined Dirac fermions in a constant magnetic field

    SciTech Connect

    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.

  4. Peccei-Quinn symmetry for Dirac seesaw and leptogenesis

    SciTech Connect

    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.

  5. Three-dimensional periodic dielectric structures having photonic Dirac points

    SciTech Connect

    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.

  6. 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.

  7. Spinor Slow-Light and Dirac Particles with Variable Mass

    SciTech Connect

    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.

  8. 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.

  9. 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.

  10. Dirac bound states of anharmonic oscillator in external fields

    SciTech Connect

    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.

  11. Interplay of Dirac fermions and heavy quasiparticles in solids.

    PubMed

    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.

  12. 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.

  13. Pairing symmetry and vortex zero mode for superconducting Dirac fermions

    SciTech Connect

    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.

  14. 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.

  15. 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.

  16. 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.

  17. Hawking radiation of Dirac particles from black strings

    SciTech Connect

    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.

  18. 2D Hybrid Nanostructured Dirac Materials for Broadband Transparent Electrodes.

    PubMed

    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.

  19. 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.

  20. 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.

  1. Dirac fermions on an anti-de Sitter background

    SciTech Connect

    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.

  2. Are the surface Fermi arcs in Dirac semimetals topologically protected?

    PubMed

    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.

  3. Are the surface Fermi arcs in Dirac semimetals topologically protected?

    PubMed Central

    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

  4. 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.

  5. 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.

  6. Dirac Fermions without bulk backscattering in rhombohedral topological insulators

    NASA Astrophysics Data System (ADS)

    Mera Acosta, Carlos; Lima, Matheus; Seixas, Leandro; da Silva, Antônio; Fazzio, Adalberto

    2015-03-01

    The realization of a spintronic device using topological insulators is not trivial, because there are inherent difficulties in achieving the surface transport regime. The majority of 3D topological insulators materials (3DTI) despite of support helical metallic surface states on an insulating bulk, forming topological Dirac fermions protected by the time-reversal symmetry, exhibit electronic scattering channels due to the presence of residual continuous bulk states near the Dirac-point. From ab initio calculations, we studied the microscopic origin of the continuous bulk states in rhombohedral topological insulators materials with the space group D3d 5 (R 3 m) , showing that it is possible to understand the emergence of residual continuous bulk states near the Dirac-point into a six bands effective model, where the breaking of the R3 symmetry beyond the Γ point has an important role in the hybridization of the px, py and pz atomic orbitals. Within these model, the mechanisms known to eliminate the bulk scattering, for instance: the stacking faults (SF), electric field and alloy, generated the similar effect in the effective states of the 3DTI. Finally, we show how the surface electronic transport is modified by perturbations of bulk with SF. We would like to thank the financial support by Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP).

  7. 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.

  8. 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.

  9. 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.

  10. Relativistic equations with fractional and pseudodifferential operators

    SciTech Connect

    Babusci, D.; Dattoli, G.; Quattromini, M.

    2011-06-15

    In this paper we use different techniques from the fractional and pseudo-operators calculus to solve partial differential equations involving operators with noninteger exponents. We apply the method to equations resembling generalizations of the heat equations and discuss the possibility of extending the procedure to the relativistic Schroedinger and Dirac equations.

  11. Kappa State Solutions of Dirac-Hulthen and Dirac-Eckart Problems with Pseudospin and Spin Symmetry

    SciTech Connect

    Soylu, A.; Bayrak, O.; Boztosun, I.

    2008-11-11

    In this study, the analytical solutions of the Dirac equation have been presented for the Hulthen and Eckart potentials by applying an approximation to centrifugal-like term in the case of spin symmetry, {delta}(r) = C = constant, and pseudospin symmetry, {sigma}(r) = C = constant, for any spin-orbit quantum number {kappa}. The energy eigenvalues and corresponding spinor wave functions are obtained in the closed-forms.

  12. Classification of stable Dirac and Weyl semimetals with reflection and rotational symmetry

    NASA Astrophysics Data System (ADS)

    Gao, Zihao; Hua, Meng; Zhang, Haijun; Zhang, Xiao

    2016-05-01

    Three-dimensional (3D) Dirac and Weyl semimetals are novel states of quantum matter. We classify stable 3D Dirac and Weyl semimetals with reflection and rotational symmetry in the presence of time reversal symmetry and spin-orbit coupling, which belong to seventeen different point groups. They have two classes of reflection symmetry, with the mirror plane parallel and perpendicular to rotation axis. In both cases two types of Dirac points, existing through accidental band crossing (ABC) or at a time reversal invariant momentum (TBC), are determined by four different reflection symmetries. We classify those two types of Dirac points with a combination of different reflection and rotational symmetries. We further classify Dirac and Weyl line nodes to show in which types of mirror plane they can exist. Finally we discuss that Weyl line nodes and Dirac points can exist at the same time taking C4 v symmetry as an example.

  13. Massive Dirac Fermion on the Surface of a Magnetically Doped Topological Insulator

    SciTech Connect

    Chen, Y.L.; Chu, J.-H.; Analytis, J.G.; Liu, Z.K.; Igarashi, K.; Kuo, H.-H.; Qi, X.L.; Mo, S.K.; Moore, R.G.; Lu, D.H.; Hashimoto, M.; Sasagawa, T.; Zhang, S.C.; Fisher, I.R.; Hussain, Z.; Shen, Z.-X.; /SLAC

    2011-05-20

    Topological insulators are characterized by a massless Dirac surface state and a bulk energy gap. An insulating massive Dirac fermion state is predicted to occur if the breaking of the time reversal symmetry opens an energy gap at the Dirac point, provided that the Fermi-energy resides inside both the surface and bulk gaps. By introducing magnetic dopants into the three dimensional topological insulator Bi{sub 2}Se{sub 3} to break the time reversal symmetry, we observed the formation of a massive Dirac fermion on the surface; simultaneous magnetic and charge doping furthermore positioned the Fermi-energy inside the Dirac gap. The insulating massive Dirac Fermion state thus obtained may provide a tool for studying a range of topological phenomena relevant to both condensed matter and particle physics.

  14. Self-Assembled Si(111) Surface States: 2D Dirac Material for THz Plasmonics

    NASA Astrophysics Data System (ADS)

    Wang, Z. F.; Liu, Feng

    2015-07-01

    Graphene, the first discovered 2D Dirac material, has had a profound impact on science and technology. In the last decade, we have witnessed huge advances in graphene related fundamental and applied research. Here, based on first-principles calculations, we propose a new 2D Dirac band on the Si(111) surface with 1 /3 monolayer halogen coverage. The s p3 dangling bonds form a honeycomb superstructure on the Si(111) surface that results in an anisotropic Dirac band with a group velocity (˜106 m /s ) comparable to that in graphene. Most remarkably, the Si-based surface Dirac band can be used to excite a tunable THz plasmon through electron-hole doping. Our results demonstrate a new way to design Dirac states on a traditional semiconductor surface, so as to make them directly compatible with Si technology. We envision this new type of Dirac material to be generalized to other semiconductor surfaces with broad applications.

  15. Electronic structure of helicoidal graphene: Massless Dirac particles on a curved surface with a screw symmetry

    NASA Astrophysics Data System (ADS)

    Watanabe, Masataka; Komatsu, Hisato; Tsuji, Naoto; Aoki, Hideo

    2015-11-01

    Massless Dirac particles on the helicoid are theoretically investigated. With its possible application being helical graphene, we explore how the peculiarities of Dirac particles appear on the curved, screw-symmetric surface. Zweibein is used to derive the massless Dirac equation on the helicoid and on general curved surfaces. We show that bound states of massless Dirac electrons on the helicoid are absent, and thus the system is fully characterized by the scattering probabilities and the phase shifts. We obtain these quantities from numerically calculated wave functions. We find the local density of states and the phase shifts behave characteristically around the axis of the helicoid. Bound states of massive Dirac electrons on the surface are also shown to be absent as an extension of the above result on massless Dirac electrons. A comparison with the nonrelativistic case is also made.

  16. The massive Dirac equation in Kerr geometry: separability in Eddington-Finkelstein-type coordinates and asymptotics

    NASA Astrophysics Data System (ADS)

    Röken, Christian

    2017-03-01

    The separability of the massive Dirac equation in the non-extreme Kerr geometry in horizon-penetrating advanced Eddington-Finkelstein-type coordinates is shown. To this end, Kerr geometry is described by a Carter tetrad and the Dirac spinors and matrices are given in a chiral Newman-Penrose dyad representation. Applying Chandrasekhar's mode ansatz, the Dirac equation is separated into systems of radial and angular ordinary differential equations. Asymptotic radial solutions at infinity, the event horizon, and the Cauchy horizon are explicitly derived. Their decay is analyzed by means of error estimates. Moreover, the eigenfunctions and eigenvalues of the angular system are discussed. Finally, as an application, the scattering of Dirac waves by the gravitational field of a Kerr black hole is studied. This work provides the basis for a Hamiltonian formulation of the massive Dirac equation in Kerr geometry in horizon-penetrating coordinates and for the construction of a functional analytic integral representation of the Dirac propagator.

  17. Two-dimensional fermionic Hong-Ou-Mandel interference with massless Dirac fermions

    NASA Astrophysics Data System (ADS)

    Khan, M. A.; Leuenberger, Michael N.

    2014-08-01

    We propose a two-dimensional Hong-Ou-Mandel (HOM) type interference experiment for massless Dirac fermions in graphene and 3D topological insulators. Since massless Dirac fermions exhibit linear dispersion, similar to photons in vacuum, they can be used to obtain the HOM interference intensity pattern as a function of the delay time between two massless Dirac fermions. We show that while the Coulomb interaction leads to a significant change in the angle dependence of the tunneling of two identical massless Dirac fermions incident from opposite sides of a potential barrier, it does not affect the HOM interference pattern. We apply our formalism to develop a massless Dirac fermion beam splitter (BS) for controlling the transmission and reflection coefficients. We calculate the resulting time-resolved correlation function for two identical massless Dirac fermions scattering off the BS.

  18. Transport Experiments of Topological Insulators and Dirac Semimetals

    NASA Astrophysics Data System (ADS)

    Xiong, Jun

    The progress in understanding the Berry phase of Bloch electrons in crystals has triggered tremendous interest in discovering novel topological phases of solids. The integration of the Berry curvature in the Brillouin zone can categorize solids into phases such as topological insulators (TI), Dirac semimetals (DSM) and Weyl semimetals (WSM). These new phases have unconventional electronic states at the boundaries, such as the spin polarized electrons on the surface of a three-dimensional TI. Under proper engineering, such edge states can carry a dissipationless current, leading to a great application potential in low-power devices and topological quantum computers. Besides TI, the newly discovered Dirac and Weyl semimetals represent another example in which electrons have a linear energy-momentum dispersion. The paired Weyl nodes have opposite chiralities, and can be regarded as positive and negative monopoles of the Berry flux. Under the time-reversal, inversion and certain crystal symmetries, as in the cases of Cd3As2 and Na3Bi, the Weyl nodes with different chiralities can coexist at the same point in the Brillouin zone and the crystal becomes a Dirac semimetal. Such semimetals provide platforms for some phenomena in high energy physics, such as the chiral anomaly effect. The above predictions lie at the heart of our experimental study of topological materials. We synthesized a topological insulator, Bi2Te2 Se, with a suppressed bulk carrier density. Analysis of the prominent Shubnikov-de Haas oscillations in Bi2Te2Se demonstrates clear evidence for the Dirac surface electrons and their pi Berry phase. We also leveraged the ionic liquid gating technique to bring the chemical potential 50% closer to the Dirac point. Additionally, we studied two types of Na3Bi, a DSM. The first type with a high chemical potential exhibits a large and linear magnetoresistance (MR), implying a transport lifetime steeply tuned by the magnetic field. In the second type of Na3Bi with a

  19. Pilots 2.0: DIRAC pilots for all the skies

    NASA Astrophysics Data System (ADS)

    Stagni, F.; Tsaregorodtsev, A.; McNab, A.; Luzzi, C.

    2015-12-01

    In the last few years, new types of computing infrastructures, such as IAAS (Infrastructure as a Service) and IAAC (Infrastructure as a Client), gained popularity. New resources may come as part of pledged resources, while others are opportunistic. Most of these new infrastructures are based on virtualization techniques. Meanwhile, some concepts, such as distributed queues, lost appeal, while still supporting a vast amount of resources. Virtual Organizations are therefore facing heterogeneity of the available resources and the use of an Interware software like DIRAC to hide the diversity of underlying resources has become essential. The DIRAC WMS is based on the concept of pilot jobs that was introduced back in 2004. A pilot is what creates the possibility to run jobs on a worker node. Within DIRAC, we developed a new generation of pilot jobs, that we dubbed Pilots 2.0. Pilots 2.0 are not tied to a specific infrastructure; rather they are generic, fully configurable and extendible pilots. A Pilot 2.0 can be sent, as a script to be run, or it can be fetched from a remote location. A pilot 2.0 can run on every computing resource, e.g.: on CREAM Computing elements, on DIRAC Computing elements, on Virtual Machines as part of the contextualization script, or IAAC resources, provided that these machines are properly configured, hiding all the details of the Worker Nodes (WNs) infrastructure. Pilots 2.0 can be generated server and client side. Pilots 2.0 are the “pilots to fly in all the skies”, aiming at easy use of computing power, in whatever form it is presented. Another aim is the unification and simplification of the monitoring infrastructure for all kinds of computing resources, by using pilots as a network of distributed sensors coordinated by a central resource monitoring system. Pilots 2.0 have been developed using the command pattern. VOs using DIRAC can tune pilots 2.0 as they need, and extend or replace each and every pilot command in an easy way. In this

  20. Direct observation of Dirac cone in multilayer silicene intercalation compound CaSi2.

    PubMed

    Noguchi, Eiichi; Sugawara, Katsuaki; Yaokawa, Ritsuko; Hitosugi, Taro; Nakano, Hideyuki; Takahashi, Takashi

    2015-02-04

    Calcium-intercalated multilayer silicene CaSi2 exhibits a massless Dirac-cone π-electron-band dispersion like graphene, while the Dirac point is about 2 eV away from the Fermi level due to diiimide-based charge transfer from the Ca atoms to the silicene layers. This indicates that the graphene-like electronic structure with a massless Dirac cone is stably formed in the metal-intercalated multilayer silicene.

  1. Hidden symmetry and protection of Dirac points on the honeycomb lattice.

    PubMed

    Hou, Jing-Min; Chen, Wei

    2015-12-07

    The honeycomb lattice possesses a novel energy band structure, which is characterized by two distinct Dirac points in the Brillouin zone, dominating most of the physical properties of the honeycomb structure materials. However, up till now, the origin of the Dirac points is unclear yet. Here, we discover a hidden symmetry on the honeycomb lattice and prove that the existence of Dirac points is exactly protected by such hidden symmetry. Furthermore, the moving and merging of the Dirac points and a quantum phase transition, which have been theoretically predicted and experimentally observed on the honeycomb lattice, can also be perfectly explained by the parameter dependent evolution of the hidden symmetry.

  2. Massless Dirac fermions in graphene under an external periodic magnetic field

    NASA Astrophysics Data System (ADS)

    Liu, Shuanglong; Nurbawono, Argo; Guo, Na; Zhang, Chun

    2013-10-01

    By solving the two-component spinor equation for massless Dirac fermions, we show that graphene under a periodic external magnetic field exhibits a unique energy spectrum. At low energies, Dirac fermions are localized inside the magnetic region with discrete Landau energy levels, while at higher energies, Dirac fermions are mainly found in non-magnetic regions with continuous energy bands originating from wavefunctions analogous to particle-in-box states of electrons. These findings offer a new methodology for the control and tuning of massless Dirac fermions in graphene.

  3. Individual complex Dirac eigenvalue distributions from random matrix theory and comparison to quenched lattice QCD with a quark chemical potential.

    PubMed

    Akemann, G; Bloch, J; Shifrin, L; Wettig, T

    2008-01-25

    We analyze how individual eigenvalues of the QCD Dirac operator at nonzero quark chemical potential are distributed in the complex plane. Exact and approximate analytical results for both quenched and unquenched distributions are derived from non-Hermitian random matrix theory. When comparing these to quenched lattice QCD spectra close to the origin, excellent agreement is found for zero and nonzero topology at several values of the quark chemical potential. Our analytical results are also applicable to other physical systems in the same symmetry class.

  4. Separability of the massive Dirac equation in 5-dimensional Myers-Perry black hole geometry and its relation to a rank-three Killing-Yano tensor

    SciTech Connect

    Wu Shuangqing

    2008-09-15

    The Dirac equation for the electron around a five-dimensional rotating black hole with two different angular momenta is separated into purely radial and purely angular equations. The general solution is expressed as a superposition of solutions derived from these two decoupled ordinary differential equations. By separating variables for the massive Klein-Gordon equation in the same spacetime background, I derive a simple and elegant form for the Staeckel-Killing tensor, which can be easily written as the square of a rank-three Killing-Yano tensor. I have also explicitly constructed a symmetry operator that commutes with the scalar Laplacian by using the Staeckel-Killing tensor, and the one with the Dirac operator by the Killing-Yano tensor admitted by the five-dimensional Myers-Perry metric, respectively.

  5. Are the surface Fermi arcs in Dirac semimetals topologically protected?

    NASA Astrophysics Data System (ADS)

    Kargarian, Mehdi; Randeria, Mohit; Lu, Yuan-Ming

    2016-08-01

    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),k=(0,0,±Q), where gapless states on the side surfaces are protected only near kz=0.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.

  6. Helical Spin Order from Topological Dirac and Weyl Semimetals

    DOE PAGES

    Sun, Xiao-Qi; Zhang, Shou-Cheng; Wang, Zhong

    2015-08-14

    In this paper, we study dynamical mass generation and the resultant helical spin orders in topological Dirac and Weyl semimetals, including the edge states of quantum spin Hall insulators, the surface states of weak topological insulators, and the bulk materials of Weyl semimetals. In particular, the helical spin textures of Weyl semimetals manifest the spin-momentum locking of Weyl fermions in a visible manner. Finally, the spin-wave fluctuations of the helical order carry electric charge density; therefore, the spin textures can be electrically controlled in a simple and predictable manner.

  7. Surface regulated arsenenes as Dirac materials: From density functional calculations

    NASA Astrophysics Data System (ADS)

    Yuan, Junhui; Xie, Qingxing; Yu, Niannian; Wang, Jiafu

    2017-02-01

    Using first principle calculations based on density functional theory (DFT), we have systematically investigated the structure stability and electronic properties of chemically decorated arsenenes, AsX (X = CN, NC, NCO, NCS and NCSe). Phonon dispersion and formation energy analysis reveal that all the five chemically decorated buckled arsenenes are energetically favorable and could be synthesized. Our study shows that wide-bandgap arsenene would turn into Dirac materials when functionalized by -X (X = CN, NC, NCO, NCS and NCSe) groups, rendering new promises in next generation high-performance electronic devices.

