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Sample records for dunkl dirac operator

  1. Dunkl-Type Operators with Projections Terms Associated to Orthogonal Subsystems in Roots System

    NASA Astrophysics Data System (ADS)

    Bouzeffour, Fethi

    2013-10-01

    In this paper, we introduce a new differential-difference operator T_ξ(ξ in {R}^N) by using projections associated to orthogonal subsystems in root systems. Similarly to Dunkl theory, we show that these operators commute and we construct an intertwining operator between T_ξ and the directional derivative partial_ξ. In the case of one variable, we prove that the Kummer functions are eigenfunctions of this operator.

  2. Chirality and Dirac Operator on Noncommutative Sphere

    NASA Astrophysics Data System (ADS)

    Carow-Watamura, Ursula; Watamura, Satoshi

    1997-01-01

    We give a derivation of the Dirac operator on the noncommutative 2-sphere within the framework of the bosonic fuzzy sphere and define Connes' triple. It turns out that there are two different types of spectra of the Dirac operator and correspondingly there are two classes of quantized algebras. As a result we obtain a new restriction on the Planck constant in Berezin's quantization. The map to the local frame in noncommutative geometry is also discussed. Acknowledgement. The authors benefited from discussions with M. Bordemann, O. Grandjean and M. Pillin. S.W. would like to thank K. Osterwalder for his hospitality during the stay in ETH where this work began. He also thanks the Canon Foundation in Europe for supporting that stay. U.C. would like to acknowledge the Japan Society for Promotion of Science for financial support.-->

  3. 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.

  4. 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.

  5. The overlap-Dirac operator: Topology and chiral symmetry breaking

    SciTech Connect

    Edwards, R.G.; Heller, U.M.; Narayanan, R.

    2000-01-01

    The authors review the spectral flow techniques for computing the index of the overlap Dirac operator including results relevant for SUSY Yang-Mills theories. They describe properties of the overlap Dirac operator, and methods to implement it numerically. They use the results from the spectral flow to illuminate the difficulties in numerical calculations involving domain wall and overlap fermions.

  6. 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.

  7. Dirac operators on quasi-Hamiltonian G-spaces

    NASA Astrophysics Data System (ADS)

    Song, Yanli

    2016-08-01

    We construct twisted spinor bundles as well as twisted pre-quantum bundles on quasi-Hamiltonian G-spaces, using the spin representation of loop group and the Hilbert space of Wess-Zumino-Witten model. We then define a Hilbert space together with a Dirac operator acting on it. The main result of this paper is that we show the Dirac operator has a well-defined index given by positive energy representation of the loop group. This generalizes the geometric quantization of Hamiltonian G-spaces to quasi-Hamiltonian G-spaces.

  8. Global boundary conditions for a Dirac operator on the solid torus

    SciTech Connect

    Klimek, Slawomir; McBride, Matt

    2011-06-15

    We study a Dirac operator subject to Atiayh-Patodi-Singer-like boundary conditions on the solid torus and shows that the corresponding boundary value problem is elliptic in the sense that the Dirac operator has a compact parametrix.

  9. Spectral statistics for the Dirac operator on graphs

    NASA Astrophysics Data System (ADS)

    Bolte, Jens; Harrison, Jonathan

    2003-03-01

    We determine conditions for the quantization of graphs using the Dirac operator for both two- and four-component spinors. According to the Bohigas-Giannoni-Schmit conjecture for such systems with time-reversal symmetry the energy level statistics are expected, in the semiclassical limit, to correspond to those of random matrices from the Gaussian symplectic ensemble. This is confirmed by numerical investigation. The scattering matrix used to formulate the quantization condition is found to be independent of the type of spinor. We derive an exact trace formula for the spectrum and use this to investigate the form factor in the diagonal approximation.

  10. Dirac operator on the sphere with attached wires

    NASA Astrophysics Data System (ADS)

    E, N. Grishanov; D, A. Eremin; D, A. Ivanov; I, Yu Popov

    2016-04-01

    An explicitly solvable model for tunnelling of relativistic spinless particles through a sphere is suggested. The model operator is constructed by an operator extensions theory method from the orthogonal sum of the Dirac operators on a semi-axis and on the sphere. The transmission coefficient is obtained. The dependence of the transmission coefficient on the particle energy has a resonant character. One observes pairs of the Breit-Wigner and the Fano resonances. It correlates with the corresponding results for a non-relativistic particle. Project partially financially supported by the Funds from the Government of the Russian Federation (Grant No. 074-U01), the Funds from the Ministry of Education and Science of the Russian Federation (GOSZADANIE 2014/190) (Grant Nos. 14.Z50.31.0031 and 1.754.2014/K), and the President Foundation of the Russian Federation (Grant No. MK-5001.2015.1).

  11. 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.

  12. A dynamical time operator in Dirac's relativistic quantum mechanics

    NASA Astrophysics Data System (ADS)

    Bauer, M.

    2014-03-01

    A self-adjoint dynamical time operator is introduced in Dirac's relativistic formulation of quantum mechanics and shown to satisfy a commutation relation with the Hamiltonian analogous to that of the position and momentum operators. The ensuing time-energy uncertainty relation involves the uncertainty in the instant of time when the wave packet passes a particular spatial position and the energy uncertainty associated with the wave packet at the same time, as envisaged originally by Bohr. The instantaneous rate of change of the position expectation value with respect to the simultaneous expectation value of the dynamical time operator is shown to be the phase velocity, in agreement with de Broglie's hypothesis of a particle associated wave whose phase velocity is larger than c. Thus, these two elements of the original basis and interpretation of quantum mechanics are integrated into its formal mathematical structure. Pauli's objection is shown to be resolved or circumvented. Possible relevance to current developments in electron channeling, in interference in time, in Zitterbewegung-like effects in spintronics, graphene and superconducting systems and in cosmology is noted.

  13. New calculations in Dirac gaugino models: operators, expansions, and effects

    NASA Astrophysics Data System (ADS)

    Carpenter, Linda M.; Goodman, Jessica

    2015-07-01

    In this work we calculate important one loop SUSY-breaking parameters in models with Dirac gauginos, which are implied by the existence of heavy messenger fields. We find that these SUSY-breaking effects are all related by a small number of parameters, thus the general theory is tightly predictive. In order to make the most accurate analyses of one loop effects, we introduce calculations using an expansion in SUSY breaking messenger mass, rather than relying on postulating the forms of effective operators. We use this expansion to calculate one loop contributions to gaugino masses, non-holomorphic SM adjoint masses, new A-like and B-like terms, and linear terms. We also test the Higgs potential in such models, and calculate one loop contributions to the Higgs mass in certain limits of R-symmetric models, finding a very large contribution in many regions of the [InlineMediaObject not available: see fulltext.], where Higgs fields couple to standard model adjoint fields.

  14. Finiteness of the L2-index of the Dirac operator of generalized Euclidean Taub NUT metrics

    NASA Astrophysics Data System (ADS)

    Moroianu, Sergiu; Visinescu, Mihai

    2006-05-01

    We prove that the axial anomaly, interpreted as the L2-index of the chiral Dirac operator, for the standard Taub-NUT metric on {\\bb R}^4 , vanishes. We show that the essential spectrum of the Dirac operator of the generalized Taub-NUT metrics introduced by Iwai and Katayama is the whole real line. We also show that the axial anomaly for the generalized Taub-NUT metric is finite although the Dirac operator is not Fredholm in L^2({\\bb R}^4,\\Sigma_4,{ds_K}^2) .

  15. 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.

  16. Dirac operators on the Taub-NUT space, monopoles and SU(2) representations

    NASA Astrophysics Data System (ADS)

    Jante, Rogelio; Schroers, Bernd J.

    2014-01-01

    We analyse the normalisable zero-modes of the Dirac operator on the TaubNUT manifold coupled to an abelian gauge field with self-dual curvature, and interpret them in terms of the zero modes of the Dirac operator on the 2-sphere coupled to a Dirac monopole. We show that the space of zero modes decomposes into a direct sum of irreducible SU(2) representations of all dimensions up to a bound determined by the spinor charge with respect to the abelian gauge group. Our decomposition provides an interpretation of an index formula due to Pope and provides a possible model for spin in recently proposed geometric models of matter.

  17. 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.

  18. 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.

  19. On spectral deformations and singular Weyl functions for one-dimensional Dirac operators

    NASA Astrophysics Data System (ADS)

    Beigl, Alexander; Eckhardt, Jonathan; Kostenko, Aleksey; Teschl, Gerald

    2015-01-01

    We investigate the connection between singular Weyl-Titchmarsh-Kodaira theory and the double commutation method for one-dimensional Dirac operators. In particular, we compute the singular Weyl function of the commuted operator in terms of the data from the original operator. These results are then applied to radial Dirac operators in order to show that the singular Weyl function of such an operator belongs to a generalized Nevanlinna class Nκ0 with κ 0 = |κ| + /1 2, where κ ∈ ℝ is the corresponding angular momentum.

  20. 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.

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

    NASA Astrophysics Data System (ADS)

    Dai, Jian; Song, Xing-Chang

    2001-07-01

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

  2. FAST TRACK COMMUNICATION: A globally diagonalizable α2-dynamo operator, SUSY QM and the Dirac equation

    NASA Astrophysics Data System (ADS)

    Günther, Uwe; Samsonov, Boris F.; Stefani, Frank

    2007-02-01

    A new class of semi-analytically solvable MHD α2-dynamos is found based on a global diagonalization of the matrix part of the dynamo differential operator. Close parallels to SUSY QM are used to relate these models to the Dirac equation and to extract non-numerical information about the dynamo spectrum.