  8. Confinement of Dirac electrons in graphene quantum dots

    NASA Astrophysics Data System (ADS)

    Jolie, Wouter; Craes, Fabian; Petrović, Marin; Atodiresei, Nicolae; Caciuc, Vasile; Blügel, Stefan; Kralj, Marko; Michely, Thomas; Busse, Carsten

    2014-04-01

    We observe spatial confinement of Dirac states on epitaxial graphene quantum dots with low-temperature scanning tunneling microscopy after using oxygen as an intercalant to suppress the surface state of Ir(111) and to effectively decouple graphene from its metal substrate. We analyze the confined electronic states with a relativistic particle-in-a-box model and find a linear dispersion relation. The oxygen-intercalated graphene is p doped [ED=0.64±0.07 eV] and has a Fermi velocity close to the one of free-standing graphene [vF=0.96±0.07×106 m/s].

  9. Time-dependent solutions to the Dirac equation

    NASA Astrophysics Data System (ADS)

    Lay Win, Khin; Petridis, Athanasios

    2006-04-01

    The time-evolution of Dirac spinors is studied using the numerical staggered-leap-frog method. This technique is shown to be very precise, stable, and fast. Numerical results regarding the zitterbewegung of the expectation values and standard deviations of the spin and the position are obtained and found to be in agreement with analytical calculations whenever those are possible. The time-development of the decay of near-resonance spinors initially set inside a potential well is studied and compared to non-relativistic results. The decay of states away from resonance is also examined. All the calculations are performed using an average personal computer.

  10. Robust state preparation in quantum simulations of Dirac dynamics

    NASA Astrophysics Data System (ADS)

    Song, Xue-Ke; Deng, Fu-Guo; Lamata, Lucas; Muga, J. G.

    2017-02-01

    A nonrelativistic system such as an ultracold trapped ion may perform a quantum simulation of a Dirac equation dynamics under specific conditions. The resulting Hamiltonian and dynamics are highly controllable, but the coupling between momentum and internal levels poses some difficulties to manipulate the internal states accurately in wave packets. We use invariants of motion to inverse engineer robust population inversion processes with a homogeneous, time-dependent simulated electric field. This exemplifies the usefulness of inverse-engineering techniques to improve the performance of quantum simulation protocols.

  11. Scaling of Dirac Fermions and the WKB approximation

    SciTech Connect

    Sabine Jeschonnek; John Tjon; Jay Van Orden

    2005-07-01

    We discuss a new method for obtaining the WKB approximation to the Dirac equation with a scalar potential and a time-like vector potential. We use the WKB solutions to investigate the scaling behavior of a confining model for quark-hadron duality. In this model, a light quark is bound to a heavy di-quark by a linear scalar potential. Absorption of virtual photons promotes the quark to bound states. The analog of the parton model for this case is for a virtual photon to eject the bound, ground-state quark directly into free continuum states. We compare the scaling limits of the response functions for these two transitions.

  12. Dirac lines in the superconducting hyper-honeycomb lattice

    NASA Astrophysics Data System (ADS)

    Bouhon, Adrien; Black-Schaffer, Annica

    Motivated by the recent discovery of the hyper-honeycomb β-Li2IrO3 studied in the context of Kitaev spin liquids, we investigate the possibility to realize superconductivity in the hyper-honeycomb lattice. Based on a t-J model we discuss the effect of the band structure and spin-orbit coupling on the most stable superconducting state. Using group theory we construct all symmetry allowed superconducting states and show that we naturally get Dirac line nodes protected by the non-symmorphic symmetries.

  13. Scaling laws for nonlinear electromagnetic responses of Dirac fermion

    NASA Astrophysics Data System (ADS)

    Morimoto, Takahiro; Nagaosa, Naoto

    2016-03-01

    We theoretically propose that the Dirac fermion in two dimensions shows the giant nonlinear responses to electromagnetic fields in the terahertz region. A scaling form is obtained for the current and magnetization as functions of the normalized electromagnetic fields E /Eω and B /Bω , where the characteristic electric (magnetic) field Eω(Bω) depends on the frequency ω as ℏ ω2/e vF(ℏ ω2/e vF2) , and is typically of the order of 80 V/cm (8 mT) in the terahertz region. Applications of the present theory to graphene and surface state of a topological insulator are discussed.

  14. Graphene on weakly interacting metals: Dirac states versus surface states

    NASA Astrophysics Data System (ADS)

    Jolie, Wouter; Craes, Fabian; Busse, Carsten

    2015-03-01

    We investigate the interplay between graphene and different, weakly interacting metal substrates by measuring the local density of states of the surface with scanning tunneling spectroscopy. Energy-resolved Friedel oscillations, confined states, and a prominent signal in point spectra are found after intercalating several monolayers of silver between graphene and Ir(111) and correspond to the shifted surface state of silver. These features outweigh spectroscopic signatures of graphene, which are retrieved when the amount of silver is reduced to one monolayer. Hence, suppressing the surface states of the metal substrate enhances the sensitivity to the Dirac states of quasi-free-standing graphene.

  15. Minimax rational approximation of the Fermi-Dirac distribution

    DOE PAGES

    Moussa, Jonathan E.

    2016-10-27

    Accurate rational approximations of the Fermi-Dirac distribution are a useful component in many numerical algorithms for electronic structure calculations. The best known approximations use O(log(βΔ)log(ϵ–1)) poles to achieve an error tolerance ϵ at temperature β–1 over an energy interval Δ. We apply minimax approximation to reduce the number of poles by a factor of four and replace Δ with Δocc, the occupied energy interval. Furthermore, this is particularly beneficial when Δ >> Δocc, such as in electronic structure calculations that use a large basis set.

  16. Phase structure of a holographic double monolayer Dirac semimetal

    NASA Astrophysics Data System (ADS)

    Grignani, Gianluca; Marini, Andrea; Pigna, Adriano-Costantino; Semenoff, Gordon W.

    2016-06-01

    We study a holographic D3/probe-D5-brane model of a double monolayer Dirac semimetal in a magnetic field and in the presence of a nonzero temperature. Intra-and inter-layer exciton condensates can form by varying the balanced charge density on the layers, the spatial separation and the temperature. Constant temperature phase diagrams for a wide range of layer separations and charge densities are found. The presence of a finite temperature makes the phase diagrams extremely rich and in particular leads to the appearance of a symmetric phase which was missing at zero temperature.

  17. Optomechanical Metamaterials: Dirac polaritons, Gauge fields, and Instabilities

    NASA Astrophysics Data System (ADS)

    Peano, Vittorio; Schmidt, Michael; Marquardt, Florian

    2014-03-01

    Freestanding photonic crystals can be used to trap both light and mechanical vibrations. These ``optomechanical crystal'' structures have already been experimentally demonstrated to yield strong coupling between a photon mode and a phonon mode, co-localized at a single defect site. Future devices may feature a regular superlattice of such defects, turning them into ``optomechanical arrays.'' We predict that tailoring the optomechanical band structure of such arrays can be used to implement Dirac physics of photons and phonons, to create a photonic gauge field via mechanical vibrations, and to observe a novel optomechanical instability. ERC Starting Grant OPTOMECH and via the DARPA program ORCHID.

  18. New Dirac fermions in periodically modulated bilayer graphene.

    PubMed

    Tan, Liang Z; Park, Cheol-Hwan; Louie, Steven G

    2011-07-13

    We investigate the effect of periodic potentials on the electronic structure of bilayer graphene and show that there is a critical value of the external potential below which new Dirac fermions are generated in the low-energy band structure, and above which a band gap is opened in the system. Our results, obtained from a self-consistent tight-binding calculation, can be simply explained by a two-band continuum model as a consequence of the pseudospin physics in graphene. The findings are robust against changes in the form of the potential, as well as bias voltages between the layers.

  19. Two-loop Dirac neutrino mass and WIMP dark matter

    NASA Astrophysics Data System (ADS)

    Bonilla, Cesar; Ma, Ernest; Peinado, Eduardo; Valle, Jose W. F.

    2016-11-01

    We propose a "scotogenic" mechanism relating small neutrino mass and cosmological dark matter. Neutrinos are Dirac fermions with masses arising only in two-loop order through the sector responsible for dark matter. Two triality symmetries ensure both dark matter stability and strict lepton number conservation at higher orders. A global spontaneously broken U(1) symmetry leads to a physical Diracon that induces invisible Higgs decays which add up to the Higgs to dark matter mode. This enhances sensitivities to spin-independent WIMP dark matter search below mh / 2.

  20. The electric charge of a dirac monopole at nonzero temperature.

    SciTech Connect

    Coriano, C.; Parwani, R. R.; High Energy Physics

    1995-11-16

    We study the effect of nonzero temperature on the induced electric charge around a Dirac monopole. While at zero temperature the charge is known to be proportional to a CP violating {prime} parameter, we find that at high temperature the charge is proportional to sin {theta}. Other features of the charge at nonzero temperature are discussed. We also compute the induced charge at nonzero temperature around an Aharonov-Bohm flux string in 2 + 1 dimensions and compare the result with an index theorem, and also with the electron-monopole problem in 3 + 1 dimensions.

  1. Lorentz-Dirac force from QED for linear acceleration

    NASA Astrophysics Data System (ADS)

    Higuchi, Atsushi; Martin, Giles D.

    2004-10-01

    We investigate the motion of a wave packet of a charged scalar particle linearly accelerated by a static potential in quantum electrodynamics. We calculate the expectation value of the position of the charged particle after the acceleration to first order in the fine structure constant in the ℏ→0 limit. We find that the change in the expectation value of the position (the position shift) due to radiation reaction agrees exactly with the result obtained using the Lorentz-Dirac force in classical electrodynamics. We also point out that the one-loop correction to the potential may contribute to the position change in this limit.

  2. Minimax rational approximation of the Fermi-Dirac distribution

    SciTech Connect

    Moussa, Jonathan E.

    2016-10-27

    Accurate rational approximations of the Fermi-Dirac distribution are a useful component in many numerical algorithms for electronic structure calculations. The best known approximations use O(log(βΔ)log(ϵ–1)) poles to achieve an error tolerance ϵ at temperature β–1 over an energy interval Δ. We apply minimax approximation to reduce the number of poles by a factor of four and replace Δ with Δocc, the occupied energy interval. Furthermore, this is particularly beneficial when Δ >> Δocc, such as in electronic structure calculations that use a large basis set.

  3. New scale-relativistic derivations of Pauli and Dirac equations

    NASA Astrophysics Data System (ADS)

    Hammad, F.

    2008-02-01

    In scale relativity, quantum mechanics is recovered by transcribing the classical equations of motion to fractal spaces and demanding, as dictated by the principle of scale relativity, that the form of these equations be preserved. In the framework of this theory, however, the form of the classical energy equations both in the relativistic and nonrelativistic cases are not preserved. Aiming to get full covariance, i.e., to restore to these equations their classical forms, we show that the scale-relativistic form of the Schrödinger equation yields the Pauli equation, whilst the Pissondes's scale-relativistic form of the Klein-Gordon equation gives the Dirac equation.

  4. Ultrafast exciton-polariton scattering towards the Dirac points.

    PubMed

    Kovalev, V M; Savenko, I G; Iorsh, I V

    2016-03-16

    Using the Feynman-Dyson diagram technique, we study nonlinear polariton-polariton scattering in a two-dimensional micropillar-based optical superlattice with hexagonal symmetry. We demonstrate that both the emerging polariton chirality and the loop Feynman diagrams up to infinite order should be strictly accounted for in the evaluation of the self-energy of the system. Further, we explicitly show that in such a design the time of polariton scattering towards the Dirac points can be drastically decreased which can be used, for instance, in engineering novel classes of polariton lasers with substantially reduced thresholds.

  5. Phase-integral method for the radial Dirac equation

    SciTech Connect

    Linnæus, Staffan

    2014-09-15

    A phase-integral (WKB) solution of the radial Dirac equation is calculated up to the third order of approximation, retaining perfect symmetry between the two components of the wave function and introducing no singularities except at the zeroth-order transition points. The potential is allowed to be of scalar, vector, or tensor type, or any combination of these. The connection problem is investigated in detail. Explicit formulas are given for single-turning-point phase shifts and single-well energy levels.

  6. Dirac mass generation from crystal symmetry breaking on the surfaces of topological crystalline insulators.

    PubMed

    Zeljkovic, Ilija; Okada, Yoshinori; Serbyn, Maksym; Sankar, R; Walkup, Daniel; Zhou, Wenwen; Liu, Junwei; Chang, Guoqing; Wang, Yung Jui; Hasan, M Zahid; Chou, Fangcheng; Lin, Hsin; Bansil, Arun; Fu, Liang; Madhavan, Vidya

    2015-03-01

    The tunability of topological surface states and controllable opening of the Dirac gap are of fundamental and practical interest in the field of topological materials. In the newly discovered topological crystalline insulators (TCIs), theory predicts that the Dirac node is protected by a crystalline symmetry and that the surface state electrons can acquire a mass if this symmetry is broken. Recent studies have detected signatures of a spontaneously generated Dirac gap in TCIs; however, the mechanism of mass formation remains elusive. In this work, we present scanning tunnelling microscopy (STM) measurements of the TCI Pb1-xSnxSe for a wide range of alloy compositions spanning the topological and non-topological regimes. The STM topographies reveal a symmetry-breaking distortion on the surface, which imparts mass to the otherwise massless Dirac electrons-a mechanism analogous to the long sought-after Higgs mechanism in particle physics. Interestingly, the measured Dirac gap decreases on approaching the trivial phase, whereas the magnitude of the distortion remains nearly constant. Our data and calculations reveal that the penetration depth of Dirac surface states controls the magnitude of the Dirac mass. At the limit of the critical composition, the penetration depth is predicted to go to infinity, resulting in zero mass, consistent with our measurements. Finally, we discover the existence of surface states in the non-topological regime, which have the characteristics of gapped, double-branched Dirac fermions and could be exploited in realizing superconductivity in these materials.

  7. Comment on 'Zero-range potentials for Dirac particles: Scattering and related continuum problems'

    SciTech Connect

    Coutinho, F. A. B.; Nogami, Y.

    2006-02-15

    In a recent paper, Szmytkowski proposed zero-range potentials for Dirac particles in three space dimensions. On the other hand, there is a theorem, proved by Svendsen a long time ago, which implies that zero-range potentials cannot be defined for the Dirac equation in two and three space dimensions. We discuss a difficulty that underlies Szmytkowski's approach.

  8. Exact analytic solutions for a Dirac electron moving in graphene under magnetic fields.

    PubMed

    Kuru, S; Negro, J; Nieto, L M

    2009-11-11

    Exact analytical solutions for the bound states of a graphene Dirac electron in various magnetic fields with translational symmetry are obtained. In order to solve the time-independent Dirac-Weyl equation the factorization method used in supersymmetric quantum mechanics is adapted to this problem. The behavior of the discrete spectrum, probability and current densities are discussed.

  9. Quasi-exact solvability of Dirac equation with Lorentz scalar potential

    SciTech Connect

    Ho, C.-L. . E-mail: hcl@mail.tku.edu.tw

    2006-09-15

    We consider exact/quasi-exact solvability of Dirac equation with a Lorentz scalar potential based on factorizability of the equation. Exactly solvable and sl (2)-based quasi-exactly solvable potentials are discussed separately in Cartesian coordinates for a pure Lorentz potential depending only on one spatial dimension, and in spherical coordinates in the presence of a Dirac monopole.

  10. Multiple unpinned Dirac points in group-Va single-layers with phosphorene structure

    NASA Astrophysics Data System (ADS)

    Lu, Yunhao; Zhou, Di; Chang, Guoqing; Guan, Shan; Chen, Weiguang; Jiang, Yinzhu; Jiang, Jianzhong; Wang, Xue-Sen; Yang, Shengyuan A.; Feng, Yuan Ping; Kawazoe, Yoshiyuki; Lin, Hsin

    2016-06-01

    Emergent Dirac fermion states underlie many intriguing properties of graphene, and the search for them constitutes one strong motivation to explore two-dimensional (2D) allotropes of other elements. Phosphorene, the ultrathin layers of black phosphorous, has been a subject of intense investigations recently, and it was found that other group-Va elements could also form 2D layers with similar puckered lattice structure. Here, by a close examination of their electronic band structure evolution, we discover two types of Dirac fermion states emerging in the low-energy spectrum. One pair of (type-I) Dirac points is sitting on high-symmetry lines, while two pairs of (type-II) Dirac points are located at generic k-points, with different anisotropic dispersions determined by the reduced symmetries at their locations. Such fully-unpinned (type-II) 2D Dirac points are discovered for the first time. In the absence of spin-orbit coupling (SOC), we find that each Dirac node is protected by the sublattice symmetry from gap opening, which is in turn ensured by any one of three point group symmetries. The SOC generally gaps the Dirac nodes, and for the type-I case, this drives the system into a quantum spin Hall insulator phase. We suggest possible ways to realise the unpinned Dirac points in strained phosphorene.

  11. Dirac mass generation from crystal symmetry breaking on the surfaces of topological crystalline insulators

    SciTech Connect

    Zeljkovic, Ilija; Okada, Yoshinori; Serbyn, Maksym; Sankar, R.; Walkup, Daniel; Zhou, Wenwen; Liu, Junwei; Chang, Guoqing; Wang, Yung Jui; Hasan, M. Zahid; Chou, Fangcheng; Lin, Hsin; Bansil, Arun; Fu, Liang; Madhavan, Vidya

    2015-02-16

    The tunability of topological surface states and controllable opening of the Dirac gap are of fundamental and practical interest in the field of topological materials. In the newly discovered topological crystalline insulators (TCIs), theory predicts that the Dirac node is protected by a crystalline symmetry and that the surface state electrons can acquire a mass if this symmetry is broken. Recent studies have detected signatures of a spontaneously generated Dirac gap in TCIs; however, the mechanism of mass formation remains elusive. In this work, we present scanning tunnelling microscopy (STM) measurements of the TCI Pb1-xSnxSe for a wide range of alloy compositions spanning the topological and non-topological regimes. The STM topographies reveal a symmetry-breaking distortion on the surface, which imparts mass to the otherwise massless Dirac electrons—a mechanism analogous to the long sought-after Higgs mechanism in particle physics. Interestingly, the measured Dirac gap decreases on approaching the trivial phase, whereas the magnitude of the distortion remains nearly constant. Our data and calculations reveal that the penetration depth of Dirac surface states controls the magnitude of the Dirac mass. At the limit of the critical composition, the penetration depth is predicted to go to infinity, resulting in zero mass, consistent with our measurements. Lastly, we discover the existence of surface states in the non-topological regime, which have the characteristics of gapped, double-branched Dirac fermions and could be exploited in realizing superconductivity in these materials.