  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. Dirac's formalism combined with complex Fourier operational matrices to solve initial and boundary value problems

    NASA Astrophysics Data System (ADS)

    Labecca, William; Guimarães, Osvaldo; Piqueira, José Roberto C.

    2014-08-01

    Approximations of functions in terms of orthogonal polynomials have been used to develop and implement numerical approaches to solve spectrally initial and boundary value problems. The main idea behind these approaches is to express differential and integral operators by using matrices, and this, in turn, makes the numerical implementation easier to be expressed in computational algebraic languages. In this paper, the application of the methodology is enlarged by using Dirac's formalism, combined with complex Fourier series.

  6. Spectral properties of the Wilson-Dirac operator and random matrix theory

    NASA Astrophysics Data System (ADS)

    Kieburg, Mario; Verbaarschot, Jacobus J. M.; Zafeiropoulos, Savvas

    2013-11-01

    Random matrix theory has been successfully applied to lattice quantum chromodynamics. In particular, a great deal of progress has been made on the understanding, numerically as well as analytically, of the spectral properties of the Wilson-Dirac operator. In this paper, we study the infrared spectrum of the Wilson-Dirac operator via random matrix theory including the three leading order a2 correction terms that appear in the corresponding chiral Lagrangian. A derivation of the joint probability density of the eigenvalues is presented. This result is used to calculate the density of the complex eigenvalues, the density of the real eigenvalues, and the distribution of the chiralities over the real eigenvalues. A detailed discussion of these quantities shows how each low-energy constant affects the spectrum. Especially we consider the limit of small and large (which is almost the mean field limit) lattice spacing. Comparisons with Monte Carlo simulations of the random matrix theory show a perfect agreement with the analytical predictions. Furthermore we present some quantities which can be easily used for comparison of lattice data and the analytical results.

  7. Ginsparg-Wilson Dirac operator in monopole backgrounds on the fuzzy 2-sphere

    SciTech Connect

    Aoki, Hajime; Maeda, Toshiharu; Iso, Satoshi

    2007-04-15

    In previous papers, we studied 't Hooft-Polyakov (TP) monopole configurations in U(2) gauge theory on the fuzzy 2-sphere, and showed that they have nonzero topological charges in the formalism based on the Ginsparg-Wilson (GW) relation. In this paper, we will show an index theorem in the TP monopole background, which is defined in the projected space, and provides meaning of the projection operator. We also extend the index theorem to general configurations which do not satisfy the equation of motion, and show that configuration space can be classified into topological sectors. We further calculate the spectrum of the GW Dirac operator in TP monopole backgrounds, and consider the index theorem in these cases.

  8. From the Dirac operator to Wess-Zumino models on spatial lattices

    SciTech Connect

    Kirchberg, A. . E-mail: A.Kirchberg@tpi.uni-jena.de; Laenge, J.D. . E-mail: jdl@tpi.uni-jena.de; Wipf, A. . E-mail: A.Wipf@tpi.uni-jena.de

    2005-04-01

    We investigate two-dimensional Wess-Zumino models in the continuum and on spatial lattices in detail. We show that a non-antisymmetric lattice derivative not only excludes chiral fermions but in addition introduces supersymmetry breaking lattice artifacts. We study the non-local and antisymmetric SLAC derivative which allows for chiral fermions without doublers and minimizes those artifacts. The supercharges of the lattice Wess-Zumino models are obtained by dimensional reduction of Dirac operators in high-dimensional spaces. The normalizable zero modes of the models with N=1 and N=2 supersymmetry are counted and constructed in the weak- and strong-coupling limits. Together with known methods from operator theory this gives us complete control of the zero mode sector of these theories for arbitrary coupling.

  9. FFT-split-operator code for solving the Dirac equation in 2+1 dimensions

    NASA Astrophysics Data System (ADS)

    Mocken, Guido R.; Keitel, Christoph H.

    2008-06-01

    The main part of the code presented in this work represents an implementation of the split-operator method [J.A. Fleck, J.R. Morris, M.D. Feit, Appl. Phys. 10 (1976) 129-160; R. Heather, Comput. Phys. Comm. 63 (1991) 446] for calculating the time-evolution of Dirac wave functions. It allows to study the dynamics of electronic Dirac wave packets under the influence of any number of laser pulses and its interaction with any number of charged ion potentials. The initial wave function can be either a free Gaussian wave packet or an arbitrary discretized spinor function that is loaded from a file provided by the user. The latter option includes Dirac bound state wave functions. The code itself contains the necessary tools for constructing such wave functions for a single-electron ion. With the help of self-adaptive numerical grids, we are able to study the electron dynamics for various problems in 2+1 dimensions at high spatial and temporal resolutions that are otherwise unachievable. Along with the position and momentum space probability density distributions, various physical observables, such as the expectation values of position and momentum, can be recorded in a time-dependent way. The electromagnetic spectrum that is emitted by the evolving particle can also be calculated with this code. Finally, for planning and comparison purposes, both the time-evolution and the emission spectrum can also be treated in an entirely classical relativistic way. Besides the implementation of the above-mentioned algorithms, the program also contains a large C++ class library to model the geometric algebra representation of spinors that we use for representing the Dirac wave function. This is why the code is called "Dirac++". Program summaryProgram title: Dirac++ or (abbreviated) d++ Catalogue identifier: AEAS_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAS_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing

  10. FFT-split-operator code for solving the Dirac equation in 2+1 dimensions

    NASA Astrophysics Data System (ADS)

    Mocken, Guido R.; Keitel, Christoph H.

    2008-06-01

    The main part of the code presented in this work represents an implementation of the split-operator method [J.A. Fleck, J.R. Morris, M.D. Feit, Appl. Phys. 10 (1976) 129-160; R. Heather, Comput. Phys. Comm. 63 (1991) 446] for calculating the time-evolution of Dirac wave functions. It allows to study the dynamics of electronic Dirac wave packets under the influence of any number of laser pulses and its interaction with any number of charged ion potentials. The initial wave function can be either a free Gaussian wave packet or an arbitrary discretized spinor function that is loaded from a file provided by the user. The latter option includes Dirac bound state wave functions. The code itself contains the necessary tools for constructing such wave functions for a single-electron ion. With the help of self-adaptive numerical grids, we are able to study the electron dynamics for various problems in 2+1 dimensions at high spatial and temporal resolutions that are otherwise unachievable. Along with the position and momentum space probability density distributions, various physical observables, such as the expectation values of position and momentum, can be recorded in a time-dependent way. The electromagnetic spectrum that is emitted by the evolving particle can also be calculated with this code. Finally, for planning and comparison purposes, both the time-evolution and the emission spectrum can also be treated in an entirely classical relativistic way. Besides the implementation of the above-mentioned algorithms, the program also contains a large C++ class library to model the geometric algebra representation of spinors that we use for representing the Dirac wave function. This is why the code is called "Dirac++". Program summaryProgram title: Dirac++ or (abbreviated) d++ Catalogue identifier: AEAS_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAS_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. The LHCb DIRAC-based production and data management operations systems

    NASA Astrophysics Data System (ADS)

    Stagni, F.; Charpentier, P.; LHCb Collaboration

    2012-06-01

    The LHCb computing model was designed in order to support the LHCb physics program, taking into account LHCb specificities (event sizes, processing times etc...). Within this model several key activities are defined, the most important of which are real data processing (reconstruction, stripping and streaming, group and user analysis), Monte-Carlo simulation and data replication. In this contribution we detail how these activities are managed by the LHCbDIRAC Data Transformation System. The LHCbDIRAC Data Transformation System leverages the workload and data management capabilities provided by DIRAC, a generic community grid solution, to support data-driven workflows (or DAGs). The ability to combine workload and data tasks within a single DAG allows to create highly sophisticated workflows with the individual steps linked by the availability of data. This approach also provides the advantage of a single point at which all activities can be monitored and controlled. While several interfaces are currently supported (including python API and CLI), we will present the ability to create LHCb workflows through a secure web interface, control their state in addition to creating and submitting jobs. To highlight the versatility of the system we present in more detail experience with real data of the 2010 and 2011 LHC run.

  17. The topology and geometry of self-adjoint and elliptic boundary conditions for Dirac and Laplace operators

    NASA Astrophysics Data System (ADS)

    Asorey, M.; Ibort, A.; Marmo, G.

    2015-06-01

    The theory of self-adjoint extensions of first- and second-order elliptic differential operators on manifolds with boundary is studied via its most representative instances: Dirac and Laplace operators. The theory is developed by exploiting the geometrical structures attached to them and, by using an adapted Cayley transform on each case, the space {M} of such extensions is shown to have a canonical group composition law structure. The obtained results are compared with von Neumann's theorem characterizing the self-adjoint extensions of densely defined symmetric operators on Hilbert spaces. The 1D case is thoroughly investigated. The geometry of the submanifold of elliptic self-adjoint extensions {M}ellip is studied and it is shown that it is a Lagrangian submanifold of the universal Grassmannian Gr. The topology of {M}ellip is also explored and it is shown that there is a canonical cycle whose dual is the Maslov class of the manifold. Such cycle, called the Cayley surface, plays a relevant role in the study of the phenomena of topology change. Self-adjoint extensions of Laplace operators are discussed in the path integral formalism, identifying a class of them for which both treatments leads to the same results. A theory of dissipative quantum systems is proposed based on this theory and a unitarization theorem for such class of dissipative systems is proved. The theory of self-adjoint extensions with symmetry of Dirac operators is also discussed and a reduction theorem for the self-adjoint elliptic Grassmannian is obtained. Finally, an interpretation of spontaneous symmetry breaking is offered from the point of view of the theory of self-adjoint extensions.