  12. Weak cosmic censorship, dyonic Kerr-Newman black holes and Dirac fields

    NASA Astrophysics Data System (ADS)

    Zsolt Tóth, Gábor

    2016-06-01

    It was investigated recently, with the aim of testing the weak cosmic censorship conjecture, whether an extremal Kerr black hole can be converted into a naked singularity by interaction with a massless classical Dirac test field, and it was found that this is possible. We generalize this result to electrically and magnetically charged rotating extremal black holes (i.e. extremal dyonic Kerr-Newman black holes) and massive Dirac test fields, allowing magnetically or electrically uncharged or nonrotating black holes and the massless Dirac field as special cases. We show that the possibility of the conversion is a direct consequence of the fact that the Einstein-Hilbert energy-momentum tensor of the classical Dirac field does not satisfy the null energy condition, and is therefore not in contradiction with the weak cosmic censorship conjecture. We give a derivation of the absence of superradiance of the Dirac field without making use of the complete separability of the Dirac equation in the dyonic Kerr-Newman background, and we determine the range of superradiant frequencies of the scalar field. The range of frequencies of the Dirac field that can be used to convert a black hole into a naked singularity partially coincides with the superradiant range of the scalar field. We apply horizon-penetrating coordinates, as our arguments involve calculating quantities at the event horizon. We describe the separation of variables for the Dirac equation in these coordinates, although we mostly avoid using it.

  13. Excitonic pairing and insulating transition in two-dimensional semi-Dirac semimetals

    NASA Astrophysics Data System (ADS)

    Wang, Jing-Rong; Liu, Guo-Zhu; Zhang, Chang-Jin

    2017-02-01

    A sufficiently strong long-range Coulomb interaction can induce excitonic pairing in gapless Dirac semimetals, which generates a finite gap and drives the semimetal-insulator quantum phase transition. This phenomenon is in close analogy to dynamical chiral symmetry breaking in high-energy physics. In most realistic Dirac semimetals, including suspended graphene, the Coulomb interaction is too weak to open an excitonic gap. The Coulomb interaction plays a more important role at low energies in a two-dimensional semi-Dirac semimetal, in which the fermion spectrum is linear in one component of momenta and quadratic in the other, than a Dirac semimetal, and indeed leads to breakdown of Fermi liquid theory. We study dynamical excitonic gap generation in a two-dimensional semi-Dirac semimetal by solving the Dyson-Schwinger equation, and show that a moderately strong Coulomb interaction suffices to induce excitonic pairing. Additional short-range four-fermion coupling tends to promote excitonic pairing. Among the available semi-Dirac semimetals, we find that the TiO2/VO2 nanostructure provides a promising candidate for the realization of an excitonic insulator. We also apply the renormalization group method to analyze the strong coupling between the massless semi-Dirac fermions and the quantum critical fluctuation of the excitonic order parameter at the semimetal-insulator quantum critical point, and reveal non-Fermi liquid behaviors of semi-Dirac fermions.

  14. Asymmetric capture of Dirac dark matter by the Sun

    SciTech Connect

    Blennow, Mattias; Clementz, Stefan

    2015-08-18

    Current problems with the solar model may be alleviated if a significant amount of dark matter from the galactic halo is captured in the Sun. We discuss the capture process in the case where the dark matter is a Dirac fermion and the background halo consists of equal amounts of dark matter and anti-dark matter. By considering the case where dark matter and anti-dark matter have different cross sections on solar nuclei as well as the case where the capture process is considered to be a Poisson process, we find that a significant asymmetry between the captured dark particles and anti-particles is possible even for an annihilation cross section in the range expected for thermal relic dark matter. Since the captured number of particles are competitive with asymmetric dark matter models in a large range of parameter space, one may expect solar physics to be altered by the capture of Dirac dark matter. It is thus possible that solutions to the solar composition problem may be searched for in these type of models.

  15. Asymmetric capture of Dirac dark matter by the Sun

    SciTech Connect

    Blennow, Mattias; Clementz, Stefan E-mail: scl@kth.se

    2015-08-01

    Current problems with the solar model may be alleviated if a significant amount of dark matter from the galactic halo is captured in the Sun. We discuss the capture process in the case where the dark matter is a Dirac fermion and the background halo consists of equal amounts of dark matter and anti-dark matter. By considering the case where dark matter and anti-dark matter have different cross sections on solar nuclei as well as the case where the capture process is considered to be a Poisson process, we find that a significant asymmetry between the captured dark particles and anti-particles is possible even for an annihilation cross section in the range expected for thermal relic dark matter. Since the captured number of particles are competitive with asymmetric dark matter models in a large range of parameter space, one may expect solar physics to be altered by the capture of Dirac dark matter. It is thus possible that solutions to the solar composition problem may be searched for in these type of models.

  16. Josephson junction detectors for Majorana modes and Dirac fermions

    NASA Astrophysics Data System (ADS)

    Maiti, M.; Kulikov, K. M.; Sengupta, K.; Shukrinov, Yu. M.

    2015-12-01

    We demonstrate that the current-voltage (I -V ) characteristics of resistively and capacitively shunted Josephson junctions (RCSJs) hosting localized subgap Majorana states provide a phase-sensitive method for their detection. The I -V characteristics of such RCSJs, in contrast to their resistively shunted counterparts, exhibit subharmonic odd Shapiro steps. These steps, owing to their subharmonic nature, exhibit qualitatively different properties compared to harmonic odd steps of conventional junctions. In addition, the RCSJs hosting Majorana bound states also display an additional sequence of steps in the devil's staircase structure seen in their I -V characteristics; such a sequence of steps makes their I -V characteristics qualitatively distinct from that of their conventional counterparts. A similar study for RCSJs with graphene superconducting junctions hosting Dirac-like quasiparticles reveals that the Shapiro step width in their I -V curves bears a signature of the transmission resonance phenomenon of their underlying Dirac quasiparticles; consequently, these step widths exhibit a π periodic oscillatory behavior with variation of the junction barrier potential. We discuss experiments which can test our theory.

  17. Quasiparticle Spectrum of 2-d Dirac Vortices in Optical Lattices

    NASA Astrophysics Data System (ADS)

    Haddad, Laith

    2009-10-01

    Bose-Einstein condensates in a honeycomb optical lattice are described by a nonlinear Dirac equaton (NLDE) in the long wavelength, mean field limit [1]. The upper and lower two-spinor equations decouple and superficially resemble the equations of previously studied NLDE's such as the Soler model for extended fermions. Although much work has been done on NLDE's, the bulk of the literature deals with models with Poincare invariant nonlinearites. In contrast our equations break Poincare symmetry providing an opportunity to study phenomenological models in cosmology and particle physics where this symmetry is not manifest. We obtain and classify localized solutions to our equations for both repulsive and attractive contact interactions. We also derive analogs of the Bogoliubov-de Gennes equations for the lattice and use these to study the stability and low energy spectrum of our solutions showing the existence of stable exotic structures such as vortices with fractional statistics.[4pt] [1] L. H. Haddad and L. D. Carr, ``The Nonlinear Dirac Equation in Bose-Einstein Condensates: Foundation and Symmetries,'' Physica D: Nonlinear Phenomena, v. 238, p. 1413 (2009). http://arxiv.org/pdf/0803.3039v1

  18. Partially Ordered Sets of Quantum Measurements and the Dirac Equation

    NASA Astrophysics Data System (ADS)

    Knuth, Kevin H.

    2012-02-01

    Events can be ordered according to whether one event influences another. This results in a partially ordered set (poset) of events often referred to as a causal set. In this framework, an observer can be represented by a chain of events. Quantification of events and pairs of events, referred to as intervals, can be performed by projecting them onto an observer chain, or even a pair of observer chains, which in specific situations leads to a Minkowski metric replete with Lorentz transformations (Bahreyni & Knuth, 2011. APS B21.00007). In this work, we unify this picture with the Process Calculus, which coincides with the Feynman rules of quantum mechanics (Goyal, Knuth, Skilling, 2010, arXiv:0907.0909; Goyal & Knuth, Symmetry 2011, 3(2), 171), by considering quantum measurements to be events. This is performed by quantifying pairs of events, which represent transitions, with a pair of numbers, or a quantum amplitude. In the 1+1D case this results in the Feynman checkerboard model of the Dirac equation (Feynman & Hibbs, 1965). We further demonstrate that in the case of 3+1 dimensions, we recover Bialnycki-Birula's (1994, Phys. Rev. D, 49(12), 6920) body-centered cubic cellular automata model of the Dirac equation studied more recently by Earle (2011, arXiv:1102.1200v1).

  19. Dirac plasmons in bipartite lattices of metallic nanoparticles

    NASA Astrophysics Data System (ADS)

    Jebb Sturges, Thomas; Woollacott, Claire; Weick, Guillaume; Mariani, Eros

    2015-03-01

    We study theoretically ‘graphene-like’ plasmonic metamaterials constituted by two-dimensional arrays of metallic nanoparticles, including perfect honeycomb structures with and without inversion symmetry, as well as generic bipartite lattices. The dipolar interactions between localized surface plasmons (LSPs) in different nanoparticles gives rise to collective plasmons (CPs) that extend over the whole lattice. We study the band structure of CPs and unveil its tunability with the orientation of the dipole moments associated with the LSPs. Depending on the dipole orientation, we identify a phase diagram of gapless or gapped phases in the CP dispersion. We show that the gapless phases in the phase diagram are characterized by CPs behaving as massless chiral Dirac particles, in analogy with electrons in graphene. When the inversion symmetry of the honeycomb structure is broken, CPs are described as gapped chiral Dirac modes with an energy-dependent Berry phase. We further relax the geometric symmetry of the honeycomb structure by analysing generic bipartite hexagonal lattices. In this case we study the evolution of the phase diagram and unveil the emergence of a sequence of topological phase transitions when one hexagonal sublattice is progressively shifted with respect to the other.

  20. Dirac Cellular Automaton from Split-step Quantum Walk

    PubMed Central

    Mallick, Arindam; Chandrashekar, C. M.

    2016-01-01

    Simulations of one quantum system by an other has an implication in realization of quantum machine that can imitate any quantum system and solve problems that are not accessible to classical computers. One of the approach to engineer quantum simulations is to discretize the space-time degree of freedom in quantum dynamics and define the quantum cellular automata (QCA), a local unitary update rule on a lattice. Different models of QCA are constructed using set of conditions which are not unique and are not always in implementable configuration on any other system. Dirac Cellular Automata (DCA) is one such model constructed for Dirac Hamiltonian (DH) in free quantum field theory. Here, starting from a split-step discrete-time quantum walk (QW) which is uniquely defined for experimental implementation, we recover the DCA along with all the fine oscillations in position space and bridge the missing connection between DH-DCA-QW. We will present the contribution of the parameters resulting in the fine oscillations on the Zitterbewegung frequency and entanglement. The tuneability of the evolution parameters demonstrated in experimental implementation of QW will establish it as an efficient tool to design quantum simulator and approach quantum field theory from principles of quantum information theory. PMID:27184159

  1. Detection of chiral anomaly and valley transport in Dirac semimetals

    NASA Astrophysics Data System (ADS)

    Zhang, Cheng; Zhang, Enze; Liu, Yanwen; Chen, Zhigang; Liang, Sihang; Cao, Junzhi; Yuan, Xiang; Tang, Lei; Li, Qian; Gu, Teng; Wu, Yizheng; Zou, Jin; Xiu, Faxian

    Chiral anomaly is a non-conservation of chiral charge pumped by the topological nontrivial gauge field, which has been predicted to exist in the emergent quasiparticle excitations in Dirac and Weyl semimetals. However, so far, such pumping process hasn't been clearly demonstrated and lacks a convincing experimental identification. Here, we report the detection of the charge pumping effect and the related valley transport in Cd3As2 driven by external electric and magnetic fields (EB). We find that the chiral imbalance leads to a non-zero gyrotropic coefficient, which can be confirmed by the EB-generated Kerr effect. By applying B along the current direction, we observe a negative magnetoresistance despite the giant positive one at other directions, a clear indication of the chiral anomaly. Remarkably, a robust nonlocal response in valley diffusion originated from the chiral anomaly is persistent up to room temperature when B is parallel to E. The ability to manipulate the valley polarization in Dirac semimetal opens up a brand-new route to understand its fundamental properties through external fields and utilize the chiral fermions in valleytronic applications.

  2. Dirac Cellular Automaton from Split-step Quantum Walk.

    PubMed

    Mallick, Arindam; Chandrashekar, C M

    2016-05-17

    Simulations of one quantum system by an other has an implication in realization of quantum machine that can imitate any quantum system and solve problems that are not accessible to classical computers. One of the approach to engineer quantum simulations is to discretize the space-time degree of freedom in quantum dynamics and define the quantum cellular automata (QCA), a local unitary update rule on a lattice. Different models of QCA are constructed using set of conditions which are not unique and are not always in implementable configuration on any other system. Dirac Cellular Automata (DCA) is one such model constructed for Dirac Hamiltonian (DH) in free quantum field theory. Here, starting from a split-step discrete-time quantum walk (QW) which is uniquely defined for experimental implementation, we recover the DCA along with all the fine oscillations in position space and bridge the missing connection between DH-DCA-QW. We will present the contribution of the parameters resulting in the fine oscillations on the Zitterbewegung frequency and entanglement. The tuneability of the evolution parameters demonstrated in experimental implementation of QW will establish it as an efficient tool to design quantum simulator and approach quantum field theory from principles of quantum information theory.

  3. Size quantization of Dirac fermions in graphene constrictions

    PubMed Central

    Terrés, B.; Chizhova, L. A.; Libisch, F.; Peiro, J.; Jörger, D.; Engels, S.; Girschik, A.; Watanabe, K.; Taniguchi, T.; Rotkin, S. V.; Burgdörfer, J.; Stampfer, C.

    2016-01-01

    Quantum point contacts are cornerstones of mesoscopic physics and central building blocks for quantum electronics. Although the Fermi wavelength in high-quality bulk graphene can be tuned up to hundreds of nanometres, the observation of quantum confinement of Dirac electrons in nanostructured graphene has proven surprisingly challenging. Here we show ballistic transport and quantized conductance of size-confined Dirac fermions in lithographically defined graphene constrictions. At high carrier densities, the observed conductance agrees excellently with the Landauer theory of ballistic transport without any adjustable parameter. Experimental data and simulations for the evolution of the conductance with magnetic field unambiguously confirm the identification of size quantization in the constriction. Close to the charge neutrality point, bias voltage spectroscopy reveals a renormalized Fermi velocity of ∼1.5 × 106 m s−1 in our constrictions. Moreover, at low carrier density transport measurements allow probing the density of localized states at edges, thus offering a unique handle on edge physics in graphene devices. PMID:27198961

  4. Dirac fields, torsion and Barbero-Immirzi parameter in cosmology

    NASA Astrophysics Data System (ADS)

    de Berredo-Peixoto, G.; Freidel, L.; Shapiro, I. L.; de Souza, C. A.

    2012-06-01

    We consider cosmological solution for Einstein gravity with massive fermions with a four-fermion coupling, which emerges from the Holst action and is related to the Barbero-Immirzi (BI) parameter. This gravitational action is an important object of investigation in a non-perturbative formalism of quantum gravity. We study the equation of motion for the Dirac field within the standard Friedman-Robertson-Walker (FRW) metric. Finally, we show the theory with BI parameter and minimally coupling Dirac field, in the zero mass limit, is equivalent to an additional term which looks like a perfect fluid with the equation of state p = wρ, with w = 1 which is independent of the BI parameter. The existence of mass imposes a variable w, which creates either an inflationary phase with w = -1, or assumes an ultra hard equation of states w = 1 for very early universe. Both phases relax to a pressure less fluid w = 0 for late universe (corresponding to the limit m → ∞).

  5. Distinguishing Dirac/Majorana sterile neutrinos at the LHC

    NASA Astrophysics Data System (ADS)

    Dib, Claudio O.; Kim, C. S.; Wang, Kechen; Zhang, Jue

    2016-07-01

    We study the purely leptonic decays of W±→e±e±μ∓ν and μ±μ±e∓ν produced at the LHC, induced by sterile neutrinos with mass mN below MW in the intermediate state. Since the final state neutrino escapes detection, one cannot tell whether this process violates lepton number, which would indicate a Majorana character for the intermediate sterile neutrino. Our study shows that when the sterile neutrino mixings with electrons and muons are different enough, one can still discriminate between the Dirac and Majorana character of this intermediate neutrino by simply counting and comparing the above decay rates. After performing collider simulations and statistical analysis, we find that at the 14 TeV LHC with an integrated luminosity of 3000 fb-1, for two benchmark scenarios mN=20 and 50 GeV, at least a 3 σ level of exclusion on the Dirac case can be achieved for disparities as mild as, e.g., |UN e|2<0.7 |UN μ|2 or |UN μ|2<0.7 |UN e|2 , provided that |UN e|2 and |UN μ|2 are both above ˜2 ×10-6.

  6. Observation of Dirac electrons in germanene on diboride thin films

    NASA Astrophysics Data System (ADS)

    Fleurence, Antoine; Friedlein, Rainer; Yamane, Hiroyuki; Kim, Howon; Awatani, Yuuto; Yoshimoto, Shinya; Mukai, Kozo; Koitaya, Takanori; Hasegawa, Yukio; Yoshinobu, Jun; Kosugi, Nobuhiro; Yamada-Takamura, Yukiko

    Germanene is a single atom thick honeycomb lattice of Ge atoms. Just like silicene, free-standing germanene is predicted to feature π bands forming graphene-like Dirac cones. Epitaxial germanene was already claimed to form on number of substrates, but no evidence for the existence of a π electronic system has been reported yet. In the present work, we demonstrate experimentally that Ge atoms segregated on the (0001) surface of zirconium diboride (ZrB2) thin films grown on Ge(111) form a germanene layer. ZrB2(0001) with germanene is (3 √3X3 √3)-reconstructed at low-temperature and (√3X √3)-reconstructed at room temperature. The (3 √3X3 √3) reconstruction originates from the matching of this unit cell with the (4X4) unit cell of a Ge honeycomb lattice. Evidence for its germanene nature stems from the observation of the Dirac cone-like dispersion at the K point of its Brillouin zone.

  7. Remarkable paramagnetic features of Fermi-Dirac-Pauli plasmas

    NASA Astrophysics Data System (ADS)

    Akbari-Moghanjoughi, M.