  18. On a characteristic of the first eigenvalue of the Dirac operator on compact spin symmetric spaces with a Kähler or Quaternion-Kähler structure

    NASA Astrophysics Data System (ADS)

    Milhorat, Jean-Louis

    2015-04-01

    It is shown that on a compact spin symmetric space with a Kähler or Quaternion-Kähler structure, the first eigenvalue of the Dirac operator is linked to a "lowest" action of the holonomy, given by the fiberwise action on spinors of the canonical forms characterized by this holonomy. The result is also verified for the symmetric space F4 /Spin9, proving that it is valid for all the "possible" holonomies in Berger's list occurring in that context. The proof is based on a characterization of the first eigenvalue of the Dirac operator given in Milhorat (2005) and Milhorat (2006). By the way, we review an incorrect statement in the proof of the first lemma in Milhorat (2005).

  19. 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.

  20. 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.

  1. Magnon Dirac materials

    NASA Astrophysics Data System (ADS)

    Fransson, J.; Black-Schaffer, A. M.; Balatsky, A. V.

    2016-08-01

    We demonstrate how a Dirac-like magnon spectrum is generated for localized magnetic moments forming a two-dimensional honeycomb lattice. The Dirac crossing point is proven to be robust against magnon-magnon interactions, as these only shift the spectrum. Local defects induce impurity resonances near the Dirac point, as well as magnon Friedel oscillations. The energy of the Dirac point is controlled by the exchange coupling, and thus a two-dimensional array of magnetic dots is an experimentally feasible realization of Dirac magnons with tunable dispersion.

  2. DIRAC RESTful API

    NASA Astrophysics Data System (ADS)

    Casajus Ramo, A.; Graciani Diaz, R.; Tsaregorodtsev, A.

    2012-12-01

    The DIRAC framework for distributed computing has been designed as a flexible and modular solution that can be adapted to the requirements of any community. Users interact with DIRAC via command line, using the web portal or accessing resources via the DIRAC python API. The current DIRAC API requires users to use a python version valid for DIRAC. Some communities have developed their own software solutions for handling their specific workload, and would like to use DIRAC as their back-end to access distributed computing resources easily. Many of these solutions are not coded in python or depend on a specific python version. To solve this gap DIRAC provides a new language agnostic API that any software solution can use. This new API has been designed following the RESTful principles. Any language with libraries to issue standard HTTP queries may use it. GSI proxies can still be used to authenticate against the API services. However GSI proxies are not a widely adopted standard. The new DIRAC API also allows clients to use OAuth for delegating the user credentials to a third party solution. These delegated credentials allow the third party software to query to DIRAC on behalf of the users. This new API will further expand the possibilities communities have to integrate DIRAC into their distributed computing models.

  3. 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.

  4. 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.

  5. 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.

  6. On the disformal invariance of the Dirac equation

    NASA Astrophysics Data System (ADS)

    Bittencourt, Eduardo; Lobo, Iarley P.; Carvalho, Gabriel G.

    2015-09-01

    We analyze the invariance of the Dirac equation under disformal transformations depending on the propagating spinor field acting on the metric tensor. Using the Weyl-Cartan formalism, we construct a large class of disformal maps between different metric tensors, respecting the order of differentiability of the Dirac operator and satisfying the Clifford algebra in both metrics. We split the analysis in some cases according to the spinor mass and the norm of the Dirac current, exhibiting sufficient conditions to find classes of solutions which keep the Dirac operator invariant under the action of the disformal group.

  7. Qualitative uncertainty principles for the generalized Fourier transform associated to a Dunkl type operator on the real line

    NASA Astrophysics Data System (ADS)

    Mejjaoli, Hatem; Trimèche, Khalifa

    2016-06-01

    In this paper, we prove various mathematical aspects of the qualitative uncertainty principle, including Hardy's, Cowling-Price's theorem, Morgan's theorem, Beurling, Gelfand-Shilov, Miyachi theorems.

  8. 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.

  9. 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)

  10. 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.

  11. Topological Superconductivity in Dirac Semimetals

    NASA Astrophysics Data System (ADS)

    Sato, Masatoshi; Kobayashi, Shingo

    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 Cd3As2.

  12. 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.

  13. 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.

  14. Lagrangians for massive Dirac chiral superfields

    NASA Astrophysics Data System (ADS)

    Jiménez, Enrique; Vaquera-Araujo, C. A.

    2016-06-01

    A variant for the superspin one-half massive superparticle in 4D, N = 1, based on Dirac superfields, is offered. As opposed to the current known models that use spinor chiral superfields, the propagating fields of the supermultiplet are those of the lowest mass dimensions possible: scalar, Dirac and vector fields. Besides the supersymmetric chiral condition, the Dirac superfields are not further constrained, allowing a very straightforward implementation of the path-integral method. The corresponding superpropagators are presented. In addition, an interaction super Yukawa potential, formed by Dirac and scalar chiral superfields, is given in terms of their component fields. The model is first presented for the case of two superspin one-half superparticles related by the charged conjugation operator, but in order to treat the case of neutral superparticles, the Majorana condition on the Dirac superfields is also studied. We compare our proposal with the known models of spinor superfields for the one-half superparticle and show that it is equivalent to them.

  15. Quaternion Dirac Equation and Supersymmetry

    NASA Astrophysics Data System (ADS)

    Rawat, Seema; Negi, O. P. S.

    2009-08-01

    Quaternion Dirac equation has been analyzed and its supersymmetrization has been discussed consistently. It has been shown that the quaternion Dirac equation automatically describes the spin structure with its spin up and spin down components of two component quaternion Dirac spinors associated with positive and negative energies. It has also been shown that the supersymmetrization of quaternion Dirac equation works well for different cases associated with zero mass, nonzero mass, scalar potential and generalized electromagnetic potentials. Accordingly we have discussed the splitting of supersymmetrized Dirac equation in terms of electric and magnetic fields.

  16. On the Chirality of a Discrete Dirac-Kähler Equation

    NASA Astrophysics Data System (ADS)

    Sushch, Volodymyr

    2015-10-01

    We discuss a discrete analogue of the Dirac-Kähler equation in which chiral properties of the continuum counterpart are captured. We pay special attention to a discrete Hodge star operator. To build such an operator combinatorial construction of a double complex is used. We describe discrete exterior calculus operations on a double complex and obtain the discrete Dirac-Kähler equation using these tools. Self-dual and anti-self-dual discrete inhomogeneous forms are presented. The chiral invariance of the massless discrete Dirac-Kähler equation is shown. Moreover, in the massive case we prove that a discrete Dirac-Kähler operator flips the chirality.

  17. Deformation of the Dirac equation

    NASA Astrophysics Data System (ADS)

    Faizal, Mir; Kruglov, Sergey I.

    2016-10-01

    In this paper, we will first clarify the physical meaning of having a minimum measurable time. Then we will combine the deformation of the Dirac equation due to the existence of minimum measurable length and time scales with its deformation due to the doubly special relativity. We will also analyze this deformed Dirac equation in curved spacetime, and observe that this deformation of the Dirac equation also leads to a nontrivial modification of general relativity. Finally, we will analyze the stochastic quantization of this deformed Dirac equation on curved spacetime.

  18. Qualitative analysis of trapped Dirac fermions in graphene

    SciTech Connect

    Jakubský, Vít Krejčiřík, David

    2014-10-15

    We study the confinement of Dirac fermions in graphene and in carbon nanotubes by an external magnetic field, mechanical deformations or inhomogeneities in the substrate. By applying variational principles to the square of the Dirac operator, we obtain sufficient and necessary conditions for confinement of the quasi-particles. The rigorous theoretical results are illustrated on the realistic examples of the three classes of traps.

  19. Effective theory of Dirac dark matter

    SciTech Connect

    Harnik, Roni; Kribs, Graham D.

    2009-05-01

    A stable Dirac fermion with four-fermion interactions to leptons suppressed by a scale {lambda}{approx}1 TeV is shown to provide a viable candidate for dark matter. The thermal relic abundance matches cosmology, while nuclear recoil direct detection bounds are automatically avoided in the absence of (large) couplings to quarks. The annihilation cross section in the early Universe is the same as the annihilation in our Galactic neighborhood. This allows Dirac fermion dark matter to naturally explain the positron ratio excess observed by PAMELA with a minimal boost factor, given present astrophysical uncertainties. We use the Galprop program for propagation of signal and background; we discuss in detail the uncertainties resulting from the propagation parameters and, more importantly, the injected spectra. Fermi/GLAST has an opportunity to see a feature in the gamma-ray spectrum at the mass of the Dirac fermion. The excess observed by ATIC/PPB-BETS may also be explained with Dirac dark matter that is heavy. A supersymmetric model with a Dirac bino provides a viable UV model of the effective theory. The dominance of the leptonic operators, and thus the observation of an excess in positrons and not in antiprotons, is naturally explained by the large hypercharge and low mass of sleptons as compared with squarks. Minimizing the boost factor implies the right-handed selectron is the lightest slepton, which is characteristic of our model. Selectrons (or sleptons) with mass less than a few hundred GeV are an inescapable consequence awaiting discovery at the LHC.

  20. An Effective Theory of Dirac Dark Matter

    SciTech Connect

    Harnik, Roni; Kribs, Graham D.; /Oregon U.

    2010-06-11

    A stable Dirac fermion with four-fermion interactions to leptons suppressed by a scale {Lambda} {approx} 1 TeV is shown to provide a viable candidate for dark matter. The thermal relic abundance matches cosmology, while nuclear recoil direct detection bounds are automatically avoided in the absence of (large) couplings to quarks. The annihilation cross section in the early Universe is the same as the annihilation in our galactic neighborhood. This allows Dirac fermion dark matter to naturally explain the positron ratio excess observed by PAMELA with a minimal boost factor, given present astrophysical uncertainties. We use the Galprop program for propagation of signal and background; we discuss in detail the uncertainties resulting from the propagation parameters and, more importantly, the injected spectra. Fermi/GLAST has an opportunity to see a feature in the gamma-ray spectrum at the mass of the Dirac fermion. The excess observed by ATIC/PPB-BETS may also be explained with Dirac dark matter that is heavy. A supersymmetric model with a Dirac bino provides a viable UV model of the effective theory. The dominance of the leptonic operators, and thus the observation of an excess in positrons and not in anti-protons, is naturally explained by the large hypercharge and low mass of sleptons as compared with squarks. Minimizing the boost factor implies the right-handed selectron is the lightest slepton, which is characteristic of our model. Selectrons (or sleptons) with mass less than a few hundred GeV are an inescapable consequence awaiting discovery at the LHC.

  1. Dirac's Claim and the Chemists

    NASA Astrophysics Data System (ADS)

    Simões, Ana

    In 1929 Paul A. M. Dirac claimed that ``the underlying physical laws necessary for the mathematical theory of ... the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble.'' This sentence of Dirac's is cited frequently by historians and philosophers of chemistry in the context of discussions on the hypothetical reduction of chemistry to physics. But how did chemists themselves react to Dirac's claim? Did they feel threatened by physicists who felt they could do their job better than themselves? Did they feel indifferent, or did they simply not care? Was Dirac's paper often cited by chemists? Why was it cited? In this paper, I provide answers to these questions on the basis of an analysis of citations to Dirac's 1929 paper in the Science Citation Index.

  2. 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.

  3. Symmetry Breaking And The Nilpotent Dirac Equation

    NASA Astrophysics Data System (ADS)

    Rowlands, Peter

    2004-08-01

    A multivariate 4-vector representation for space-time and a quaternion representation for mass and the electric, strong and weak charges leads to a nilpotent form of the Dirac equation, which packages the entire physical information available about a fermion state. The nilpotent state vector breaks the symmetry between the strong, electric and weak interactions, by associating their respective charges with vector, scalar and pseudoscalar operators, leading directly to the SU(3) × SU(2)L × U(1) symmetry, and to particle structures and mass-generating states. In addition, the nilpotent Dirac equation has just three solutions for spherically-symmetric distance-dependent potentials, and these correspond once again to those that would be expected for the three interactions: linear for the strong interaction; inverse linear for the electromagnetic; and a harmonic oscillator-type solution, which can be equated with the dipolar annihilation and creation mechanisms of the weak interaction.

  4. The q-deformed Dirac oscillator in 2 + 1 dimensions

    NASA Astrophysics Data System (ADS)

    Hatami, N.; Setare, M. R.

    2016-10-01

    In this paper we obtain the Hamiltonian of Dirac oscillator in an external magnetic field in terms of q-deformed creation and annihilation operators in 2 + 1 dimensions. For this system, we find coordinate representations of q-deformed creation and annihilation operators, eigenvalues and eigenfunctions. We also construct the lowest Landau levels exactly by applying the q-deformed Dirac annihilation operator to the vacuum state. This system may be considered for the study of graphene in the q-deformed version.

  5. 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.

  6. Time Delay for the Dirac Equation

    NASA Astrophysics Data System (ADS)

    Naumkin, Ivan; Weder, Ricardo

    2016-10-01

    We consider time delay for the Dirac equation. A new method to calculate the asymptotics of the expectation values of the operator {intlimits0 ^{∞}e^{iH0t}ζ(\\vert x\\vert /R) e^{-iH0t}dt}, as {R → ∞}, is presented. Here, H 0 is the free Dirac operator and {ζ(t)} is such that {ζ(t) = 1} for {0 ≤ t ≤ 1} and {ζ(t) = 0} for {t > 1}. This approach allows us to obtain the time delay operator {δ {T}(f)} for initial states f in {{H} 2^{3/2+ɛ}({R}3;{C}4)}, {ɛ > 0}, the Sobolev space of order {3/2+ɛ} and weight 2. The relation between the time delay operator {δ{T}(f)} and the Eisenbud-Wigner time delay operator is given. In addition, the relation between the averaged time delay and the spectral shift function is presented.

  7. Time Delay for the Dirac Equation

    NASA Astrophysics Data System (ADS)

    Naumkin, Ivan; Weder, Ricardo

    2016-07-01

    We consider time delay for the Dirac equation. A new method to calculate the asymptotics of the expectation values of the operator {intlimits0 ^{∞}e^{iH0t}ζ(\\vert x\\vert /R) e^{-iH0t}dt} , as {R → ∞} , is presented. Here, H 0 is the free Dirac operator and {ζ(t)} is such that {ζ(t) = 1} for {0 ≤ t ≤ 1} and {ζ(t) = 0} for {t > 1} . This approach allows us to obtain the time delay operator {δ {T}(f)} for initial states f in {{H} 2^{3/2+ɛ}({R}3;{C}4)} , {ɛ > 0} , the Sobolev space of order {3/2+ɛ} and weight 2. The relation between the time delay operator {δ{T}(f)} and the Eisenbud-Wigner time delay operator is given. In addition, the relation between the averaged time delay and the spectral shift function is presented.

  8. DIRAC: a community grid solution

    NASA Astrophysics Data System (ADS)

    Tsaregorodtsev, A.; Bargiotti, M.; Brook, N.; Ramo, A. C.; Castellani, G.; Charpentier, P.; Cioffi, C.; Closier, J.; Diaz, R. G.; Kuznetsov, G.; Li, Y. Y.; Nandakumar, R.; Paterson, S.; Santinelli, R.; Smith, A. C.; Miguelez, M. S.; Jimenez, S. G.

    2008-07-01

    The DIRAC system was developed in order to provide a complete solution for using the distributed computing resources of the LHCb experiment at CERN for data production and analysis. It allows a concurrent use of over 10K CPUs and 10M file replicas distributed over many tens of sites. The sites can be part of a Computing Grid such as WLCG or standalone computing clusters all integrated in a single management structure. DIRAC is a generic system with the LHCb specific functionality incorporated through a number of plug-in modules. It can be easily adapted to the needs of other communities. Special attention is paid to the resilience of the DIRAC components to allow an efficient use of non-reliable resources. The DIRAC production management components provide a framework for building highly automated data production systems including data distribution and data driven workload scheduling. In this paper we give an overview of the DIRAC system architecture and design choices. We show how different components are put together to compose an integrated data processing system including all the aspects of the LHCb experiment - from the MC production and raw data reconstruction to the final user analysis.

  9. Spectrally isomorphic Dirac systems: Graphene in an electromagnetic field

    NASA Astrophysics Data System (ADS)

    Jakubský, Vít

    2015-02-01

    We construct the new one-dimensional Dirac Hamiltonians that are spectrally isomorphic (not isospectral) with the known exactly solvable models. Explicit formulas for their spectra and eigenstates are provided. The operators are utilized for the description of Dirac fermions in graphene in the presence of an inhomogeneous electromagnetic field. We discuss explicit, physically relevant, examples of spectrally isomorphic systems with both nonperiodic and periodic electromagnetic barriers. In the latter case, spectrally isomorphic two- and three-gap systems associated with the Ablowitz-Kaup-Newell-Segur hierarchy are considered.

  10. Reconstruction of symmetric Dirac-Maxwell equations using nonassociative algebra

    NASA Astrophysics Data System (ADS)

    Kalauni, Pushpa; Barata, J. C. A.

    2015-01-01

    In the presence of sources, the usual Maxwell equations are neither symmetric nor invariant with respect to the duality transformation between electric and magnetic fields. Dirac proposed the existence of magnetic monopoles for symmetrizing the Maxwell equations. In the present work, we obtain the fully symmetric Dirac-Maxwell's equations (i.e. with electric and magnetic charges and currents) as a single equation by using 4 × 4 matrix presentation of fields and derivative operators. This matrix representation has been derived with the help of the algebraic properties of quaternions and octonions. Such description gives a compact representation of electric and magnetic counterparts of the field in a single equation.

  11. 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.