    2011-07-01

    In this paper by using the relativistic magnetic susceptibility of a Fermi-Dirac (relativistically degenerate) plasma, quantum magnetohydrodynamics model is used to investigate the propagation of spin-induced (SI) magnetosonic nonlinear excitations in a normally and relativistically degenerate dense electron-ion plasma in the presence of the spin magnetization effect. Based on the conventional pseudopotential method the matching criterion for the evolution of SI solitary structures is evaluated. It is found that, the plasma mass density and strength of the magnetic field have significant effects on excitation and evolution of magnetosonic nonlinear structures in Fermi-Dirac plasmas. Only rarefactive SI magnetosonic solitary structures are found to excite in such plasmas. Furthermore, fundamental differences are shown to exist in magnetosonic soliton dynamics in the two distinct plasma degeneracy regimes, which are due to interplay between the negative pressure-like paramagnetism and positive relativistic degeneracy pressure of electrons. Current investigation can help better understand the electron spin effects on nonlinear wave propagations in strongly magnetized dense astrophysical objects such as white dwarfs and pulsar magnetospheres.

  8. Size quantization of Dirac fermions in graphene constrictions.

    PubMed

    Terrés, B; Chizhova, L A; Libisch, F; Peiro, J; Jörger, D; Engels, S; Girschik, A; Watanabe, K; Taniguchi, T; Rotkin, S V; Burgdörfer, J; Stampfer, C

    2016-05-20

    Quantum point contacts are cornerstones of mesoscopic physics and central building blocks for quantum electronics. Although the Fermi wavelength in high-quality bulk graphene can be tuned up to hundreds of nanometres, the observation of quantum confinement of Dirac electrons in nanostructured graphene has proven surprisingly challenging. Here we show ballistic transport and quantized conductance of size-confined Dirac fermions in lithographically defined graphene constrictions. At high carrier densities, the observed conductance agrees excellently with the Landauer theory of ballistic transport without any adjustable parameter. Experimental data and simulations for the evolution of the conductance with magnetic field unambiguously confirm the identification of size quantization in the constriction. Close to the charge neutrality point, bias voltage spectroscopy reveals a renormalized Fermi velocity of ∼1.5 × 10(6) m s(-1) in our constrictions. Moreover, at low carrier density transport measurements allow probing the density of localized states at edges, thus offering a unique handle on edge physics in graphene devices.

  9. Beyond the standard gauging: gauge symmetries of Dirac sigma models

    NASA Astrophysics Data System (ADS)

    Chatzistavrakidis, Athanasios; Deser, Andreas; Jonke, Larisa; Strobl, Thomas

    2016-08-01

    In this paper we study the general conditions that have to be met for a gauged extension of a two-dimensional bosonic σ-model to exist. In an inversion of the usual approach of identifying a global symmetry and then promoting it to a local one, we focus directly on the gauge symmetries of the theory. This allows for action functionals which are gauge invariant for rather general background fields in the sense that their invariance conditions are milder than the usual case. In particular, the vector fields that control the gauging need not be Killing. The relaxation of isometry for the background fields is controlled by two connections on a Lie algebroid L in which the gauge fields take values, in a generalization of the common Lie-algebraic picture. Here we show that these connections can always be determined when L is a Dirac structure in the H-twisted Courant algebroid. This also leads us to a derivation of the general form for the gauge symmetries of a wide class of two-dimensional topological field theories called Dirac σ-models, which interpolate between the G/G Wess-Zumino-Witten model and the (Wess-Zumino-term twisted) Poisson sigma model.

  10. Superconductivity in two-dimensional disordered Dirac semimetals

    NASA Astrophysics Data System (ADS)

    Wang, Jing; Zhao, Peng-Lu; Wang, Jing-Rong; Liu, Guo-Zhu

    2017-02-01

    In two-dimensional Dirac semimetals, Cooper pairing instability occurs only when the attractive interaction strength |u | is larger than some critical value | uc| because the density of states vanishes at Dirac points. Disorders enhance the low-energy density of states but meanwhile shorten the lifetime of fermions, which tend to promote and suppress superconductivity, respectively. To determine which of the two competing effects wins, we study the interplay of Cooper pairing interaction and disorder scattering by means of renormalization group method. We consider three types of disorders, including random mass, random gauge potential, and random chemical potential, and show that the first two suppress superconductivity. In particular, the critical BCS coupling | uc| is increased to certain larger value if the system contains only random mass or random gauge potential, which makes the onset of superconductivity more difficult. In the case of random chemical potential, the effective disorder parameter flows to the strong coupling regime, where the perturbation expansion breaks down and cannot provide a clear answer concerning the fate of superconductivity. When different types of disorder coexist in one system, their strength parameters all flow to strong couplings. In the strong coupling regime, the perturbative renormalization group method becomes invalid, and one needs to employ other methods to treat the disorder effects. We perform a simple gap equation analysis of the impact of random chemical potential on superconductivity by using the Abrikosov-Gorkov diagrammatic approach, and also briefly discuss the possible generalization of this approach.

  11. Light confinement at a Dirac point in honeycomb-like lattice photonic crystal

    NASA Astrophysics Data System (ADS)

    Mao, Qiuping; Xie, Kang; Hu, Lei; Li, Qian; Zhang, Wei; Jiang, Haiming; Hu, Zhijia; Wang, Erlei

    2017-02-01

    Optical waveguides and cavities are important components among modern optical devices. Traditional optical cavities rely on total internal reflection or photonic bandgaps to achieve field confinement. Recently, a new type of trapped mode, the Dirac mode, has been reported to occur in triangular or honeycomb lattice photonic crystal. This novel localized mode is attribute to neither of the traditional light-guiding mechanisms and owns different characteristics. Here we report the discovery of the Dirac mode in honeycomb-like photonic crystal lattice. The Dirac mode occurs at a Dirac frequency, which is beyond the complete photonic bandgaps. It has a different algebraic-decay feature. Our discovery extends applicability of the Dirac mode in designing for optical devices.

  12. Giant optical nonlocality near the Dirac point in metal-dielectric multilayer metamaterials.

    PubMed

    Sun, Lei; Gao, Jie; Yang, Xiaodong

    2013-09-09

    The giant optical nonlocality near the Dirac point in lossless metal-dielectric multilayer metamaterials is revealed and investigated through the analysis of the band structure of the multilayer stack in the three-dimensional ω-k space, according to the transfer-matrix method with the optical nonlocal effect. The position of the Dirac point is analytically located in the ω-k space. It is revealed that the emergence of the Dirac point is due to the degeneracy of the symmetric and the asymmetric eigenmodes of the coupled surface plasmon polaritons. The optical nonlocality induced epsilon-near-zero frequency shift for the multilayer stack compared to the effective medium is studied. Furthermore, the giant optical nonlocality around the Dirac point is explored with the iso-frequency contour analysis, while the beam splitting phenomenon at the Dirac point due to the optical nonlocal effect is also demonstrated.

  13. Transport properties of disordered photonic crystals around a Dirac-like point.

    PubMed

    Wang, Xiao; Jiang, Haitao; Li, Yuan; Yan, Chao; Deng, Fusheng; Sun, Yong; Li, Yunhui; Shi, Yunlong; Chen, Hong

    2015-02-23

    At the Dirac-like point at the Brillouin zone center, the photonic crystals (PhCs) can mimic a zero-index medium. In the band structure, an additional flat band of longitudinal mode will intersect the Dirac cone. This longitudinal mode can be excited in PhCs with finite sizes at the Dirac-like point. By introducing positional shift in the PhCs, we study the dependence of the longitudinal mode on the disorder. At the Dirac-like point, the transmission peak induced by the longitudinal mode decreases as the random degree increases. However, at a frequency slightly above the Dirac-like point, in which the longitudinal mode is absent, the transmission is insensitive to the disorder because the effective index is still near zero and the effective wavelength in the PhC is very large.

  14. A semi-Dirac point and an electromagnetic topological transition in a dielectric photonic crystal.

    PubMed

    Wu, Ying

    2014-01-27

    Accidental degeneracy in a photonic crystal consisting of a square array of elliptical dielectric cylinders leads to both a semi-Dirac point at the center of the Brillouin zone and an electromagnetic topological transition (ETT). A perturbation method is deduced to affirm the peculiar linear-parabolic dispersion near the semi-Dirac point. An effective medium theory is developed to explain the simultaneous semi-Dirac point and ETT and to show that the photonic crystal is either a zero-refractive-index material or an epsilon-near-zero material at the semi-Dirac point. Drastic changes in the wave manipulation properties at the semi-Dirac point, resulting from ETT, are described.

  15. Electric-field tunable Dirac semimetal state in phosphorene thin films

    NASA Astrophysics Data System (ADS)

    Ghosh, Barun; Singh, Bahadur; Prasad, R.; Agarwal, Amit

    2016-11-01

    We study the electric-field tunable electronic properties of phosphorene thin films, using the framework of density functional theory. We show that phosphorene thin films offer a versatile material platform to study two-dimensional Dirac fermions on application of a transverse electric field. Increasing the strength of the transverse electric field beyond a certain critical value in phosphorene thin films leads to the formation of two symmetry protected gapless Dirac fermions states with anisotropic energy dispersion. The spin-orbit coupling splits each of these Dirac states into two spin-polarized Dirac cones which are also protected by nonsymmorphic crystal symmetries. Our study shows that the position as well as the carrier velocity of the spin-polarized Dirac cone states can be controlled by the strength of the external electric field.

  16. Observation of an anisotropic Dirac cone reshaping and ferrimagnetic spin polarization in an organic conductor.

    PubMed

    Hirata, Michihiro; Ishikawa, Kyohei; Miyagawa, Kazuya; Tamura, Masafumi; Berthier, Claude; Basko, Denis; Kobayashi, Akito; Matsuno, Genki; Kanoda, Kazushi

    2016-08-31

    The Coulomb interaction among massless Dirac fermions in graphene is unscreened around the isotropic Dirac points, causing a logarithmic velocity renormalization and a cone reshaping. In less symmetric Dirac materials possessing anisotropic cones with tilted axes, the Coulomb interaction can provide still more exotic phenomena, which have not been experimentally unveiled yet. Here, using site-selective nuclear magnetic resonance, we find a non-uniform cone reshaping accompanied by a bandwidth reduction and an emergent ferrimagnetism in tilted Dirac cones that appear on the verge of charge ordering in an organic compound. Our theoretical analyses based on the renormalization-group approach and the Hubbard model show that these observations are the direct consequences of the long-range and short-range parts of the Coulomb interaction, respectively. The cone reshaping and the bandwidth renormalization, as well as the magnetic behaviour revealed here, can be ubiquitous and vital for many Dirac materials.

  17. Observation of an anisotropic Dirac cone reshaping and ferrimagnetic spin polarization in an organic conductor

    PubMed Central

    Hirata, Michihiro; Ishikawa, Kyohei; Miyagawa, Kazuya; Tamura, Masafumi; Berthier, Claude; Basko, Denis; Kobayashi, Akito; Matsuno, Genki; Kanoda, Kazushi

    2016-01-01

    The Coulomb interaction among massless Dirac fermions in graphene is unscreened around the isotropic Dirac points, causing a logarithmic velocity renormalization and a cone reshaping. In less symmetric Dirac materials possessing anisotropic cones with tilted axes, the Coulomb interaction can provide still more exotic phenomena, which have not been experimentally unveiled yet. Here, using site-selective nuclear magnetic resonance, we find a non-uniform cone reshaping accompanied by a bandwidth reduction and an emergent ferrimagnetism in tilted Dirac cones that appear on the verge of charge ordering in an organic compound. Our theoretical analyses based on the renormalization-group approach and the Hubbard model show that these observations are the direct consequences of the long-range and short-range parts of the Coulomb interaction, respectively. The cone reshaping and the bandwidth renormalization, as well as the magnetic behaviour revealed here, can be ubiquitous and vital for many Dirac materials. PMID:27578363

  18. Aharonov–Bohm oscillations in Dirac semimetal Cd3As2 nanowires

    PubMed Central

    Wang, Li-Xian; Li, Cai-Zhen; Yu, Da-Peng; Liao, Zhi-Min

    2016-01-01

    Three-dimensional Dirac semimetals, three-dimensional analogues of graphene, are unusual quantum materials with massless Dirac fermions, which can be further converted to Weyl fermions by breaking time reversal or inversion symmetry. Topological surface states with Fermi arcs are predicted on the surface and have been observed by angle-resolved photoemission spectroscopy experiments. Although the exotic transport properties of the bulk Dirac cones have been demonstrated, it is still a challenge to reveal the surface states via transport measurements due to the highly conductive bulk states. Here, we show Aharonov–Bohm oscillations in individual single-crystal Cd3As2 nanowires with low carrier concentration and large surface-to-volume ratio, providing transport evidence of the surface state in three-dimensional Dirac semimetals. Moreover, the quantum transport can be modulated by tuning the Fermi level using a gate voltage, enabling a deeper understanding of the rich physics residing in Dirac semimetals. PMID:26902716

  19. Experimental observation of two massless Dirac-fermion gases in graphene-topological insulator heterostructure

    NASA Astrophysics Data System (ADS)

    Bian, Guang; Chung, Ting-Fung; Chen, Chaoyu; Liu, Chang; Chang, Tay-Rong; Wu, Tailung; Belopolski, Ilya; Zheng, Hao; Xu, Su-Yang; Sanchez, Daniel S.; Alidoust, Nasser; Pierce, Jonathan; Quilliams, Bryson; Barletta, Philip P.; Lorcy, Stephane; Avila, José; Chang, Guoqing; Lin, Hsin; Jeng, Horng-Tay; Asensio, Maria-Carmen; Chen, Yong P.; Zahid Hasan, M.

    2016-06-01

    Graphene and topological insulators (TI) possess two-dimensional (2D) Dirac fermions with distinct physical properties. Integrating these two Dirac materials in a single device creates interesting opportunities for exploring new physics of interacting massless Dirac fermions. Here we report on a practical route to experimental fabrication of graphene-Sb2Te3 heterostructure. The graphene-TI heterostructures are prepared by using a dry transfer of chemical-vapor-deposition grown graphene film. ARPES measurements confirm the coexistence of topological surface states of Sb2Te3 and Dirac π bands of graphene, and identify the twist angle in the graphene-TI heterostructure. The results suggest a potential tunable electronic platform in which two different Dirac low-energy states dominate the transport behavior.

  20. Aharonov-Bohm oscillations in Dirac semimetal Cd3As2 nanowires

    NASA Astrophysics Data System (ADS)

    Wang, Li-Xian; Li, Cai-Zhen; Yu, Da-Peng; Liao, Zhi-Min

    2016-02-01

    Three-dimensional Dirac semimetals, three-dimensional analogues of graphene, are unusual quantum materials with massless Dirac fermions, which can be further converted to Weyl fermions by breaking time reversal or inversion symmetry. Topological surface states with Fermi arcs are predicted on the surface and have been observed by angle-resolved photoemission spectroscopy experiments. Although the exotic transport properties of the bulk Dirac cones have been demonstrated, it is still a challenge to reveal the surface states via transport measurements due to the highly conductive bulk states. Here, we show Aharonov-Bohm oscillations in individual single-crystal Cd3As2 nanowires with low carrier concentration and large surface-to-volume ratio, providing transport evidence of the surface state in three-dimensional Dirac semimetals. Moreover, the quantum transport can be modulated by tuning the Fermi level using a gate voltage, enabling a deeper understanding of the rich physics residing in Dirac semimetals.

  1. Heavy Dirac fermions in a graphene/topological insulator hetero-junction

    NASA Astrophysics Data System (ADS)

    Cao, Wendong; Zhang, Rui-Xing; Tang, Peizhe; Yang, Gang; Sofo, Jorge; Duan, Wenhui; Liu, Chao-Xing

    2016-09-01

    The low energy physics of both graphene and surface states of three-dimensional topological insulators (TIs) is described by gapless Dirac fermions with linear dispersion. In this work, we predict the emergence of a ‘heavy’ Dirac fermion in a graphene/TI hetero-junction, where the linear term almost vanishes and the corresponding energy dispersion becomes highly nonlinear. By combining ab initio calculations and an effective low-energy model, we show explicitly how strong hybridization between Dirac fermions in graphene and the surface states of TIs can reduce the Fermi velocity of Dirac fermions. Due to the negligible linear term, interaction effects will be greatly enhanced and can drive ‘heavy’ Dirac fermion states into the half quantum Hall state with non-zero Hall conductance.

  2. Discovery of a three-dimensional topological Dirac semimetal, Na3Bi.

    PubMed

    Liu, Z K; Zhou, B; Zhang, Y; Wang, Z J; Weng, H M; Prabhakaran, D; Mo, S-K; Shen, Z X; Fang, Z; Dai, X; Hussain, Z; Chen, Y L

    2014-02-21

    Three-dimensional (3D) topological Dirac semimetals (TDSs) represent an unusual state of quantum matter that can be viewed as "3D graphene." In contrast to 2D Dirac fermions in graphene or on the surface of 3D topological insulators, TDSs possess 3D Dirac fermions in the bulk. By investigating the electronic structure of Na3Bi with angle-resolved photoemission spectroscopy, we detected 3D Dirac fermions with linear dispersions along all momentum directions. Furthermore, we demonstrated the robustness of 3D Dirac fermions in Na3Bi against in situ surface doping. Our results establish Na3Bi as a model system for 3D TDSs, which can serve as an ideal platform for the systematic study of quantum phase transitions between rich topological quantum states.

  3. Observation of an anisotropic Dirac cone reshaping and ferrimagnetic spin polarization in an organic conductor

    NASA Astrophysics Data System (ADS)

    Hirata, Michihiro; Ishikawa, Kyohei; Miyagawa, Kazuya; Tamura, Masafumi; Berthier, Claude; Basko, Denis; Kobayashi, Akito; Matsuno, Genki; Kanoda, Kazushi

    2016-08-01

    The Coulomb interaction among massless Dirac fermions in graphene is unscreened around the isotropic Dirac points, causing a logarithmic velocity renormalization and a cone reshaping. In less symmetric Dirac materials possessing anisotropic cones with tilted axes, the Coulomb interaction can provide still more exotic phenomena, which have not been experimentally unveiled yet. Here, using site-selective nuclear magnetic resonance, we find a non-uniform cone reshaping accompanied by a bandwidth reduction and an emergent ferrimagnetism in tilted Dirac cones that appear on the verge of charge ordering in an organic compound. Our theoretical analyses based on the renormalization-group approach and the Hubbard model show that these observations are the direct consequences of the long-range and short-range parts of the Coulomb interaction, respectively. The cone reshaping and the bandwidth renormalization, as well as the magnetic behaviour revealed here, can be ubiquitous and vital for many Dirac materials.

  4. Aharonov-Bohm oscillations in Dirac semimetal Cd3As2 nanowires.

    PubMed

    Wang, Li-Xian; Li, Cai-Zhen; Yu, Da-Peng; Liao, Zhi-Min

    2016-02-23

    Three-dimensional Dirac semimetals, three-dimensional analogues of graphene, are unusual quantum materials with massless Dirac fermions, which can be further converted to Weyl fermions by breaking time reversal or inversion symmetry. Topological surface states with Fermi arcs are predicted on the surface and have been observed by angle-resolved photoemission spectroscopy experiments. Although the exotic transport properties of the bulk Dirac cones have been demonstrated, it is still a challenge to reveal the surface states via transport measurements due to the highly conductive bulk states. Here, we show Aharonov-Bohm oscillations in individual single-crystal Cd3As2 nanowires with low carrier concentration and large surface-to-volume ratio, providing transport evidence of the surface state in three-dimensional Dirac semimetals. Moreover, the quantum transport can be modulated by tuning the Fermi level using a gate voltage, enabling a deeper understanding of the rich physics residing in Dirac semimetals.