  12. Superconductivity in doped Dirac semimetals

    NASA Astrophysics Data System (ADS)

    Hashimoto, Tatsuki; Kobayashi, Shingo; Tanaka, Yukio; Sato, Masatoshi

    2016-07-01

    We theoretically study intrinsic superconductivity in doped Dirac semimetals. Dirac semimetals host bulk Dirac points, which are formed by doubly degenerate bands, so the Hamiltonian is described by a 4 ×4 matrix and six types of k -independent pair potentials are allowed by the Fermi-Dirac statistics. We show that the unique spin-orbit coupling leads to characteristic superconducting gap structures and d vectors on the Fermi surface and the electron-electron interaction between intra and interorbitals gives a novel phase diagram of superconductivity. It is found that when the interorbital attraction is dominant, an unconventional superconducting state with point nodes appears. To verify the experimental signature of possible superconducting states, we calculate the temperature dependence of bulk physical properties such as electronic specific heat and spin susceptibility and surface state. In the unconventional superconducting phase, either dispersive or flat Andreev bound states appear between point nodes, which leads to double peaks or a single peak in the surface density of states, respectively. As a result, possible superconducting states can be distinguished by combining bulk and surface measurements.

  13. 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

  14. 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.

  15. Dequantization of the Dirac Equation: the Semiclassical Dirac Mechanics.

    NASA Astrophysics Data System (ADS)

    Katz, Alan R.

    1987-09-01

    A relativistic Hamiltonian mechanics for a Dirac particle is derived as the semi-classical limit of the Dirac equation. The theory bears much resemblance to ordinary classical mechanics, except that some of the phase space variables are four by four matrices. This is necessary because of the spin degrees of freedom of the particle. Constraints in the theory connect the four by four matrices with observables. In finding the semi-classical limit of the Dirac equation, we first find it useful to apply a WKB type of approximation to a scalar Superfield theory. By eliminating second class constraints, we obtain the Brink and Schwarz formulation of Casalbuoni's superspace Pseudomechanics. The spin 1/2 sector is then examined to find the corresponding WKB limit of the Dirac equation, a semi-classical mechanics. We next reformulate this Dirac mechanics in terms of ast-products utilizing phase space methods, guided in interpretation by what was obtained via the WKB method. With the formalism in hand, we consider a Dirac particle in a homogeneous electromagnetic field. We are able to demonstrate that the g factor is equal to two, obtain the usual equation of motion for the position and momentum, and are able to DERIVE directly from QED the relativistic spin precession equation of Bargmann, Michel, and Telegdi; an equation originally given as just a simple relativization of the expression for non-relativistic precession. This establishes a vital link between QED theory and what is actually observed in the g - 2 experiments. With this method, we can find a spin precession equation for inhomogeneous fields which contains quantum corrections to the usual equation and we present the general method. Some of these corrections may be easily deduced from gauge invariance, but only if everything is expressed in terms of ast-products, not ordinary products. The equation of motion for any observable is always given as an explicit series in Planck's constant, thus allowing a classical

  16. Meissner Effect of Dirac Electrons in Superconducting State Due to Inter-Band Effect

    NASA Astrophysics Data System (ADS)

    Mizoguchi, Tomonari; Ogata, Masao

    2015-08-01

    Dirac electrons in solids show characteristic physical properties due to their linear dispersion relation and two-band nature. Although the transport phenomena of Dirac electrons in a normal state have intensively been studied, the transport phenomena in a superconducting state have not been fully understood. In particular, it is not clear whether Dirac electrons in a superconducting state show Meissner effect (ME), since a diamagnetic term of a current operator is absent as a result of the linear dispersion. We investigate the ME of three dimensional massive Dirac electrons in a superconducting state on the basis of Kubo formula, and clarify that Meissner kernel becomes finite by use of the inter-band contribution. This mechanism of the ME for Dirac electrons is completely different from that for the electrons in usual metals. Our result shows that the Meissner kernel remains finite even when the superconducting gap vanishes. This is an unavoidable problem in the Dirac electron system as reported in the previous works. Thus, we use a prescription in which we subtract the normal state contribution. In order to justify this prescription, we develop a specific model where the Meissner kernel is obtained by the prescription. We also derive the result for the electron gas by taking the non-relativistic limit of Dirac Hamiltonian, and clarify that the diamagnetic term of the Meissner kernel can be regarded as the inter-band contribution between electrons and positrons in terms of the Dirac model.

  17. 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. PMID:26352476

  18. 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.

  19. DIRAC pilot framework and the DIRAC Workload Management System

    NASA Astrophysics Data System (ADS)

    Casajus, Adrian; Graciani, Ricardo; Paterson, Stuart; Tsaregorodtsev, Andrei; LHCb DIRAC Team

    2010-04-01

    DIRAC, the LHCb community Grid solution, has pioneered the use of pilot jobs in the Grid. Pilot Jobs provide a homogeneous interface to an heterogeneous set of computing resources. At the same time, Pilot Jobs allow to delay the scheduling decision to the last moment, thus taking into account the precise running conditions at the resource and last moment requests to the system. The DIRAC Workload Management System provides one single scheduling mechanism for jobs with very different profiles. To achieve an overall optimisation, it organizes pending jobs in task queues, both for individual users and production activities. Task queues are created with jobs having similar requirements. Following the VO policy a priority is assigned to each task queue. Pilot submission and subsequent job matching are based on these priorities following a statistical approach.

  20. 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.

  1. Parabolic metamaterials and Dirac bridges

    NASA Astrophysics Data System (ADS)

    Colquitt, D. J.; Movchan, N. V.; Movchan, A. B.

    2016-10-01

    A new class of multi-scale structures, referred to as `parabolic metamaterials' is introduced and studied in this paper. For an elastic two-dimensional triangular lattice, we identify dynamic regimes, which corresponds to so-called `Dirac Bridges' on the dispersion surfaces. Such regimes lead to a highly localised and focussed unidirectional beam when the lattice is excited. We also show that the flexural rigidities of elastic ligaments are essential in establishing the `parabolic metamaterial' regimes.

  2. 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.

  3. Dirac and Weyl superconductors in three dimensions.

    PubMed

    Yang, Shengyuan A; Pan, Hui; Zhang, Fan

    2014-07-25

    We introduce the concept of three-dimensional Dirac (Weyl) superconductors (SC), which have protected bulk fourfold (twofold) nodal points and surface Majorana arcs at zero energy. We provide a sufficient criterion for realizing them in centrosymmetric SCs with odd-parity pairing and mirror symmetry. Pairs of Dirac nodes appear in a mirror-invariant plane when the mirror winding number is nontrivial. Breaking mirror symmetry may gap Dirac nodes producing a topological SC. Each Dirac node evolves to a nodal ring when inversion-gauge symmetry is broken, whereas it splits into a pair of Weyl nodes when, and only when, time-reversal symmetry is broken. PMID:25105637

  4. First Experimental Realization of the Dirac Oscillator

    NASA Astrophysics Data System (ADS)

    Franco-Villafañe, J. A.; Sadurní, E.; Barkhofen, S.; Kuhl, U.; Mortessagne, F.; Seligman, T. H.

    2013-10-01

    We present the first experimental microwave realization of the one-dimensional Dirac oscillator, a paradigm in exactly solvable relativistic systems. The experiment relies on a relation of the Dirac oscillator to a corresponding tight-binding system. This tight-binding system is implemented as a microwave system by a chain of coupled dielectric disks, where the coupling is evanescent and can be adjusted appropriately. The resonances of the finite microwave system yield the spectrum of the one-dimensional Dirac oscillator with and without a mass term. The flexibility of the experimental setup allows the implementation of other one-dimensional Dirac-type equations.

  5. 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…

  6. The causal perturbation expansion revisited: Rescaling the interacting Dirac sea

    SciTech Connect

    Finster, Felix; Grotz, Andreas

    2010-07-15

    The causal perturbation expansion defines the Dirac sea in the presence of a time-dependent external field. It yields an operator whose image generalizes the vacuum solutions of negative energy and thus gives a canonical splitting of the solution space into two subspaces. After giving a self-contained introduction to the ideas and techniques, we show that this operator is, in general, not idempotent. We modify the standard construction by a rescaling procedure giving a projector on the generalized negative-energy subspace. The resulting rescaled causal perturbation expansion uniquely defines the fermionic projector in terms of a series of distributional solutions of the Dirac equation. The technical core of the paper is to work out the combinatorics of the expansion in detail. It is also shown that the fermionic projector with interaction can be obtained from the free projector by a unitary transformation. We finally analyze the consequences of the rescaling procedure on the light-cone expansion.

  7. Halogenated arsenenes as Dirac materials

    NASA Astrophysics Data System (ADS)

    Tang, Wencheng; Sun, Minglei; Ren, Qingqiang; Wang, Sake; Yu, Jin

    2016-07-01

    Arsenene is the graphene-like arsenic nanosheet, which has been predicted very recently [S. Zhang, Z. Yan, Y. Li, Z. Chen, and H. Zeng, Angewandte Chemie, 127 (2015) 3155-3158]. Using first-principles calculations, we systematically investigate the structures and electronic properties of fully-halogenated arsenenes. Formation energy analysis reveals that all the fully-halogenated arsenenes except iodinated arsenene are energetically favorable and could be synthesized. We have revealed the presence of Dirac cone in fully-halogenated arsenene compounds. They may have great potential applications in next generation of high-performance devices.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. Field emission from Dirac and Weyl semimetals

    NASA Astrophysics Data System (ADS)

    Mao, Ling-Feng; Li, X.; Ning, H.; Hu, Changjun; Wang, Gaofeng

    2016-09-01

    Based on theoretical investigation on characteristics of the field emission current of Dirac/Weyl semimetals, the dependence of the field emission current on the applied bias is deduced and studied. This theoretical study demonstrates that the field emission current of a Dirac semimetal is much smaller than that of a conventional material when they have similar carrier parameters. This makes Dirac semimetal a better candidate for gate/base electrode material than gold and other conventional metals for an ultra-thin gate oxide metal-oxide-semiconductor field effect transistor. The field emission current of a Dirac semimetal decreases with the effective electron mass, while it increases for a conventional material. This implies that such an effective mass dependence can be used as a simple criterion to probe a Dirac semimetal in practice.

  13. An interpolation between the wave and diffusion equations through the fractional evolution equations Dirac like

    SciTech Connect

    Pierantozzi, T.; Vazquez, L.

    2005-11-01

    Through fractional calculus and following the method used by Dirac to obtain his well-known equation from the Klein-Gordon equation, we analyze a possible interpolation between the Dirac and the diffusion equations in one space dimension. We study the transition between the hyperbolic and parabolic behaviors by means of the generalization of the D'Alembert formula for the classical wave equation and the invariance under space and time inversions of the interpolating fractional evolution equations Dirac like. Such invariance depends on the values of the fractional index and is related to the nonlocal property of the time fractional differential operator. For this system of fractional evolution equations, we also find an associated conserved quantity analogous to the Hamiltonian for the classical Dirac case.

  14. ‘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

  15. Neutrino Masses from a Pseudo-Dirac Bino.

    PubMed

    Coloma, Pilar; Ipek, Seyda

    2016-09-01

    We show that, in U(1)_{R}-symmetric supersymmetric models, the bino and its Dirac partner (the singlino) can play the role of right-handed neutrinos and generate the neutrino masses and mixing, without the need for traditional bilinear or trilinear R-parity violating operators. The two particles form a pseudo-Dirac pair, the "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. PMID:27661681

  16. Simulation of Maxwell-Dirac equations in graphene nanostructures

    NASA Astrophysics Data System (ADS)

    Zhang, Xuecang

    2014-09-01

    In this paper, for the first time, we derive the appropriate form of Maxwell-Dirac equations for simulation of the coupling transport of electromagnetic fields and carriers in graphene nanostructures, and propose a time splitting spectral method for the numerical solution of this multiphysics problem.In this time splitting spectral method, we split each time step into three substeps. In each substep, we split the linear and nonlinear parts of the complicated nonlinear coupling Maxwell-Dirac system, then iteratively solving each simple part by linearizing the nonlinear part. The time derivatives are discretized by finite difference method with second order accuracy schemes. The spatial differential operators are approximated by spectral differentiation matrices. The proposed numerical method is validated by numerical examples that simulate the propagation of electromagnetic wave in graphene nanowaveguides.

  17. Dirac fermions in blue-phosphorus

    NASA Astrophysics Data System (ADS)

    Li, Yuanchang; Chen, Xiaobin

    2014-12-01

    We propose that Dirac cones can be engineered in phosphorene with fourfold-coordinated phosphorus atoms. The key is to separate the energy levels of the in-plane (s, px, and py) and out-of-plane (pz) oribtals through the sp2 configuration, yielding respective σ- and π-character Dirac cones, and then quench the latter. As a proof-of-principle study, we create σ-character Dirac cones in hydrogenated and fluorinated phosphorene with a honeycomb lattice. The obtained Dirac cones are at K-points, slightly anisotropic, with Fermi velocities of 0.91 and 1.23 times that of graphene along the ΓK and KM direction, and maintain good linearity up to ˜2 eV for holes. A substantive advantage of a σ-character Dirac cone is its convenience in tuning the Dirac gap via in-plane strain. Our findings pave the way for development of high-performance electronic devices based on Dirac materials.

  18. 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.

  19. On the Neuberger overlap operator

    NASA Astrophysics Data System (ADS)

    Boriçi, Artan

    1999-04-01

    We compute Neuberger's overlap operator by the Lanczos algorithm applied to the Wilson-Dirac operator. Locality of the operator for quenched QCD data and its eigenvalue spectrum in an instanton background are studied.

  20. Dirac equation on a curved surface

    NASA Astrophysics Data System (ADS)

    Brandt, F. T.; Sánchez-Monroy, J. A.

    2016-09-01

    The dynamics of Dirac particles confined to a curved surface is examined employing the thin-layer method. We perform a perturbative expansion to first-order and split the Dirac field into normal and tangential components to the surface. In contrast to the known behavior of second order equations like Schrödinger, Maxwell and Klein-Gordon, we find that there is no geometric potential for the Dirac equation on a surface. This implies that the non-relativistic limit does not commute with the thin-layer method. Although this problem can be overcome when second-order terms are retained in the perturbative expansion, this would preclude the decoupling of the normal and tangential degrees of freedom. Therefore, we propose to introduce a first-order term which rescues the non-relativistic limit and also clarifies the effect of the intrinsic and extrinsic curvatures on the dynamics of the Dirac particles.

  1. Leptogenesis origin of Dirac gaugino dark matter

    SciTech Connect

    Chun, Eung Jin

    2011-03-01

    The Dirac nature of the gauginos (and also the Higgsinos) can be realized in R-symmetric supersymmetry models. In this class of models, the Dirac bino (or wino) with a small mixture of the Dirac Higgsinos is a good dark matter candidate. When the seesaw mechanism with Higgs triplet superfields is implemented to account for the neutrino masses and mixing, the leptogenesis driven by the heavy triplet decay is shown to produce not only the matter-antimatter asymmetry, but also the asymmetric relic density of the Dirac gaugino dark matter. The dark matter mass turns out to be controlled by the Yukawa couplings of the heavy Higgs triplets, and it can be naturally at the weak scale for a mild hierarchy of the Yukawa couplings.

  2. Lepton flavor violation and supersymmetric Dirac leptogenesis

    SciTech Connect

    Thomas, Brooks; Toharia, Manuel

    2007-01-01

    Dirac leptogenesis (or Dirac neutrinogenesis), in which neutrinos are purely Dirac particles, is an interesting alternative to the standard leptogenesis scenario. In its supersymmetric version, the modified form of the superpotential required for successful baryogenesis contributes new, generically nonflavor-diagonal terms to the slepton and sneutrino mass matrices. In this work, we examine how current experimental bounds on flavor-changing effects in the lepton sector (and particularly the bound on {mu}{yields}e{gamma}) constrain Dirac leptogenesis and we find that it is capable of succeeding with superpartner masses as low as {approx}100 GeV. For such light scalars and electroweakinos, upcoming experiments such as MEG are generically expected to observe signals of lepton flavor violation.

  3. 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.

  4. 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.

  5. 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.

  6. Some chirality-related properties of the 4D massive Dirac propagator and determinant in an arbitrary gauge field

    SciTech Connect

    Hur, Jin; Lee, Choonkyu; Min, Hyunsoo

    2010-10-15

    For a 4D massive Dirac field in the background of arbitrary gauge fields, we show that the Dirac propagator and functional determinant are completely determined by knowledge of the corresponding quantities for just one of the chirality sectors of the second-order Dirac operator. This generalizes the related, previously known, statements in (anti)self-dual background gauge fields. The logarithms of the (renormalized) functional determinants from the two chirality sectors are shown to be different only by a term reflecting the integrated chiral anomaly.

  7. 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.

  8. 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

  9. 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.

  10. 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.

  11. 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.

  12. Phase transitions of Dirac electrons in bismuth.

    PubMed

    Li, Lu; Checkelsky, J G; Hor, Y S; Uher, C; Hebard, A F; Cava, R J; Ong, N P

    2008-07-25

    The Dirac Hamiltonian, which successfully describes relativistic fermions, applies equally well to electrons in solids with linear energy dispersion, for example, in bismuth and graphene. A characteristic of these materials is that a magnetic field less than 10 tesla suffices to force the Dirac electrons into the lowest Landau level, with resultant strong enhancement of the Coulomb interaction energy. Moreover, the Dirac electrons usually come with multiple flavors or valley degeneracy. These ingredients favor transitions to a collective state with novel quantum properties in large field. By using torque magnetometry, we have investigated the magnetization of bismuth to fields of 31 tesla. We report the observation of sharp field-induced phase transitions into a state with striking magnetic anisotropy, consistent with the breaking of the threefold valley degeneracy. PMID:18653888

  13. Asymptotic formula for eigenvalues of one dimensional Dirac system

    NASA Astrophysics Data System (ADS)

    Ulusoy, Ismail; Penahlı, Etibar

    2016-06-01

    In this paper, we study the spectral problem for one dimensional Dirac system with Dirichlet boundary conditions. By using Counting lemma, we give an asymptotic formulas of eigenvalues of Dirac system.

  14. 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.

  15. Dirac equations for generalised Yang-Mills systems

    NASA Astrophysics Data System (ADS)

    Lechtenfeld, O.; Nahm, W.; Tchrakian, D. H.

    1985-11-01

    We present Dirac equations in 4 p dimensions for the generalised Yang-Mills (GYM) theories introduced earlier. These Dirac equations are related to the self-duality equations of the GYM and are checked to be elliptic in a “BPST” background. In this background these Dirac equations are integrated exactly. The possibility of imposing supersymmetry in the GYM-Dirac system is investigated, with negative results.