  5. Photonic crystal surface-emitting lasers enabled by an accidental Dirac point

    SciTech Connect

    Chua, Song Liang; Lu, Ling; Soljacic, Marin

    2014-12-02

    A photonic-crystal surface-emitting laser (PCSEL) includes a gain medium electromagnetically coupled to a photonic crystal whose energy band structure exhibits a Dirac cone of linear dispersion at the center of the photonic crystal's Brillouin zone. This Dirac cone's vertex is called a Dirac point; because it is at the Brillouin zone center, it is called an accidental Dirac point. Tuning the photonic crystal's band structure (e.g., by changing the photonic crystal's dimensions or refractive index) to exhibit an accidental Dirac point increases the photonic crystal's mode spacing by orders of magnitudes and reduces or eliminates the photonic crystal's distributed in-plane feedback. Thus, the photonic crystal can act as a resonator that supports single-mode output from the PCSEL over a larger area than is possible with conventional PCSELs, which have quadratic band edge dispersion. Because output power generally scales with output area, this increase in output area results in higher possible output powers.

  6. Terahertz-induced acceleration of massive Dirac electrons in semimetal bismuth.

    PubMed

    Minami, Yasuo; Araki, Kotaro; Dao, Thang Duy; Nagao, Tadaaki; Kitajima, Masahiro; Takeda, Jun; Katayama, Ikufumi

    2015-11-02

    Dirac-like electrons in solid state have been of great interest since they exhibit many peculiar physical behaviors analogous to relativistic mechanics. Among them, carriers in graphene and surface states of topological insulators are known to behave as massless Dirac fermions with a conical band structure in the two-dimensional momentum space, whereas electrons in semimetal bismuth (Bi) are expected to behave as massive Dirac-like fermions in the three-dimensional momentum space, whose dynamics is of particular interest in comparison with that of the massless Dirac fermions. Here, we demonstrate that an intense terahertz electric field transient accelerates the massive Dirac-like fermions in Bi from classical Newtonian to the relativistic regime; the electrons are accelerated approaching the effective "speed of light" with the "relativistic" beta β = 0.89 along the asymptotic linear band structure. As a result, the effective electron mass is enhanced by a factor of 2.4.

  7. Tunneling conductance in a two-dimensional Dirac semimetal protected by nonsymmorphic symmetry

    NASA Astrophysics Data System (ADS)

    Habe, Tetsuro

    2017-03-01

    We theoretically study a tunneling effect in a two-dimensional Dirac semimetal with two Dirac points protected by nonsymmorphic symmetries. The tunnel barrier can be arranged by a magnetic exchange potential which opens a gap at the Dirac points which can be induced by a magnetic proximity effect of a ferromagnetic insulator. We found that the tunnel decay length increases with a decrease in the strength of the spin-orbit coupling, and moreover the dependence is attributed to the correlation of sublattice and spin degrees of freedom which lead to symmetry-protected Dirac points. The tunnel probability is quite different in two Dirac points, and thus the tunnel effect can be applied to the highly selective valley filter.

  8. Tight-binding modeling and low-energy behavior of the semi-Dirac point.

    PubMed

    Banerjee, S; Singh, R R P; Pardo, V; Pickett, W E

    2009-07-03

    We develop a tight-binding model description of semi-Dirac electronic spectra, with highly anisotropic dispersion around point Fermi surfaces, recently discovered in electronic structure calculations of VO2-TiO2 nanoheterostructures. We contrast their spectral properties with the well-known Dirac points on the honeycomb lattice relevant to graphene layers and the spectra of bands touching each other in zero-gap semiconductors. We also consider the lowest order dispersion around one of the semi-Dirac points and calculate the resulting electronic energy levels in an external magnetic field. In spite of apparently similar electronic structures, Dirac and semi-Dirac systems support diverse low-energy physics.

  9. Time-dependent scattering theory for charged Dirac fields on a Reissner-Nordström black hole

    NASA Astrophysics Data System (ADS)

    Thierry, Daudé

    2010-10-01

    In this paper, we prove a complete time-dependent scattering theory for charged (massive or not) Dirac fields outside a Reissner-Nordström black hole. We shall take the point of view of observers static at infinity, well described by the Schwarzschild system of coordinates. For such observers, the exterior of a Reissner-Nordström black hole is a smooth manifold having two distinct asymptotic regions: the horizon and spacelike infinity. We first simplify the later analysis using the spherical symmetry of the Reissner-Nordström black hole and we reduce the initial 3+1 dimensional evolution equation of hyperbolic type into a 1+1 dimensional one. Then, we establish various propagation estimates for such fields in the same spirit as in the works by Dereziński and Gérard [Scattering Theory of Classical and Quantum N-Particle Systems (Springer-Verlag, Berlin, 1997)]. We construct the asymptotic velocity operators P+/- and we show that their spectra are equal to σ(P+)={-1}∪[0,1] and σ(P-)=[-1,0]∪{1}. This information points out the very distinct behaviors of Dirac fields near the two asymptotic regions of the black hole. As a consequence of this construction, we prove the existence and asymptotic completeness of (Dollard modified at infinity) wave operators.

  10. Stochastic calculation of the Dirac spectrum on the lattice and a determination of chiral condensate in 2 + 1-flavor QCD†

    NASA Astrophysics Data System (ADS)

    Cossu, Guido; Fukaya, Hidenori; Hashimoto, Shoji; Kaneko, Takashi; Noaki, Jun-Ichi

    2016-09-01

    We compute the chiral condensate in 2 + 1-flavor QCD through the spectrum of low-lying eigenmodes of the Dirac operator. The number of eigenvalues of the Dirac operator is evaluated using a stochastic method with an eigenvalue filtering technique on the background gauge configurations generated by lattice QCD simulations including the effects of dynamical up, down, and strange quarks described by the Möbius domain-wall fermion formulation. The low-lying spectrum is related to the chiral condensate, which is one of the leading-order low-energy constants in chiral effective theory, as dictated by the Banks-Casher relation. The spectrum shape and its dependence on the sea quark masses calculated in numerical simulations are consistent with the expectation from one-loop chiral perturbation theory. After taking the chiral limit as well as the continuum limit using the data at three lattice spacings in the range 0.080-0.045 fm, we obtain Σ(2 GeV) = 270.0(4.9) MeV, with the error combining those from statistical and various sources of systematic error. The finite volume effect is confirmed to be under control by a direct comparison of the results from two different volumes at the lightest available sea quarks corresponding to 230 MeV pions.

  11. Electronic structure, Dirac points and Fermi arc surface states in three-dimensional Dirac semimetal Na3Bi from angle-resolved photoemission spectroscopy

    NASA Astrophysics Data System (ADS)

    Aiji, Liang; Chaoyu, Chen; Zhijun, Wang; Youguo, Shi; Ya, Feng; Hemian, Yi; Zhuojin, Xie; Shaolong, He; Junfeng, He; Yingying, Peng; Yan, Liu; Defa, Liu; Cheng, Hu; Lin, Zhao; Guodong, Liu; Xiaoli, Dong; Jun, Zhang; M, Nakatake; H, Iwasawa; K, Shimada; M, Arita; H, Namatame; M, Taniguchi; Zuyan, Xu; Chuangtian, Chen; Hongming, Weng; Xi, Dai; Zhong, Fang; Xing-Jiang, Zhou

    2016-07-01

    The three-dimensional (3D) Dirac semimetals have linearly dispersive 3D Dirac nodes where the conduction band and valence band are connected. They have isolated 3D Dirac nodes in the whole Brillouin zone and can be viewed as a 3D counterpart of graphene. Recent theoretical calculations and experimental results indicate that the 3D Dirac semimetal state can be realized in a simple stoichiometric compound A 3Bi (A = Na, K, Rb). Here we report comprehensive high-resolution angle-resolved photoemission (ARPES) measurements on the two cleaved surfaces, (001) and (100), of Na3Bi. On the (001) surface, by comparison with theoretical calculations, we provide a proper assignment of the observed bands, and in particular, pinpoint the band that is responsible for the formation of the three-dimensional Dirac cones. We observe clear evidence of 3D Dirac cones in the three-dimensional momentum space by directly measuring on the k x -k y plane and by varying the photon energy to get access to different out-of-plane k z s. In addition, we reveal new features around the Brillouin zone corners that may be related with surface reconstruction. On the (100) surface, our ARPES measurements over a large momentum space raise an issue on the selection of the basic Brillouin zone in the (100) plane. We directly observe two isolated 3D Dirac nodes on the (100) surface. We observe the signature of the Fermi-arc surface states connecting the two 3D Dirac nodes that extend to a binding energy of ˜150 meV before merging into the bulk band. Our observations constitute strong evidence on the existence of the Dirac semimetal state in Na3Bi that are consistent with previous theoretical and experimental work. In addition, our results provide new information to clarify on the nature of the band that forms the 3D Dirac cones, on the possible formation of surface reconstruction of the (001) surface, and on the issue of basic Brillouin zone selection for the (100) surface. Project supported by the

  12. A self-adjoint decomposition of the radial momentum operator

    NASA Astrophysics Data System (ADS)

    Liu, Q. H.; Xiao, S. F.

    2015-12-01

    With acceptance of the Dirac's observation that the canonical quantization entails using Cartesian coordinates, we examine the operator erPr rather than Pr itself and demonstrate that there is a decomposition of erPr into a difference of two self-adjoint but noncommutative operators, in which one is the total momentum and another is the transverse one. This study renders the operator Pr indirectly measurable and physically meaningful, offering an explanation of why the mean value of Pr over a quantum mechanical state makes sense and supporting Dirac's claim that Pr "is real and is the true momentum conjugate to r".

  13. Type-II Dirac fermions in the PtSe2 class of transition metal dichalcogenides

    NASA Astrophysics Data System (ADS)

    Huang, Huaqing; Zhou, Shuyun; Duan, Wenhui

    2016-09-01

    Recently, a new "type-II" Weyl fermion, which exhibits exotic phenomena, such as an angle-dependent chiral anomaly, was discovered in a new phase of matter where electron and hole pockets contact at isolated Weyl points [Nature (London) 527, 495 (2015), 10.1038/nature15768]. This raises an interesting question about whether its counterpart, i.e., a type-II Dirac fermion, exists in real materials. Here, we predict the existence of symmetry-protected type-II Dirac fermions in a class of transition metal dichalcogenide materials. Our first-principles calculations on PtSe2 reveal its bulk type-II Dirac fermions which are characterized by strongly tilted Dirac cones, novel surface states, and exotic doping-driven Lifshitz transition. Our results show that the existence of type-II Dirac fermions in PtSe2-type materials is closely related to its structural P 3 ¯m 1 symmetry, which provides useful guidance for the experimental realization of type-II Dirac fermions and intriguing physical properties distinct from those of the standard Dirac fermions known before.

  14. Lifshitz transition and Van Hove singularity in a three-dimensional topological Dirac semimetal

    NASA Astrophysics Data System (ADS)

    Xu, Su-Yang; Liu, Chang; Belopolski, I.; Kushwaha, S. K.; Sankar, R.; Krizan, J. W.; Chang, T.-R.; Polley, C. M.; Adell, J.; Balasubramanian, T.; Miyamoto, K.; Alidoust, N.; Bian, Guang; Neupane, M.; Jeng, H.-T.; Huang, C.-Y.; Tsai, W.-F.; Okuda, T.; Bansil, A.; Chou, F. C.; Cava, R. J.; Lin, H.; Hasan, M. Z.

    2015-08-01

    A three-dimensional (3D) Dirac semimetal is a novel state of quantum matter which has recently attracted much attention as an apparent 3D version of graphene. In this paper, we report results on the electronic structure of the 3D Dirac semimetal Na3Bi at a surface that reveals its nontrivial ground state. Our studies reveal that the two 3D Dirac cones go through a topological change in the constant energy contour as a function of the binding energy, featuring a Lifshitz point, which is missing in a strict 3D analog of graphene. Our results identify an example of a band saddle-point singularity in 3D Dirac materials. This is in contrast to its two-dimensional analogs such as graphene and the Dirac surface states of a topological insulator. The observation of multiple Dirac nodes in Na3Bi connecting via a Lifshitz point along its crystalline rotational axis away from the Kramers point serves as a decisive signature for the symmetry-protected nature of the Dirac semimetal's topological bulk ground state.

  15. Nearly massless Dirac fermions hosted by Sb square net in BaMnSb2.

    PubMed

    Liu, Jinyu; Hu, Jin; Cao, Huibo; Zhu, Yanglin; Chuang, Alyssa; Graf, D; Adams, D J; Radmanesh, S M A; Spinu, L; Chiorescu, I; Mao, Zhiqiang

    2016-07-28

    Layered compounds AMnBi2 (A = Ca, Sr, Ba, or rare earth element) have been established as Dirac materials. Dirac electrons generated by the two-dimensional (2D) Bi square net in these materials are normally massive due to the presence of a spin-orbital coupling (SOC) induced gap at Dirac nodes. Here we report that the Sb square net in an isostructural compound BaMnSb2 can host nearly massless Dirac fermions. We observed strong Shubnikov-de Haas (SdH) oscillations in this material. From the analyses of the SdH oscillations, we find key signatures of Dirac fermions, including light effective mass (~0.052m0; m0, mass of free electron), high quantum mobility (1280 cm(2)V(-1)S(-1)) and a π Berry phase accumulated along cyclotron orbit. Compared with AMnBi2, BaMnSb2 also exhibits much more significant quasi two-dimensional (2D) electronic structure, with the out-of-plane transport showing nonmetallic conduction below 120 K and the ratio of the out-of-plane and in-plane resistivity reaching ~670. Additionally, BaMnSb2 also exhibits a G-type antiferromagnetic order below 283 K. The combination of nearly massless Dirac fermions on quasi-2D planes with a magnetic order makes BaMnSb2 an intriguing platform for seeking novel exotic phenomena of massless Dirac electrons.

  16. Precise identification of Dirac-like point through a finite photonic crystal square matrix

    PubMed Central

    Dong, Guoyan; Zhou, Ji; Yang, Xiulun; Meng, Xiangfeng

    2016-01-01

    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. PMID:27857145

  17. Nearly massless Dirac fermions hosted by Sb square net in BaMnSb2

    PubMed Central

    Liu, Jinyu; Hu, Jin; Cao, Huibo; Zhu, Yanglin; Chuang, Alyssa; Graf, D.; Adams, D. J.; Radmanesh, S. M. A.; Spinu, L.; Chiorescu, I.; Mao, Zhiqiang

    2016-01-01

    Layered compounds AMnBi2 (A = Ca, Sr, Ba, or rare earth element) have been established as Dirac materials. Dirac electrons generated by the two-dimensional (2D) Bi square net in these materials are normally massive due to the presence of a spin-orbital coupling (SOC) induced gap at Dirac nodes. Here we report that the Sb square net in an isostructural compound BaMnSb2 can host nearly massless Dirac fermions. We observed strong Shubnikov-de Haas (SdH) oscillations in this material. From the analyses of the SdH oscillations, we find key signatures of Dirac fermions, including light effective mass (~0.052m0; m0, mass of free electron), high quantum mobility (1280 cm2V−1S−1) and a π Berry phase accumulated along cyclotron orbit. Compared with AMnBi2, BaMnSb2 also exhibits much more significant quasi two-dimensional (2D) electronic structure, with the out-of-plane transport showing nonmetallic conduction below 120 K and the ratio of the out-of-plane and in-plane resistivity reaching ~670. Additionally, BaMnSb2 also exhibits a G-type antiferromagnetic order below 283 K. The combination of nearly massless Dirac fermions on quasi-2D planes with a magnetic order makes BaMnSb2 an intriguing platform for seeking novel exotic phenomena of massless Dirac electrons. PMID:27466151

  18. A beautiful sea: P. A. M. Dirac's epistemology and ontology of the vacuum.

    PubMed

    Wright, Aaron Sidney

    2016-07-01

    This paper charts P.A.M. Dirac's development of his theory of the electron, and its radical picture of empty space as an almost-full plenum. Dirac's Quantum Electrodynamics famously accomplished more than the unification of special relativity and quantum mechanics. It also accounted for the 'duplexity phenomena' of spectral line splitting that we now attribute to electron spin. But the extra mathematical terms that allowed for spin were not alone, and this paper charts Dirac's struggle to ignore or account for them as a sea of strange, negative-energy, particles with positive 'holes'. This work was not done in solitude, but rather in exchanges with Dirac's correspondence network. This social context for Dirac's work contests his image as a lone genius, and documents a community wrestling with the ontological consequences of their work. Unification, consistency, causality, and community are common factors in explanations in the history of physics. This paper argues on the basis of materials in Dirac's archive that --- in addition --- mathematical beauty was an epistemological factor in the development of the electron and hole theory. In fact, if we believe that Dirac's beautiful mathematics captures something of the world, then there is both an epistemology and an ontology of mathematical beauty.

  19. Nearly massless Dirac fermions hosted by Sb square net in BaMnSb2

    NASA Astrophysics Data System (ADS)

    Liu, Jinyu; Hu, Jin; Cao, Huibo; Zhu, Yanglin; Chuang, Alyssa; Graf, D.; Adams, D. J.; Radmanesh, S. M. A.; Spinu, L.; Chiorescu, I.; Mao, Zhiqiang

    2016-07-01

    Layered compounds AMnBi2 (A = Ca, Sr, Ba, or rare earth element) have been established as Dirac materials. Dirac electrons generated by the two-dimensional (2D) Bi square net in these materials are normally massive due to the presence of a spin-orbital coupling (SOC) induced gap at Dirac nodes. Here we report that the Sb square net in an isostructural compound BaMnSb2 can host nearly massless Dirac fermions. We observed strong Shubnikov-de Haas (SdH) oscillations in this material. From the analyses of the SdH oscillations, we find key signatures of Dirac fermions, including light effective mass (~0.052m0 m0, mass of free electron), high quantum mobility (1280 cm2V‑1S‑1) and a π Berry phase accumulated along cyclotron orbit. Compared with AMnBi2, BaMnSb2 also exhibits much more significant quasi two-dimensional (2D) electronic structure, with the out-of-plane transport showing nonmetallic conduction below 120 K and the ratio of the out-of-plane and in-plane resistivity reaching ~670. Additionally, BaMnSb2 also exhibits a G-type antiferromagnetic order below 283 K. The combination of nearly massless Dirac fermions on quasi-2D planes with a magnetic order makes BaMnSb2 an intriguing platform for seeking novel exotic phenomena of massless Dirac electrons.

  20. Finger-gate manipulated quantum transport in Dirac materials.

    PubMed

    Kleftogiannis, Ioannis; Tang, Chi-Shung; Cheng, Shun-Jen

    2015-05-27

    We investigate the quantum transport properties of multichannel nanoribbons made of materials described by the Dirac equation, under an in-plane magnetic field. In the low energy regime, positive and negative finger-gate potentials allow the electrons to make intra-subband transitions via hole-like or electron-like quasibound states (QBS), respectively, resulting in dips in the conductance. In the high energy regime, double dip structures in the conductance are found, attributed to spin-flip or spin-nonflip inter-subband transitions through the QBSs. Inverting the finger-gate polarity offers the possibility to manipulate the spin polarized electronic transport to achieve a controlled spin-switch.

  1. Adjunctation and Scalar Product in the Dirac Equation - I

    NASA Astrophysics Data System (ADS)

    Dima, M.

    2016-02-01

    The Bargmann-Pauli adjunctator (hermitiser) of {C}{l}_{_{1,3}}(C) is derived in a representation independent way, circumventing the early derivations (Pauli, Ann. inst. Henri Poincaré 6, 109 and 121 1936) using representation-dependent arguments. Relations for the adjunctator's transformation with the scalar product and space generator set are given. The S U(2) adjunctator is shown to determine the {C}{l}_{_{1,3}}(C) adjunctator. Part-II of the paper will approach the problem of the two scalar products used in Dirac theory - an unphysical situation of "piece-wise physics" with erroneous results. The adequate usage of scalar product - via calibration - will be presented, in particular under boosts, yielding the known covariant transformations of physical quantities.

  2. Dirac's Dream - the Search for the Magnetic Monopole

    SciTech Connect

    Pinfold, James L.

    2010-11-24

    I first quickly summarize the history of the Magnetic Monopole leading to the quantum theory of magnetic charge that started with a 1931 paper by Paul Dirac who showed that the existence of magnetic monopoles was consistent with Maxwell's equations only if electric charges are quantized. Next I will briefly review the status of monopole searches. Last, but not least I discuss in more detail the MoEDAL experiment--the latest accelerator experiment designed to search for direct production of magnetic monopoles or dyons (particles with electric and magnetic charge) and other highly ionizing particles - such as heavy (pseudo-) stable particles with conventional electric charge - at the LHC. The MoEDAL experiment employs nuclear track-etch detectors deployed in the VELO vertex region of the LHCb experiment.

  3. Dirac Line Nodes in Inversion-Symmetric Crystals.

    PubMed

    Kim, Youngkuk; Wieder, Benjamin J; Kane, C L; Rappe, Andrew M

    2015-07-17

    We propose and characterize a new Z2 class of topological semimetals with a vanishing spin-orbit interaction. The proposed topological semimetals are characterized by the presence of bulk one-dimensional (1D) Dirac line nodes (DLNs) and two-dimensional (2D) nearly flat surface states, protected by inversion and time-reversal symmetries. We develop the Z2 invariants dictating the presence of DLNs based on parity eigenvalues at the parity-invariant points in reciprocal space. Moreover, using first-principles calculations, we predict DLNs to occur in Cu_{3}N near the Fermi energy by doping nonmagnetic transition metal atoms, such as Zn and Pd, with the 2D surface states emerging in the projected interior of the DLNs. This Letter includes a brief discussion of the effects of spin-orbit interactions and symmetry breaking as well as comments on experimental implications.

  4. States of the Dirac equation in confining potentials.

    PubMed

    Giachetti, Riccardo; Sorace, Emanuele

    2008-11-07

    We study the Dirac equation in confining potentials with pure vector coupling, proving the existence of metastable states with longer and longer lifetimes as the nonrelativistic limit is approached and eventually merging with continuity into the Schrödinger bound states. The existence of these states could concern high energy models and possible resonant scattering effects in systems like graphene. We present numerical results for the linear and the harmonic cases and we show that the density of the states of the continuous spectrum is well described by a sum of Breit-Wigner lines. The width of the line with lowest positive energy well reproduces the Schwinger pair production rate for a linear potential: this gives an explanation of the Klein paradox for bound states and a new concrete way to get information on pair production in unbounded, nonuniform electric fields, where very little is known.

  5. Heptagraphene: Tunable Dirac Cones in a Graphitic Structure

    NASA Astrophysics Data System (ADS)

    Lopez-Bezanilla, Alejandro; Martin, Ivar; Littlewood, Peter B.

    2016-09-01

    We predict the existence and dynamical stability of heptagraphene, a new graphitic structure formed of rings of 10 carbon atoms bridged by carbene groups yielding seven-membered rings. Despite the rectangular unit cell, the band structure is topologically equivalent to that of strongly distorted graphene. Density-functional-theory calculations demonstrate that heptagraphene has Dirac cones on symmetry lines that are robust against biaxial strain but which open a gap under shear. At high deformation values bond reconstructions lead to different electronic band arrangements in dynamically stable configurations. Within a tight-binding framework this richness of the electronic behavior is identified as a direct consequence of the symmetry breaking within the cell which, unlike other graphitic structures, leads to band gap opening. A combined approach of chemical and physical modification of graphene unit cell unfurls the opportunity to design carbon-based systems in which one aims to tune an electronic band gap.

  6. Transverse Instability of Line Solitary Waves in Massive Dirac Equations

    NASA Astrophysics Data System (ADS)

    Pelinovsky, Dmitry; Shimabukuro, Yusuke

    2016-04-01

    Working in the context of localized modes in periodic potentials, we consider two systems of the massive Dirac equations in two spatial dimensions. The first system, a generalized massive Thirring model, is derived for the periodic stripe potentials. The second one, a generalized massive Gross-Neveu equation, is derived for the hexagonal potentials. In both cases, we prove analytically that the line solitary waves are spectrally unstable with respect to periodic transverse perturbations of large periods. The spectral instability is induced by the spatial translation for the generalized massive Thirring model and by the gauge rotation for the generalized massive Gross-Neveu model. We also observe numerically that the spectral instability holds for the transverse perturbations of any period in the generalized massive Thirring model and exhibits a finite threshold on the period of the transverse perturbations in the generalized massive Gross-Neveu model.

  7. Dirac Line Nodes in Inversion-Symmetric Crystals

    NASA Astrophysics Data System (ADS)

    Kim, Youngkuk; Wieder, Benjamin J.; Kane, C. L.; Rappe, Andrew M.

    2015-07-01

    We propose and characterize a new Z2 class of topological semimetals with a vanishing spin-orbit interaction. The proposed topological semimetals are characterized by the presence of bulk one-dimensional (1D) Dirac line nodes (DLNs) and two-dimensional (2D) nearly flat surface states, protected by inversion and time-reversal symmetries. We develop the Z2 invariants dictating the presence of DLNs based on parity eigenvalues at the parity-invariant points in reciprocal space. Moreover, using first-principles calculations, we predict DLNs to occur in Cu3N near the Fermi energy by doping nonmagnetic transition metal atoms, such as Zn and Pd, with the 2D surface states emerging in the projected interior of the DLNs. This Letter includes a brief discussion of the effects of spin-orbit interactions and symmetry breaking as well as comments on experimental implications.

  8. Simple five-dimensional wave equation for a Dirac particle

    SciTech Connect

    Redington, N.; Lodhi, M. A. K.

    2007-02-15

    A first-order relativistic wave equation is constructed in five dimensions. Its solutions are eight-component spinors, interpreted as single-particle fermion wave functions in four-dimensional space-time. Use of a ''cylinder condition'' (the removal of explicit dependence on the fifth coordinate) reduces each eight-component solution to a pair of degenerate four-component spinors. It is shown that, when the cylinder condition is applied, the results obtained from the new equation are the same as those obtained from the Dirac equation. Without the cylinder condition, on the other hand, the equation implies the existence of a scalar potential, and for zero-mass particles it leads to a four-dimensional fermionic equation analogous to Maxwell's equation with sources.

  9. Propagation of Dirac electrons in Cantor graphene multilayers

    SciTech Connect

    Rodríguez-González, R.; Martínez-Orozco, J. C.; Madrigal-Melchor, J.; Rodríguez-Vargas, I.

    2014-05-15

    In this work we use the standard T-matrix method to study the tunneling of Dirac electrons through graphene multilayers. A graphene sheet is deposited on top of slabs of Silicon-Oxide (SiO{sub 2}) and Silicon-Carbide (SiC) substrates, in which we applied the Cantor’s series. We calculate the transmittance as a function of energy for different incident angles and different generations of the Cantor’s series. Comparing the transmittance, we found three types of self-similarity: (a) local - into generations, (b) between incident angles and (c) between generations. We also compute the angular distribution of the transmittance for fixed energies finding a self-similar pattern between generations. To our knowledge is the first time that four different self-similar patterns are presented in Cantor-based multilayers.

  10. Universal thermoelectric effect of Dirac fermions in graphene.

    PubMed

    Zhu, Lijun; Ma, Rong; Sheng, Li; Liu, Mei; Sheng, Dong-Ning

    2010-02-19

    We numerically study the thermoelectric transports of Dirac fermions in graphene in the presence of a strong magnetic field and disorder. We find that the thermoelectric transport coefficients demonstrate universal behavior depending on the ratio between the temperature and the width of the disorder-broadened Landau levels (LLs). The transverse thermoelectric conductivity alpha{xy} reaches a universal quantum value at the center of each LL in the high temperature regime, and it has a linear temperature dependence at low temperatures. The calculated Nernst signal has a peak at the central LL with heights of the order of k{B}/e, and changes sign near other LLs, while the thermopower has an opposite behavior, in good agreement with experimental data. The validity of the generalized Mott relation between the thermoelectric and electrical transport coefficients is verified in a wide range of temperatures.

  11. All-optical band engineering of gapped Dirac materials

    NASA Astrophysics Data System (ADS)

    Kibis, O. V.; Dini, K.; Iorsh, I. V.; Shelykh, I. A.

    2017-03-01

    We demonstrate theoretically that the interaction of electrons in gapped Dirac materials (gapped graphene and transition-metal dichalchogenide monolayers) with a strong off-resonant electromagnetic field (dressing field) substantially renormalizes the band gaps and the spin-orbit splitting. Moreover, the renormalized electronic parameters drastically depend on the field polarization. Namely, a linearly polarized dressing field always decreases the band gap (and, particularly, can turn the gap into zero), whereas a circularly polarized field breaks the equivalence of valleys in different points of the Brillouin zone and can both increase and decrease corresponding band gaps. As a consequence, the dressing field can serve as an effective tool to control spin and valley properties of the materials and be potentially exploited in optoelectronic applications.

  12. Dirac-fermion-induced parity mixing in superconducting topological insulators

    NASA Astrophysics Data System (ADS)

    Mizushima, Takeshi; Yamakage, Ai; Sato, Masatoshi; Tanaka, Yukio

    2014-11-01

    We self-consistently study surface states of superconducting topological insulators. We clarify that, if a topologically trivial bulk s -wave pairing symmetry is realized, parity mixing of the pair potential near the surface is anomalously enhanced by surface Dirac fermions, opening an additional surface gap larger than the bulk one. In contrast to classical s -wave superconductors, the resulting surface density of state hosts an extra coherent peak at the induced gap besides a conventional peak at the bulk gap. We also find that no such extra peak appears for odd-parity superconductors with a cylindrical Fermi surface. Our calculation suggests that the simple U-shaped scanning tunneling microscope spectrum in CuxBi2Se3 does not originate from s -wave superconductivity, but can be explained by odd-parity superconductivity with a cylindrical Fermi surface.

  13. Screening of scalar fields in Dirac-Born-Infeld theory

    NASA Astrophysics Data System (ADS)

    Burrage, Clare; Khoury, Justin

    2014-07-01

    We study a new screening mechanism which is present in Dirac-Born-Infeld (DBI)-like theories. A scalar field with a DBI-like Lagrangian is minimally coupled to matter. In the vicinity of sufficiently dense sources, nonlinearities in the scalar dominate and result in an approximately constant acceleration on a test particle, thereby suppressing the scalar force relative to gravity. Unlike generic P(X) or chameleon theories, screening happens within the regime of validity of the effective field theory thanks to the DBI symmetry. We derive an exact form for the field profile around multiple sources and determine the constraints on the theory parameters from tests of gravity. Perturbations around the spherically-symmetric background propagate superluminally, but we argue for a chronology protection analogous to Galileons. This is the first example of a screening mechanism for which quantum corrections to the theory are under control and exact solutions to cosmological N-body problems can be found.

  14. Robustness of Rashba and Dirac Fermions against Strong Disorder

    PubMed Central

    Di Sante, Domenico; Barone, Paolo; Plekhanov, Evgeny; Ciuchi, Sergio; Picozzi, Silvia

    2015-01-01

    By addressing the interplay between substitutional disorder and spin-orbit-coupling in chalcogenide alloys, we predict a strong robustness of spectral features at the Fermi energy. Indeed, supplementing our state of the art first-principles calculations with modeling analysis, we show that the disorder self-energy is vanishingly small close to the band gap, thus i) allowing for bulk Rashba-like spin splitting to be observed in ferroelectric alloys by means of Angle Resolved PhotoEmission Spectroscopy, and ii) protecting the band-character inversion related to the topological transition in recently discovered Topological Crystalline Insulators. Such a protection against strong disorder, which we demonstrate to be general for three dimensional Dirac systems, has potential and valuable implications for novel technologies, as spintronics and/or spinorbitronics. PMID:26067146

  15. Relativistic quantum Darwinism in Dirac fermion and graphene systems

    NASA Astrophysics Data System (ADS)

    Ni, Xuan; Huang, Liang; Lai, Ying-Cheng; Pecora, Louis

    2012-02-01

    We solve the Dirac equation in two spatial dimensions in the setting of resonant tunneling, where the system consists of two symmetric cavities connected by a finite potential barrier. The shape of the cavities can be chosen to yield both regular and chaotic dynamics in the classical limit. We find that certain pointer states about classical periodic orbits can exist, which are signatures of relativistic quantum Darwinism (RQD). These localized states suppress quantum tunneling, and the effect becomes less severe as the underlying classical dynamics in the cavity is chaotic, leading to regularization of quantum tunneling. Qualitatively similar phenomena have been observed in graphene. A physical theory is developed to explain relativistic quantum Darwinism and its effects based on the spectrum of complex eigenenergies of the non-Hermitian Hamiltonian describing the open cavity system.

  16. Signatures of Dirac fermion-mediated magnetic order.

    PubMed

    Sessi, Paolo; Reis, Felix; Bathon, Thomas; Kokh, Konstantin A; Tereshchenko, Oleg E; Bode, Matthias

    2014-10-30

    The spin-momentum locking of topological states offers an ideal platform to explore novel magnetoelectric effects. These intimately depend on the ability to manipulate the spin texture in a controlled way. Here we combine scanning tunnelling microscopy with single-atom deposition to map the evolution of topological states under the influence of different magnetic perturbations. We obtain signatures of Dirac fermion-mediated magnetic order for extremely dilute adatom concentrations. This striking observation is found to critically depend on the single adatoms' magnetic anisotropy and the position of the Fermi level. Our findings open new perspectives in spin engineering topological states at the atomic scale and pave the way to explore novel spin-related topological phenomena with promising potential for applications.

  17. Realization of unidirectional transmission under accidental degenerated Dirac point

    NASA Astrophysics Data System (ADS)

    Lou, Qun; Zhang, Yichi; Poo, Yin; Ma, HuiFeng; Wu, Ruixin

    2017-04-01

    We demonstrated a good unidirectional transmission (UT) with high transmission efficiency without breaking time-reversal symmetry both theoretically and experimentally. By adjusting the topological structure and designing the component of all-dielectric photonic crystal, an accidental degenerated Dirac point is built at Γ point. We obtained simultaneous zero permittivity and zero permeability. Truncating the PC into a bow-tie shape, we observed a total reflection in one direction but a total transmission in the opposite direction. The good agreement between the theoretical and experimental data verifies such model supports a good UT even considering the material's loss. Due to the PC's scale invariance, this kind of UT can be conveniently exploited into terahertz or optical frequency, providing a great promising application to optical communication and optical circuit.

  18. Dirac fields in loop quantum gravity and big bang nucleosynthesis

    SciTech Connect

    Bojowald, Martin; Das, Rupam; Scherrer, Robert J.

    2008-04-15

    Big bang nucleosynthesis requires a fine balance between equations of state for photons and relativistic fermions. Several corrections to equation of state parameters arise from classical and quantum physics, which are derived here from a canonical perspective. In particular, loop quantum gravity allows one to compute quantum gravity corrections for Maxwell and Dirac fields. Although the classical actions are very different, quantum corrections to the equation of state are remarkably similar. To lowest order, these corrections take the form of an overall expansion-dependent multiplicative factor in the total density. We use these results, along with the predictions of big bang nucleosynthesis, to place bounds on these corrections and especially the patch size of discrete quantum gravity states.

  19. Spin-resolved conductance of Dirac electrons through multibarrier arrays

    NASA Astrophysics Data System (ADS)

    Dahal, Dipendra; Gumbs, Godfrey; Iurov, Andrii

    We use a transfer matrix method to calculate the transmission coefficient of Dirac electrons through an arbitrary number of square potential barrier in gapped monolayer graphene(MLG) and bilayer graphene (BLG). The widths of barriers may not be chosen equal. The shift in the angle of incidence and the width of the barrier required for resonance are investigated numerically for both MLG and BLG. We compare the effects due to energy gap on these two transmission coefficient for each of these two structures (MLG and BLG). We present our results as functions of barrier width, height as well as incoming electron energy as well as band gap and examine the conditions for which perfect reflection or transmission occurs. Our transmission data are further used to calculate conductivity.

  20. Heptagraphene: Tunable Dirac Cones in a Graphitic Structure.

    PubMed

    Lopez-Bezanilla, Alejandro; Martin, Ivar; Littlewood, Peter B

    2016-09-13

    We predict the existence and dynamical stability of heptagraphene, a new graphitic structure formed of rings of 10 carbon atoms bridged by carbene groups yielding seven-membered rings. Despite the rectangular unit cell, the band structure is topologically equivalent to that of strongly distorted graphene. Density-functional-theory calculations demonstrate that heptagraphene has Dirac cones on symmetry lines that are robust against biaxial strain but which open a gap under shear. At high deformation values bond reconstructions lead to different electronic band arrangements in dynamically stable configurations. Within a tight-binding framework this richness of the electronic behavior is identified as a direct consequence of the symmetry breaking within the cell which, unlike other graphitic structures, leads to band gap opening. A combined approach of chemical and physical modification of graphene unit cell unfurls the opportunity to design carbon-based systems in which one aims to tune an electronic band gap.

  1. Heptagraphene: Tunable Dirac Cones in a Graphitic Structure

    PubMed Central

    Lopez-Bezanilla, Alejandro; Martin, Ivar; Littlewood, Peter B.