  16. Spin eigen-states of Dirac equation for quasi-two-dimensional electrons

    SciTech Connect

    Eremko, Alexander; Brizhik, Larissa; Loktev, Vadim

    2015-10-15

    Dirac equation for electrons in a potential created by quantum well is solved and the three sets of the eigen-functions are obtained. In each set the wavefunction is at the same time the eigen-function of one of the three spin operators, which do not commute with each other, but do commute with the Dirac Hamiltonian. This means that the eigen-functions of Dirac equation describe three independent spin eigen-states. The energy spectrum of electrons confined by the rectangular quantum well is calculated for each of these spin states at the values of energies relevant for solid state physics. It is shown that the standard Rashba spin splitting takes place in one of such states only. In another one, 2D electron subbands remain spin degenerate, and for the third one the spin splitting is anisotropic for different directions of 2D wave vector.

  17. Analytical Solution to the Dirac Equation for Few-Electron Ions of Transuranium Elements

    NASA Astrophysics Data System (ADS)

    Ulyanov, Anton S.; Sadovoy, Alexander A.

    2014-08-01

    The paper presents relativistic generalization of the well-known method of multidimensional angular Coulomb functions. Two-component multidimensional angular functions have been constructed and they are used as a basis for expanding in series the many- electron wave function of the many-particle Dirac equation. A system of ordinary differential equations which factors are expressed in terms of matrix elements of various operators of the Dirac equation has been obtained for the expansion amplitudes. The binding energy of helium-, lithium-, beryllium- and carbon-like ions of transuranium elements has been calculated (Z = 92-101). Wave functions have been constructed for some states of transuranium ions. The developed method allows taking into account the many-particle effects during the calculation of relativistic many-electron systems which are described by the manyparticle Dirac equation with Coulomb interactions. The obtained results can be applied to specify the probability of transitions and particle paths in high energydensity processes.

  18. Ground state and the spin precession of the Dirac electron in counterpropagating plane electromagnetic waves

    NASA Astrophysics Data System (ADS)

    Borzdov, G. N.

    2016-06-01

    The fundamental solution of the Dirac equation for an electron in an electromagnetic field with harmonic dependence on space-time coordinates is obtained. The field is composed of three standing plane harmonic waves with mutually orthogonal phase planes and the same frequency. Each standing wave consists of two eigenwaves with different complex amplitudes and opposite directions of propagation. The fundamental solution is obtained in the form of the projection operator defining the subspace of solutions to the Dirac equation. It is illustrated by the analysis of the ground state and the spin precession of the Dirac electron in the field of two counterpropagating plane waves with left and right circular polarizations. Interrelations between the fundamental solution and approximate partial solutions is discussed and a criterion for evaluating the accuracy of approximate solutions is suggested.

  19. A short biography of Paul A. M. Dirac and historical development of Dirac delta function

    NASA Astrophysics Data System (ADS)

    Debnath, Lokenath

    2013-12-01

    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 spin and helicity of electrons. Special attention is given to Dirac's original visionary work on the existence of the magnetic monopole, and on his Large Number Hypothesis that led to the conclusion that physical quantities universally considered as constant of nature are not really constants, but they vary with cosmological time. Some concluding remarks with personal reminiscence are added in the end of the paper.

  20. 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…

  1. Theory and phenomenology of Dirac leptogenesis

    NASA Astrophysics Data System (ADS)

    Thomas, Brooks D.

    2007-07-01

    Dirac leptogenesis, in which neutrinos are purely Dirac and develop small but nonzero effective masses without the aid of the see-saw mechanism, provides an interesting alternative to the standard leptogenesis picture. Here we review the theory and phenomenology of Dirac leptogenesis and show that it is a viable theory capable of simultaneously satisfying all relevant bounds from cosmology, neutrino physics, and flavor violation. In addition, we also explore several potential extensions of the model, such as the possibility of right-handed sneutrino dark matter and the potential for relating the leptogenesis mechanism to the origin of the mu-term. Theories with a heavy gravitino and gaugino masses generated by anomaly mediation emerge as one natural context for Dirac leptogenesis. In such models the lightest neutralino is often expected to be predominately wino or Higgsino, and is a viable dark matter candidate. We conclude with an examination of the prospects for detecting the effectively monoenergetic photon signal that results from the annihilation of such a dark matter particle in the galactic halo.

  2. Quantum simulation of the Dirac equation.

    PubMed

    Gerritsma, R; Kirchmair, G; Zähringer, F; Solano, E; Blatt, R; Roos, C F

    2010-01-01

    The Dirac equation successfully merges quantum mechanics with special relativity. It provides a natural description of the electron spin, predicts the existence of antimatter and is able to reproduce accurately the spectrum of the hydrogen atom. The realm of the Dirac equation-relativistic quantum mechanics-is considered to be the natural transition to quantum field theory. However, the Dirac equation also predicts some peculiar effects, such as Klein's paradox and 'Zitterbewegung', an unexpected quivering motion of a free relativistic quantum particle. These and other predicted phenomena are key fundamental examples for understanding relativistic quantum effects, but are difficult to observe in real particles. In recent years, there has been increased interest in simulations of relativistic quantum effects using different physical set-ups, in which parameter tunability allows access to different physical regimes. Here we perform a proof-of-principle quantum simulation of the one-dimensional Dirac equation using a single trapped ion set to behave as a free relativistic quantum particle. We measure the particle position as a function of time and study Zitterbewegung for different initial superpositions of positive- and negative-energy spinor states, as well as the crossover from relativistic to non-relativistic dynamics. The high level of control of trapped-ion experimental parameters makes it possible to simulate textbook examples of relativistic quantum physics. PMID:20054392

  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. On solvable Dirac equation with polynomial potentials

    SciTech Connect

    Stachowiak, Tomasz

    2011-01-15

    One-dimensional Dirac equation is analyzed with regard to the existence of exact (or closed-form) solutions for polynomial potentials. The notion of Liouvillian functions is used to define solvability, and it is shown that except for the linear potentials the equation in question is not solvable.

  6. The GridPP DIRAC project - DIRAC for non-LHC communities

    NASA Astrophysics Data System (ADS)

    Bauer, D.; Colling, D.; Currie, R.; Fayer, S.; Huffman, A.; Martyniak, J.; Rand, D.; Richards, A.

    2015-12-01

    The GridPP consortium in the UK is currently testing a multi-VO DIRAC service aimed at non-LHC VOs. These VOs (Virtual Organisations) are typically small and generally do not have a dedicated computing support post. The majority of these represent particle physics experiments (e.g. NA62 and COMET), although the scope of the DIRAC service is not limited to this field. A few VOs have designed bespoke tools around the EMI-WMS & LFC, while others have so far eschewed distributed resources as they perceive the overhead for accessing them to be too high. The aim of the GridPP DIRAC project is to provide an easily adaptable toolkit for such VOs in order to lower the threshold for access to distributed resources such as Grid and cloud computing. As well as hosting a centrally run DIRAC service, we will also publish our changes and additions to the upstream DIRAC codebase under an open-source license. We report on the current status of this project and show increasing adoption of DIRAC within the non-LHC communities.

  7. 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. PMID:21041227

  8. Two-body Dirac equations for meson spectroscopy

    NASA Astrophysics Data System (ADS)

    Crater, Horace W.; van Alstine, Peter

    1988-04-01

    Recently we used Dirac's constraint mechanics and supersymmetries to derive two coupled compatible 16-component Dirac equations that govern two relativistic spinning particles interacting through world scalar and vector potentials. They reduce exactly to four decoupled four-component local Schrödinger-like equations with energy-dependent quasipotentials Φw. Their nonperturbative covariant structure [leading to perturbative and O(1/c2) expansions that agree with field-theoretic approaches] suit these equations ideally for phenomenological applications in which the potentials have some links with relativistic field theories. (These equations are exactly solvable for singlet positronium producing a spectrum correct through order α4.) Here we use our equations to extend the validity of various one- or two-parameter models for the heavy-quark static potential to the relativistic light-quark regime. These models include the leading-log model (for all length scales) of Adler and Piran and Richardson's potential modified by flavor-dependent vacuum corrections. They significantly improve the good results that we obtained using Richardson's potential alone. Both nonperturbative and perturbative properties of the constraint approach are responsible for the spin-dependent consequences of the potential that result in a good overall fit to the meson masses. The nonperturbative structure dictated by the compatibility of our two Dirac equations enforces an approximate chiral symmetry that may account for the goodness of our pion fit. Perturbatively, for weak potentials, the upper-upper components of our equations reduce to the appropriate Todorov equation and then for low velocities to the Breit Hamiltonian. Thus, our approach reproduces the semirelativistic spin-dependent consequences of a quantum field theory. We strengthen this connection by deriving the Todorov inhomogeneous quasipotential equation for Φw from the Bethe-Salpeter equation using an operator generalization of

  9. 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.

  10. 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

  11. Plexciton Dirac points and topological modes

    NASA Astrophysics Data System (ADS)

    Yuen-Zhou, Joel; Saikin, Semion K.; Zhu, Tony; Onbasli, Mehmet C.; Ross, Caroline A.; Bulovic, Vladimir; Baldo, Marc A.

    2016-06-01

    Plexcitons are polaritonic modes that result from the strong coupling between excitons and plasmons. Here, we consider plexcitons emerging from the interaction of excitons in an organic molecular layer with surface plasmons in a metallic film. We predict the emergence of Dirac cones in the two-dimensional band-structure of plexcitons due to the inherent alignment of the excitonic transitions in the organic layer. An external magnetic field opens a gap between the Dirac cones if the plexciton system is interfaced with a magneto-optical layer. The resulting energy gap becomes populated with topologically protected one-way modes, which travel at the interface of this plexcitonic system. Our theoretical proposal suggests that plexcitons are a convenient and simple platform for the exploration of exotic phases of matter and for the control of energy flow at the nanoscale.