    2016-01-01

    We predict the existence and dynamical stability of heptagraphene, a new graphitic structure formed of rings of 10 carbon atoms bridged by carbene groups yielding seven-membered rings. Despite the rectangular unit cell, the band structure is topologically equivalent to that of strongly distorted graphene. Density-functional-theory calculations demonstrate that heptagraphene has Dirac cones on symmetry lines that are robust against biaxial strain but which open a gap under shear. At high deformation values bond reconstructions lead to different electronic band arrangements in dynamically stable configurations. Within a tight-binding framework this richness of the electronic behavior is identified as a direct consequence of the symmetry breaking within the cell which, unlike other graphitic structures, leads to band gap opening. A combined approach of chemical and physical modification of graphene unit cell unfurls the opportunity to design carbon-based systems in which one aims to tune an electronic band gap. PMID:27622775

  2. Application of the DIRAC framework to CTA: first evaluation

    NASA Astrophysics Data System (ADS)

    Arrabito, L.; Barbier, C.; Graciani Diaz, R.; Khélifi, B.; Komin, N.; Lamanna, G.; Lavalley, C.; Le Flour, T.; Lenain, Jp; Lorca, A.; Renaud, M.; Sterzel, M.; Szepieniec, T.; Vasileiadis, G.; Vuerli, C.

    2012-12-01

    The Cherenkov Telescope Array (CTA) - an array of several tens of Cherenkov telescopes - is the next generation of ground-based instrument in the field of very high energy gamma-ray astronomy. The CTA observatory is expected to produce a main data stream for permanent storage of the order of 1-to-5 GB/s for about 1000 hours of observation per year, thus producing a total data volume of the order of several PB per year. The CPU time needed to calibrate and process one hour of data taking will be of the order of some thousands CPU hours with current technology. The high data rate of CTA, together with the large computing power requirements for Monte Carlo (MC) simulations, need dedicated computing resources. Massive MC simulations are needed to study the physics of cosmic-ray atmospheric showers as well as telescope response and performance for different detectors and layout configurations. Given these large storage and computing requirements, the Grid approach is well suited, and a vast number of MC simulations are already running on the European Grid Infrastructure (EGI). In order to optimize resource usage and to handle all production and future analysis activities in a coherent way, a high-level framework with advanced functionalities is desirable. For this purpose we have preliminarly evaluated the DIRAC framework for distributed computing and tested it for the CTA workload and data management systems. In this paper we present a possible implementation of a Distributed Computing Infrastructure (DCI) Computing Model for CTA as well as the benchmark test results of DIRAC.

  3. A B-spline Galerkin method for the Dirac equation

    NASA Astrophysics Data System (ADS)

    Froese Fischer, Charlotte; Zatsarinny, Oleg

    2009-06-01

    The B-spline Galerkin method is first investigated for the simple eigenvalue problem, y=-λy, that can also be written as a pair of first-order equations y=λz, z=-λy. Expanding both y(r) and z(r) in the B basis results in many spurious solutions such as those observed for the Dirac equation. However, when y(r) is expanded in the B basis and z(r) in the dB/dr basis, solutions of the well-behaved second-order differential equation are obtained. From this analysis, we propose a stable method ( B,B) basis for the Dirac equation and evaluate its accuracy by comparing the computed and exact R-matrix for a wide range of nuclear charges Z and angular quantum numbers κ. When splines of the same order are used, many spurious solutions are found whereas none are found for splines of different order. Excellent agreement is obtained for the R-matrix and energies for bound states for low values of Z. For high Z, accuracy requires the use of a grid with many points near the nucleus. We demonstrate the accuracy of the bound-state wavefunctions by comparing integrals arising in hyperfine interaction matrix elements with exact analytic expressions. We also show that the Thomas-Reiche-Kuhn sum rule is not a good measure of the quality of the solutions obtained by the B-spline Galerkin method whereas the R-matrix is very sensitive to the appearance of pseudo-states.

  4. A novel quantum-mechanical interpretation of the Dirac equation

    NASA Astrophysics Data System (ADS)

    K-H Kiessling, M.; Tahvildar-Zadeh, A. S.

    2016-04-01

    A novel interpretation is given of Dirac’s ‘wave equation for the relativistic electron’ as a quantum-mechanical one-particle equation. In this interpretation the electron and the positron are merely the two different ‘topological spin’ states of a single more fundamental particle, not distinct particles in their own right. The new interpretation is backed up by the existence of such ‘bi-particle’ structures in general relativity, in particular the ring singularity present in any spacelike section of the spacetime singularity of the maximal-analytically extended, topologically non-trivial, electromagnetic Kerr-Newman (KN)spacetime in the zero-gravity limit (here, ‘zero-gravity’ means the limit G\\to 0, where G is Newton’s constant of universal gravitation). This novel interpretation resolves the dilemma that Dirac’s wave equation seems to be capable of describing both the electron and the positron in ‘external’ fields in many relevant situations, while the bi-spinorial wave function has only a single position variable in its argument, not two—as it should if it were a quantum-mechanical two-particle wave equation. A Dirac equation is formulated for such a ring-like bi-particle which interacts with a static point charge located elsewhere in the topologically non-trivial physical space associated with the moving ring particle, the motion being governed by a de Broglie-Bohm type law extracted from the Dirac equation. As an application, the pertinent general-relativistic zero-gravity hydrogen problem is studied in the usual Born-Oppenheimer approximation. Its spectral results suggest that the zero-G KN magnetic moment be identified with the so-called ‘anomalous magnetic moment of the physical electron,’ not with the Bohr magneton, so that the ring radius is only a tiny fraction of the electron’s reduced Compton wavelength.

  5. Magnetotransport study of Dirac fermions in YbMnBi2 antiferromagnet

    NASA Astrophysics Data System (ADS)

    Wang, Aifeng; Zaliznyak, I.; Ren, Weijun; Wu, Lijun; Graf, D.; Garlea, V. O.; Warren, J. B.; Bozin, E.; Zhu, Yimei; Petrovic, C.

    2016-10-01

    We report quantum transport and Dirac fermions in YbMnBi2 single crystals. YbMnBi2 is a layered material with anisotropic conductivity and magnetic order below 290 K. Magnetotransport properties, nonzero Berry phase, and small cyclotron mass indicate the presence of Dirac fermions. Angular-dependent magnetoresistance indicates a possible quasi-two-dimensional Fermi surface, whereas the deviation from the nontrivial Berry phase expected for Dirac states suggests the contribution of parabolic bands at the Fermi level or spin-orbit coupling.

  6. Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion

    SciTech Connect

    Lamata, L.; Leon, J.; Schaetz, T.; Solano, E.

    2007-06-22

    We present a method of simulating the Dirac equation in 3+1 dimensions for a free spin-1/2 particle in a single trapped ion. The Dirac bispinor is represented by four ionic internal states, and position and momentum of the Dirac particle are associated with the respective ionic variables. We show also how to simulate the simplified 1+1 case, requiring the manipulation of only two internal levels and one motional degree of freedom. Moreover, we study relevant quantum-relativistic effects, like the Zitterbewegung and Klein's paradox, the transition from massless to massive fermions, and the relativistic and nonrelativistic limits, via the tuning of controllable experimental parameters.

  7. The (2 + 1) curved Dirac equation in polar coordinates in the presence of electromagnetic field

    NASA Astrophysics Data System (ADS)

    Panahi, H.; Jahangiri, L.

    2015-03-01

    In this work we study the covariant Dirac equation in (2 + 1) dimensional space-time in the presence of electromagnetic field. In polar coordinates, we show that by using a unitary transformation which implies a constraint between the components of gauge field, the covariant Dirac equation can be transformed into a Schrodinger-like differential equation for one of the spinor components. We also obtain the relativistic energy and spinor wave function for two different kinds of electrostatic potentials. The non-relativistic limit of the Dirac equation is also studied and it is shown that the upper spinor component satisfies the Pauli equation.

  8. Pseudo-Dirac Hamiltonians and Flux Phases of SU(N) magnets

    NASA Astrophysics Data System (ADS)

    Burnell, F. J.; Sondhi, S. L.; Shankar, R.

    2008-03-01

    The lattice Dirac Hamiltonian describes a particle hopping on a lattice in a particular background magnetic field. We present a family of hopping Hamiltonians in other background fields that generalize many aspects of the Dirac Hamiltonian to lines and planes of nodes. In our canonical case, hopping on the pyrochlore lattice gives rise to a half filled fermi surface that consists of four intersecting [111] lines. This spectrum is invariant under tetrahedral rotations, rather than all rotations as in the Dirac case, resulting in a more complex matrix anti-commutation structure. This structure arises in a large N treatment of the SU(N) Heisenberg model on the pyrochlore.

  9. Magnetotransport study of Dirac fermions in YbMnBi2 antiferromagnet

    DOE PAGES

    Wang, Aifeng; Zaliznyak, I.; Ren, Weijun; ...

    2016-10-15

    We report quantum transport and Dirac fermions in YbMnBi2 single crystals. YbMnBi2 is a layered material with anisotropic conductivity and magnetic order below 290 K. Magnetotransport properties, nonzero Berry phase, and small cyclotron mass indicate the presence of Dirac fermions. Lastly, angular-dependent magnetoresistance indicates a possible quasi-two-dimensional Fermi surface, whereas the deviation from the nontrivial Berry phase expected for Dirac states suggests the contribution of parabolic bands at the Fermi level or spin-orbit coupling.

  10. Quasinormal modes of a quantum-corrected Schwarzschild black hole: gravitational and Dirac perturbations

    NASA Astrophysics Data System (ADS)

    Saleh, Mahamat; Bouetou, Bouetou Thomas; Kofane, Timoleon Crepin

    2016-04-01

    In this work, quasinormal modes (QNMs) of the Schwarzschild black hole are investigated by taking into account the quantum fluctuations. Gravitational and Dirac perturbations were considered for this case. The Regge-Wheeler gauge and the Dirac equation were used to derive the perturbation equations of the gravitational and Dirac fields respectively and the third order Wentzel-Kramers-Brillouin (WKB) approximation method is used for the computing of the quasinormal frequencies. The results show that due to the quantum fluctuations in the background of the Schwarzschild black hole, the QNMs of the black hole damp more slowly when increasing the quantum correction factor (a), and oscillate more slowly.

  11. Imaginary Time Step Method to Solve the Dirac Equation with Nonlocal Potential

    SciTech Connect

    Zhang Ying; Liang Haozhao; Meng Jie

    2009-08-26

    The imaginary time step (ITS) method is applied to solve the Dirac equation with nonlocal potentials in coordinate space. Taking the nucleus {sup 12}C as an example, even with nonlocal potentials, the direct ITS evolution for the Dirac equation still meets the disaster of the Dirac sea. However, following the recipe in our former investigation, the disaster can be avoided by the ITS evolution for the corresponding Schroedinger-like equation without localization, which gives the convergent results exactly the same with those obtained iteratively by the shooting method with localized effective potentials.

  12. Closed-form expressions for the Dirac-Coulomb radial rt integrals

    NASA Astrophysics Data System (ADS)

    Bessis, N.; Bessis, G.; Roux, D.

    1985-10-01

    A novel procedure is devised in order to obtain closed-form expressions of the Dirac-Coulomb radial rt integrals in terms of the Dirac energy ɛ=\\{1+Z2α2/[v+(k2-Z2 α2)1/2]2\\}-1/2, where v=n-||k||, and of the Dirac quantum number k=(-1)j+l+1/2(j+(1/2)). In this procedure, well adapted for symbolic computation, the fundamental array of the rt radial integrals is obtained from the rt-1 array.

  13. Electron-hole asymmetry, Dirac fermions, and quantum magnetoresistance in BaMnBi2

    DOE PAGES

    Li, Lijun; Wang, Kefeng; Graf, D.; ...

    2016-03-28

    Here, we report two-dimensional quantum transport and Dirac fermions in BaMnBi2 single crystals. BaMnBi2 is a layered bad metal with highly anisotropic conductivity and magnetic order below 290 K. Magnetotransport properties, nonzero Berry phase, small cyclotron mass, and the first-principles band structure calculations indicate the presence of Dirac fermions in Bi square nets. Quantum oscillations in the Hall channel suggest the presence of both electron and hole pockets, whereas Dirac and parabolic states coexist at the Fermi level.

  14. Ladder Operators for Some Spherically Symmetric Potentials in Quantum Mechanics

    ERIC Educational Resources Information Center

    Newmarch, J. D.; Golding, R. M.

    1978-01-01

    The energy levels of the free field, Coulomb potential, and the three-dimensional harmonic oscillator are found using the Dirac operator formalism by the construction of suitable ladder operators. The degeneracy of each level is also discussed. (Author/GA)

  15. Space-fractional Schrödinger equation for a quadrupolar triple Dirac-δ potential: Central Dirac-δ well and barrier cases

    NASA Astrophysics Data System (ADS)

    Tare, Jeffrey D.; Esguerra, Jose Perico H.

    2015-01-01

    We solve the space-fractional Schrödinger equation for a quadrupolar triple Dirac-δ (QTD-δ) potential for all energies using the momentum-space approach. For the E < 0 solution, we consider two cases, i.e., when the strengths of the potential are V0 > 0 (QTD-δ potential with central Dirac-δ well) and V0 < 0 (QTD-δ potential with central Dirac-δ barrier) and derive expressions satisfied by the bound-state energy. For all fractional orders α considered, we find that there is one eigenenergy when V0 > 0, and there are two eigenenergies when V0 < 0. We also obtain both bound- and scattering-state (E > 0) wave functions and express them in terms of Fox's H-function.

  16. Transverse Anderson localization of light near Dirac points of photonic nanostructures.

    PubMed

    Deng, Hanying; Chen, Xianfeng; Malomed, Boris A; Panoiu, Nicolae C; Ye, Fangwei

    2015-10-26

    We perform a comparative study of the Anderson localization of light beams in disordered layered photonic nanostructures that, in the limit of periodic layer distribution, possess either a Dirac point or a Bragg gap in the spectrum of the wavevectors. In particular, we demonstrate that the localization length of the Anderson modes increases when the width of the Bragg gap decreases, such that in the vanishingly small bandgap limit, namely when a Dirac point is formed, even extremely high levels of disorder are unable to localize the optical modes residing near the Dirac point. A comparative analysis of the key features of the propagation of Anderson modes formed in the Bragg gap or near the Dirac point is also presented. Our findings could provide valuable guidelines in assessing the influence of structural disorder on the functionality of a broad array of optical nanodevices.

  17. Drive the Dirac electrons into Cooper pairs in SrxBi2Se3.

    PubMed

    Du, Guan; Shao, Jifeng; Yang, Xiong; Du, Zengyi; Fang, Delong; Wang, Jinghui; Ran, Kejing; Wen, Jinsheng; Zhang, Changjin; Yang, Huan; Zhang, Yuheng; Wen, Hai-Hu

    2017-02-15

    Topological superconductors are a very interesting and frontier topic in condensed matter physics. Despite the tremendous efforts in exploring topological superconductivity, its presence is however still under heavy debate. The Dirac electrons have been proven to exist on the surface of a topological insulator. It remains unclear whether and how the Dirac electrons fall into Cooper pairing in an intrinsic superconductor with the topological surface states. Here we show the systematic study of scanning tunnelling microscope/spectroscopy on the possible topological superconductor SrxBi2Se3. We first demonstrate that only the intercalated Sr atoms can induce superconductivity. Then we show the full superconducting gaps without any in-gap density of states as expected theoretically for a bulk topological superconductor. Finally, we find that the surface Dirac electrons will simultaneously condense into the superconducting state within the superconducting gap. This vividly demonstrates how the surface Dirac electrons are driven into Cooper pairs.

  18. Dynamical polarizability, screening and plasmons in one, two and three dimensional massive Dirac systems.

    PubMed

    Thakur, Anmol; Sachdeva, Rashi; Agarwal, Amit

    2017-03-15

    We study the density-density response function of a collection of charged massive Dirac particles and present analytical expressions for the dynamical polarization function in one, two and three dimensions. The polarization function is then used to find the dispersion of the plasmon modes, and electrostatic screening of Coulomb interactions within the random phase approximation. We find that for massive Dirac systems, the oscillating screened potential (or density) decays as r (-2) and r (-3) in two and three dimensions respectively, and as r (-1) for one dimensional non-interacting systems. However for massless Dirac systems there is no electrostatic screening or Friedel oscillation in one dimension, and the oscillating screened potential decays as r (-3) and r (-4), in two and three dimensions respectively. Our analytical results for the polarization function will be useful for exploring the physics of massive and massless Dirac electrons in different experimental systems with varying dimensionality.

  19. Ultrafast electron dynamics at the Dirac node of the topological insulator Sb2Te3.

    PubMed

    Zhu, Siyuan; Ishida, Yukiaki; Kuroda, Kenta; Sumida, Kazuki; Ye, Mao; Wang, Jiajia; Pan, Hong; Taniguchi, Masaki; Qiao, Shan; Shin, Shik; Kimura, Akio

    2015-08-21

    Topological insulators (TIs) are a new quantum state of matter. Their surfaces and interfaces act as a topological boundary to generate massless Dirac fermions with spin-helical textures. Investigation of fermion dynamics near the Dirac point (DP) is crucial for the future development of spintronic devices incorporating topological insulators. However, research so far has been unsatisfactory because of a substantial overlap with the bulk valence band and a lack of a completely unoccupied DP. Here, we explore the surface Dirac fermion dynamics in the TI Sb2Te3 by time- and angle-resolved photoemission spectroscopy (TrARPES). Sb2Te3 has an in-gap DP located completely above the Fermi energy (EF). The excited electrons in the upper Dirac cone stay longer than those below the DP to form an inverted population. This was attributed to a reduced density of states (DOS) near the DP.

  20. Dirac State in the FeB2 Monolayer with Graphene-Like Boron Sheet.

    PubMed

    Zhang, Haijun; Li, Yafei; Hou, Jianhou; Du, Aijun; Chen, Zhongfang

    2016-10-12

    By introducing the commonly utilized Fe atoms into a two-dimensional (2D) honeycomb boron network, we theoretically designed a new Dirac material of FeB2 monolayer with a Fermi velocity in the same order of graphene. The electron transfer from Fe atoms to B networks not only effectively stabilizes the FeB2 networks but also leads to the strong interaction between the Fe and B atoms. The Dirac state in FeB2 system primarily arises from the Fe d orbitals and hybridized orbital from Fe-d and B-p states. The newly predicted FeB2 monolayer has excellent dynamic and thermal stabilities and is also the global minimum of 2D FeB2 system, implying its experimental feasibility. Our results are beneficial to further uncovering the mechanism of the Dirac cones and providing a feasible strategy for Dirac materials design.

  1. Bound states for multiple Dirac-δ wells in space-fractional quantum mechanics

    SciTech Connect

    Tare, Jeffrey D. Esguerra, Jose Perico H.

    2014-01-15

    Using the momentum-space approach, we obtain bound states for multiple Dirac-δ wells in the framework of space-fractional quantum mechanics. Introducing first an attractive Dirac-comb potential, i.e., Dirac comb with strength −g (g > 0), in the space-fractional Schrödinger equation we show that the problem of obtaining eigenenergies of a system with N Dirac-δ wells can be reduced to a problem of obtaining the eigenvalues of an N × N matrix. As an illustration we use the present matrix formulation to derive expressions satisfied by the bound-state energies of N = 1, 2, 3 delta wells. We also obtain the corresponding wave functions and express them in terms of Fox's H-function.

  2. Drive the Dirac electrons into Cooper pairs in SrxBi2Se3

    PubMed Central

    Du, Guan; Shao, Jifeng; Yang, Xiong; Du, Zengyi; Fang, Delong; Wang, Jinghui; Ran, Kejing; Wen, Jinsheng; Zhang, Changjin; Yang, Huan; Zhang, Yuheng; Wen, Hai-Hu

    2017-01-01

    Topological superconductors are a very interesting and frontier topic in condensed matter physics. Despite the tremendous efforts in exploring topological superconductivity, its presence is however still under heavy debate. The Dirac electrons have been proven to exist on the surface of a topological insulator. It remains unclear whether and how the Dirac electrons fall into Cooper pairing in an intrinsic superconductor with the topological surface states. Here we show the systematic study of scanning tunnelling microscope/spectroscopy on the possible topological superconductor SrxBi2Se3. We first demonstrate that only the intercalated Sr atoms can induce superconductivity. Then we show the full superconducting gaps without any in-gap density of states as expected theoretically for a bulk topological superconductor. Finally, we find that the surface Dirac electrons will simultaneously condense into the superconducting state within the superconducting gap. This vividly demonstrates how the surface Dirac electrons are driven into Cooper pairs. PMID:28198378

  3. Mapping the effect of defect-induced strain disorder on the Dirac states of topological insulators

    NASA Astrophysics Data System (ADS)

    Storz, Oliver; Cortijo, Alberto; Wilfert, Stefan; Kokh, K. A.; Tereshchenko, O. E.; Vozmediano, María A. H.; Bode, Matthias; Guinea, Francisco; Sessi, Paolo

    2016-09-01

    We provide a detailed microscopic characterization of the influence of defect-induced disorder on the Dirac spectrum of three-dimensional topological insulators. By spatially resolved Landau-level spectroscopy measurements, we reveal the existence of nanoscale fluctuations of both the Dirac point energy as well as of the Dirac-fermion velocity which is found to spatially change in opposite direction for electrons and holes, respectively. These results evidence a scenario which goes beyond the existing picture based on chemical potential fluctuations. The findings are consistently explained by considering the microscopic effects of local stain introduced by defects, which our model calculations show to effectively couple to topological states, reshaping their Dirac-like dispersion over a large energy range. In particular, our results indicate that the presence of microscopic spatially varying stain, inevitably present in crystals because of the random distribution of defects, effectively couple to topological states and should be carefully considered for correctly describing the effects of disorder.

  4. Creating stable Floquet-Weyl semimetals by laser-driving of 3D Dirac materials.

    PubMed

    Hübener, Hannes; Sentef, Michael A; De Giovannini, Umberto; Kemper, Alexander F; Rubio, Angel

    2017-01-17

    Tuning and stabilizing topological states, such as Weyl semimetals, Dirac semimetals or topological insulators, is emerging as one of the major topics in materials science. Periodic driving of many-body systems offers a platform to design Floquet states of matter with tunable electronic properties on ultrafast timescales. Here we show by first principles calculations how femtosecond laser pulses with circularly polarized light can be used to switch between Weyl semimetal, Dirac semimetal and topological insulator states in a prototypical three-dimensional (3D) Dirac material, Na3Bi. Our findings are general and apply to any 3D Dirac semimetal. We discuss the concept of time-dependent bands and steering of Floquet-Weyl points and demonstrate how light can enhance topological protection against lattice perturbations. This work has potential practical implications for the ultrafast switching of materials properties, such as optical band gaps or anomalous magnetoresistance.

  5. Analysis of Dirac Point in the Organic Conductor α-(BEDT-TTF)2I3

    NASA Astrophysics Data System (ADS)

    Suzumura, Yoshikazu

    2016-05-01

    The Dirac electron in the organic conductor α-(BEDT-TTF)2I3 under pressure is analyzed using a tight-binding model with nearest-neighbor transfer energies and four molecules per unit cell. By noting that the Dirac point between the first and second energy bands emerges or merges followed by the level crossing at a time-reversal invariant momentum (TRIM), an effective Hamiltonian is derived on the basis of these two wave functions at the TRIM, which have different parities associated with an inversion symmetry around the inversion center. We demonstrate that the Dirac point is determined by an intersection of two kinds of lines originating from the Hamiltonian described by symmetric and antisymmetric functions around the TRIM. The present method quantitatively gives a reasonable location of the Dirac point of α-(BEDT-TTF)2I3 in a wide pressure range.

  6. Topological Node-Line Semimetal and Dirac Semimetal State in Antiperovskite Cu3PdN.

    PubMed

    Yu, Rui; Weng, Hongming; Fang, Zhong; Dai, Xi; Hu, Xiao

    2015-07-17

    Based on first-principles calculation and effective model analysis, we propose that the cubic antiperovskite material Cu3PdN can host a three-dimensional (3D) topological node-line semimetal state when spin-orbit coupling (SOC) is ignored, which is protected by the coexistence of time-reversal and inversion symmetry. There are three node-line circles in total due to the cubic symmetry. Drumheadlike surface flat bands are also derived. When SOC is included, each node line evolves into a pair of stable 3D Dirac points as protected by C4 crystal symmetry. This is remarkably distinguished from the Dirac semimetals known so far, such as Na3Bi and Cd3As2, both having only one pair of Dirac points. Once C4 symmetry is broken, the Dirac points are gapped and the system becomes a strong topological insulator with (1;111) Z2 indices.

  7. Topological phase transitions with SO(4) symmetry in (2+1)D interacting Dirac fermions

    NASA Astrophysics Data System (ADS)

    Xu, Xiao Yan; Beach, K. S. D.; Sun, Kai; Assaad, F. F.; Meng, Zi Yang

    2017-02-01

    Interaction-driven topological phase transitions in Dirac semimetals are investigated by means of large-scale quantum Monte Carlo simulations. The interaction among Dirac fermions is introduced by coupling them to Ising spins that realize the quantum dynamics of the two-dimensional transverse field Ising model. The ground-state phase diagram, in which the tuning parameters are the transverse field and the coupling between fermion and Ising spins, is determined. At weak and intermediate coupling, a second-order Ising quantum phase transition and a first-order topological phase transition between two topologically distinct Dirac semimetals are observed. Interestingly, at the latter, the Dirac points smear out to form nodal lines in the Brillouin zone, and collective bosonic fluctuations with SO(4) symmetry are strongly enhanced. At strong coupling, these two phase boundaries merge into a first-order transition.

  8. Topological Node-Line Semimetal and Dirac Semimetal State in Antiperovskite Cu3PdN

    NASA Astrophysics Data System (ADS)

    Yu, Rui; Weng, Hongming; Fang, Zhong; Dai, Xi; Hu, Xiao

    2015-07-01

    Based on first-principles calculation and effective model analysis, we propose that the cubic antiperovskite material Cu3PdN can host a three-dimensional (3D) topological node-line semimetal state when spin-orbit coupling (SOC) is ignored, which is protected by the coexistence of time-reversal and inversion symmetry. There are three node-line circles in total due to the cubic symmetry. Drumheadlike surface flat bands are also derived. When SOC is included, each node line evolves into a pair of stable 3D Dirac points as protected by C4 crystal symmetry. This is remarkably distinguished from the Dirac semimetals known so far, such as Na3Bi and Cd3As2 , both having only one pair of Dirac points. Once C4 symmetry is broken, the Dirac points are gapped and the system becomes a strong topological insulator with (1;111) Z2 indices.

  9. J J THOMSON'S ELECTRON: The Dirac equation. Cosmic implications of a tidy electron

    NASA Astrophysics Data System (ADS)

    Miller, David

    1997-07-01

    Dirac devised the quantum theory of the electron itself, which required him to generalize Schrödinger's famous equation to cover relativistic motion. He interpreted the resulting equation as showing that an antiparticle to the electron must exist.

  10. Ultrafast electron dynamics at the Dirac node of the topological insulator Sb2Te3

    PubMed Central

    Zhu, Siyuan; Ishida, Yukiaki; Kuroda, Kenta; Sumida, Kazuki; Ye, Mao; Wang, Jiajia; Pan, Hong; Taniguchi, Masaki; Qiao, Shan; Shin, Shik; Kimura, Akio

    2015-01-01

    Topological insulators (TIs) are a new quantum state of matter. Their surfaces and interfaces act as a topological boundary to generate massless Dirac fermions with spin-helical textures. Investigation of fermion dynamics near the Dirac point (DP) is crucial for the future development of spintronic devices incorporating topological insulators. However, research so far has been unsatisfactory because of a substantial overlap with the bulk valence band and a lack of a completely unoccupied DP. Here, we explore the surface Dirac fermion dynamics in the TI Sb2Te3 by time- and angle-resolved photoemission spectroscopy (TrARPES). Sb2Te3 has an in-gap DP located completely above the Fermi energy (EF). The excited electrons in the upper Dirac cone stay longer than those below the DP to form an inverted population. This was attributed to a reduced density of states (DOS) near the DP. PMID:26294343

  11. Dynamical polarizability, screening and plasmons in one, two and three dimensional massive Dirac systems

    NASA Astrophysics Data System (ADS)

    Thakur, Anmol; Sachdeva, Rashi; Agarwal, Amit

    2017-03-01

    We study the density–density response function of a collection of charged massive Dirac particles and present analytical expressions for the dynamical polarization function in one, two and three dimensions. The polarization function is then used to find the dispersion of the plasmon modes, and electrostatic screening of Coulomb interactions within the random phase approximation. We find that for massive Dirac systems, the oscillating screened potential (or density) decays as r ‑2 and r ‑3 in two and three dimensions respectively, and as r ‑1 for one dimensional non-interacting systems. However for massless Dirac systems there is no electrostatic screening or Friedel oscillation in one dimension, and the oscillating screened potential decays as r ‑3 and r ‑4, in two and three dimensions respectively. Our analytical results for the polarization function will be useful for exploring the physics of massive and massless Dirac electrons in different experimental systems with varying dimensionality.

  12. Creating stable Floquet-Weyl semimetals by laser-driving of 3D Dirac materials

    NASA Astrophysics Data System (ADS)

    Hübener, Hannes; Sentef, Michael A.; de Giovannini, Umberto; Kemper, Alexander F.; Rubio, Angel

    2017-01-01

    Tuning and stabilizing topological states, such as Weyl semimetals, Dirac semimetals or topological insulators, is emerging as one of the major topics in materials science. Periodic driving of many-body systems offers a platform to design Floquet states of matter with tunable electronic properties on ultrafast timescales. Here we show by first principles calculations how femtosecond laser pulses with circularly polarized light can be used to switch between Weyl semimetal, Dirac semimetal and topological insulator states in a prototypical three-dimensional (3D) Dirac material, Na3Bi. Our findings are general and apply to any 3D Dirac semimetal. We discuss the concept of time-dependent bands and steering of Floquet-Weyl points and demonstrate how light can enhance topological protection against lattice perturbations. This work has potential practical implications for the ultrafast switching of materials properties, such as optical band gaps or anomalous magnetoresistance.

  13. Transverse Anderson localization of light near Dirac points of photonic nanostructures

    PubMed Central

    Deng, Hanying; Chen, Xianfeng; Malomed, Boris A.; Panoiu, Nicolae C.; Ye, Fangwei

    2015-01-01

    We perform a comparative study of the Anderson localization of light beams in disordered layered photonic nanostructures that, in the limit of periodic layer distribution, possess either a Dirac point or a Bragg gap in the spectrum of the wavevectors. In particular, we demonstrate that the localization length of the Anderson modes increases when the width of the Bragg gap decreases, such that in the vanishingly small bandgap limit, namely when a Dirac point is formed, even extremely high levels of disorder are unable to localize the optical modes residing near the Dirac point. A comparative analysis of the key features of the propagation of Anderson modes formed in the Bragg gap or near the Dirac point is also presented. Our findings could provide valuable guidelines in assessing the influence of structural disorder on the functionality of a broad array of optical nanodevices. PMID:26498634

  14. Drive the Dirac electrons into Cooper pairs in SrxBi2Se3

    NASA Astrophysics Data System (ADS)

    Du, Guan; Shao, Jifeng; Yang, Xiong; Du, Zengyi; Fang, Delong; Wang, Jinghui; Ran, Kejing; Wen, Jinsheng; Zhang, Changjin; Yang, Huan; Zhang, Yuheng; Wen, Hai-Hu

    2017-02-01

    Topological superconductors are a very interesting and frontier topic in condensed matter physics. Despite the tremendous efforts in exploring topological superconductivity, its presence is however still under heavy debate. The Dirac electrons have been proven to exist on the surface of a topological insulator. It remains unclear whether and how the Dirac electrons fall into Cooper pairing in an intrinsic superconductor with the topological surface states. Here we show the systematic study of scanning tunnelling microscope/spectroscopy on the possible topological superconductor SrxBi2Se3. We first demonstrate that only the intercalated Sr atoms can induce superconductivity. Then we show the full superconducting gaps without any in-gap density of states as expected theoretically for a bulk topological superconductor. Finally, we find that the surface Dirac electrons will simultaneously condense into the superconducting state within the superconducting gap. This vividly demonstrates how the surface Dirac electrons are driven into Cooper pairs.

  15. Dirac cones in artificial structures of 3d transitional-metals doped Mg-Al spinels

    SciTech Connect

    Lu, Yuan; Zuo, Xu; Feng, Min; Shao, Bin

    2014-05-07

    Motivated by recent theoretical predications for Dirac cone in two-dimensional (2D) triangular lattice [H. Ishizuka, Phys. Rev. Lett. 109, 237207 (2012)], first-principles studies are performed to predict Dirac cones in artificial structures of 3d transitional-metals (TM = Ti, V, Cr, Mn, Fe, Co, Ni, and Cu) doped Mg-Al spinels. In investigated artificial structures, TM dopants substitute specific positions of the B sub-lattice in Mg-Al spinel, and form a quasi-2D triangular lattice in the a-b plane. Calculated results illustrate the existence of the spin-polarized Dirac cones formed in d-wave bands at (around) the K-point in the momentum space. The study provides a promising route for engineering Dirac physics in condensed matters.

  16. Dirac cones in artificial structures of 3d transitional-metals doped Mg-Al spinels

    NASA Astrophysics Data System (ADS)

    Lu, Yuan; Feng, Min; Shao, Bin; Zuo, Xu

    2014-05-01

    Motivated by recent theoretical predications for Dirac cone in two-dimensional (2D) triangular lattice [H. Ishizuka, Phys. Rev. Lett. 109, 237207 (2012)], first-principles studies are performed to predict Dirac cones in artificial structures of 3d transitional-metals (TM = Ti, V, Cr, Mn, Fe, Co, Ni, and Cu) doped Mg-Al spinels. In investigated artificial structures, TM dopants substitute specific positions of the B sub-lattice in Mg-Al spinel, and form a quasi-2D triangular lattice in the a-b plane. Calculated results illustrate the existence of the spin-polarized Dirac cones formed in d-wave bands at (around) the K-point in the momentum space. The study provides a promising route for engineering Dirac physics in condensed matters.

  17. A model for pseudo-Dirac neutrinos: leptogenesis and ultra-high energy neutrinos

    NASA Astrophysics Data System (ADS)

    Ahn, Y. H.; Kang, Sin Kyu; Kim, C. S.

    2016-10-01

    We propose a model where sterile neutrinos are introduced to make light neutrinos to be pseudo-Dirac particles. It is shown how tiny mass splitting necessary for realizing pseudo-Dirac neutrinos can be achieved. Within the model, we show how leptogenesis can be successfully generated. Motivated by the recent observation of very high energy neutrino events at IceCube, we study a possibility to observe the effects of the pseudo-Dirac property of neutrinos by performing astronomical-scale baseline experiments to uncover the oscillation effects of very tiny mass splitting. We also discuss future prospect to observe the effects of the pseudo-Dirac property of neutrinos at high energy neutrino experiments.

  18. Creating stable Floquet–Weyl semimetals by laser-driving of 3D Dirac materials

    PubMed Central

    Hübener, Hannes; Sentef, Michael A.; De Giovannini, Umberto; Kemper, Alexander F.; Rubio, Angel

    2017-01-01

    Tuning and stabilizing topological states, such as Weyl semimetals, Dirac semimetals or topological insulators, is emerging as one of the major topics in materials science. Periodic driving of many-body systems offers a platform to design Floquet states of matter with tunable electronic properties on ultrafast timescales. Here we show by first principles calculations how femtosecond laser pulses with circularly polarized light can be used to switch between Weyl semimetal, Dirac semimetal and topological insulator states in a prototypical three-dimensional (3D) Dirac material, Na3Bi. Our findings are general and apply to any 3D Dirac semimetal. We discuss the concept of time-dependent bands and steering of Floquet–Weyl points and demonstrate how light can enhance topological protection against lattice perturbations. This work has potential practical implications for the ultrafast switching of materials properties, such as optical band gaps or anomalous magnetoresistance. PMID:28094286

  19. A simple efficient methodology for Dirac equation in minimal length quantum mechanics

    NASA Astrophysics Data System (ADS)

    Hassanabadi, H.; Zarrinkamar, S.; Rajabi, A. A.

    2013-01-01

    We solve the modified Dirac equation by adding a harmonic oscillator potential and implementing the Nikiforov-Uvarov technique. The closed forms of solutions are reported in a quite simple and systematic manner.

  20. Switching of Dirac-Fermion Mass at the Interface of Ultrathin Ferromagnet and Rashba Metal.

    PubMed

    Honma, K; Sato, T; Souma, S; Sugawara, K; Tanaka, Y; Takahashi, T

    2015-12-31

    We have performed spin- and angle-resolved photoemission spectroscopy on tungsten (110) interfaced with an ultrathin iron (Fe) layer to study an influence of ferromagnetism on the Dirac-cone-like surface-interface states. We found an unexpectedly large energy gap of 340 meV at the Dirac point, and have succeeded in switching the Dirac-fermion mass by controlling the direction of Fe spins (in plane or out of plane) through tuning the thickness of the Fe overlayer or adsorbing oxygen on it. Such a manipulation of Dirac-fermion mass via the magnetic proximity effect opens a promising platform for realizing new spintronic devices utilizing a combination of exchange and Rashba-spin-orbit interactions.