  12. 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

  13. 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.

  14. 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.

  15. 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.

  16. Plexciton Dirac points and topological modes.

    PubMed

    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

  17. Plexciton Dirac points and topological modes

    DOE PAGESBeta

    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 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

  18. 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.

  19. Dynamical seesaw mechanism for Dirac neutrinos

    NASA Astrophysics Data System (ADS)

    Valle, José W. F.; Vaquera-Araujo, C. A.

    2016-04-01

    So far we have not been able to establish that, as theoretically expected, neutrinos are their own anti-particles. Here we propose a dynamical way to account for the Dirac nature of neutrinos and the smallness of their mass in terms of a new variant of the seesaw paradigm in which the energy scale of neutrino mass generation could be accessible to the current LHC experiments.

  20. Iterative solutions to the Dirac equation

    SciTech Connect

    Ciftci, Hakan; Hall, Richard L.; Saad, Nasser

    2005-08-15

    We consider a single particle which is bound by a central potential and obeys the Dirac equation in d dimensions. We first apply the asymptotic iteration method to recover the known exact solutions for the pure Coulomb case. For a screened Coulomb potential and for a Coulomb plus linear potential with linear scalar confinement, the method is used to obtain accurate approximate solutions for both eigenvalues and wave functions.

  1. Dirac particle in a pseudoscalar potential

    SciTech Connect

    Moreno, Matias; Zentella-Dehesa, Arturo

    1996-02-20

    We study the problem of a Dirac particle with a pseudoscalar interaction in the potential approximation. It is shown how nonperturbative relativistic solutions arise. The case of the central pseudoscalar potential is explicitly worked out also in a closed form. The angular functions are worked out in general for this central case. Finally for the special case of the spherical well the radial solutions are shown to behave like Bessel-type functions.

  2. Dirac particle in a pseudoscalar potential

    SciTech Connect

    Moreno, M.; Zentella-Dehesa, A.

    1996-02-01

    We study the problem of a Dirac particle with a pseudoscalar interaction in the potential approximation. It is shown how nonperturbative relativistic solutions arise. The case of the central pseudoscalar potential is explicitly worked out also in a closed form. The angular functions are worked out in general for this central case. Finally for the special case of the spherical well the radial solutions are shown to behave like Bessel-type functions. {copyright} {ital 1996 American Institute of Physics.}

  3. Manipulation of Dirac Cones in Mechanical Graphene.

    PubMed

    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

  4. 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.

  5. 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.

  6. 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

  7. 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

  8. 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.

  9. Pseudo-Dirac Dark Matter Leaves a Trace

    SciTech Connect

    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.

  10. The GridPP DIRAC project: Implementation of a multi-VO DIRAC service

    NASA Astrophysics Data System (ADS)

    Bauer, D.; Colling, D.; Currie, R.; Fayer, S.; Huffman, A.; Martyniak, J.; Rand, D.; Richards, A.

    2015-12-01

    The GridPP consortium provides computing support to many high energy physics projects in the UK. As part of this GridPP offers access to a large amount of highly distributed resources across the UK for multiple collaborations. The userbase supported by GridPP includes hundreds of users spanning multiple virtual organisations with many different computing requirements. In order to provide a common interface to these distributed a centralised DIRAC instance has been setup at Imperial College London. This paper describes the experiences learnt from deploying this DIRAC instance and the modifications that have made to support the GridPP use case.

  11. Flat photonic surface bands pinned between Dirac points.

    PubMed

    Jukić, Dario; Buljan, Hrvoje; Lee, Dung-Hai; Joannopoulos, John D; Soljačić, Marin

    2012-12-15

    We point out that 2D photonic crystals (PhCs) can support surface bands that are pinned to Dirac points. These bands can be made very flat by optimizing the parameters of the system. Surface modes are found at the interface of two different cladding materials: one is a PhC with Dirac linear dispersion for the TE mode, and the other is a PhC that has a broad TE gap at the Dirac frequency. PMID:23258072

  12. Supersymmetrization of Quaternion Dirac Equation for Generalized Fields of Dyons

    NASA Astrophysics Data System (ADS)

    Rawat, A. S.; Rawat, Seema; Li, Tianjun; Negi, O. P. S.

    2012-10-01

    The quaternion Dirac equation in presence of generalized electromagnetic field has been discussed in terms of two gauge potentials of dyons. Accordingly, the supersymmetry has been established consistently and thereafter the one, two and component Dirac Spinors of generalized quaternion Dirac equation of dyons for various energy and spin values are obtained for different cases in order to understand the duality invariance between the electric and magnetic constituents of dyons.

  13. Wave Function of the Dirac Equation for an Electron in the Field of a Nucleus Expressed in Terms of an Eigenfunction of the Spin Projection Operator and a Wave Function of the Schrödinger Equation. Radiative Processes of a Hydrogen-Like Atom and Selection Rules

    NASA Astrophysics Data System (ADS)

    Skobelev, V. V.

    2016-05-01

    A solution of the Dirac equation for an electron in the field of a point nucleus (Ze), expressed in terms of an eigenfunction of the operator of the spin projection onto the third axis and the corresponding solution of the Schrödinger equation is derived. This solution is suitable for practical calculations. On the basis of this solution, using ordinary methods of QED and field theory, general principles for the emission of photons, axions, and neutrinos {(Ze)}^{*}to (Ze)+γ, a, voverline{v} by a hydrogen-like atom are formulated which take into account the spin state of the electron and, in the case of photons, their polarization. This range of questions pertaining to a comparative characteristic of processes of emission of massless or almost massless particles has, to this day, not been discussed from this point of view in the literature. Selection rules for γ, a,voverline{v} emission processes are also obtained, where for axions and neutrinos they coincide with the existing selection rules in the literature ∆m = 0,±1; with ∆l = ±1 pertaining to photons, but for photon emission a few of them do in fact differ from them with the hypothesis of odd values of ∆l, not established by us and additional to the usual values ∆l = ±1 of variation of the azimuthal quantum number l due to the appearance of "new" integrals over the spherical angle θ for ∆m = ±1, where for ∆m = 0, as before, ∆l = ±1. Moreover, the dependence of the amplitude of the photon emission process on the quantum numbers is in principle different than in the previously adopted approach to the problem although the lifetime in the excited state for small values of the quantum numbers coincides in order of magnitude with the accepted value 10-9 s.

  14. Exact parapositroniumlike solution to two-body Dirac equations

    NASA Astrophysics Data System (ADS)

    van Alstine, Peter; Crater, Horace

    1986-09-01

    Recently we used a supersymmetric version of Dirac's constraint mechanics to derive coupled Dirac equations for a quark and antiquark in mutual chromodynamiclike interaction. Here we investigate the properties of our equations for two spinning particles in mutual electromagneticlike interaction. In the chiral Dirac matrix representation we explicitly obtain a family of exact 16-component solutions with closed-form energy spectrum that agrees with that of parapositronium through order α4. We also find that various rearrangements of our Dirac equations simultaneously yield (for weak potentials) the relativistic wave equations of Todorov and Pilkuhn as well as (for weak potentials and slow motion) the semirelativistic interaction structure of Breit.

  15. Physical account of Weyl anomaly from Dirac Sea

    NASA Astrophysics Data System (ADS)

    Habara, Yoshinobu; Nielsen, Holger B.; Ninomiya, Masao

    2015-09-01

    We rederive in a physical manner the Weyl anomaly in two-dimensional space-time by considering the Dirac Sea. It is regularized by some bosonic extra species which are formally negatively counted. In fact, we calculate the trace of the energy-momentum tensor in the Dirac Sea in presence of background gravitational field. It has to be regularized, since the Dirac Sea is bottomless and thus causes divergence. The new regularization method consists in adding various massive bosonic species some of which are to be counted negative in the Dirac Sea. The mass terms in the Lagrangian of the regularization fields have a dependence on the background gravitational field.

  16. 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.

  17. Consistency of multi-time Dirac equations with general interaction potentials

    NASA Astrophysics Data System (ADS)

    Deckert, Dirk-André; Nickel, Lukas

    2016-07-01

    In 1932, Dirac proposed a formulation in terms of multi-time wave functions as candidate for relativistic many-particle quantum mechanics. A well-known consistency condition that is necessary for existence of solutions strongly restricts the possible interaction types between the particles. It was conjectured by Petrat and Tumulka that interactions described by multiplication operators are generally excluded by this condition, and they gave a proof of this claim for potentials without spin-coupling. Under suitable assumptions on the differentiability of possible solutions, we show that there are potentials which are admissible, give an explicit example, however, show that none of them fulfills the physically desirable Poincaré invariance. We conclude that in this sense, Dirac's multi-time formalism does not allow to model interaction by multiplication operators, and briefly point out several promising approaches to interacting models one can instead pursue.

  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. Cosmic String Global Superconducting Dirac Born Infeld

    NASA Astrophysics Data System (ADS)

    Ikrima, Ika; Ramadhan, Handhika S.; Mart, Terry

    2016-08-01

    Superconducting cosmic string possibly plays an important role in the formation of the universe structure. The physics of this phenomenon has been explored by studying the field theory in the string interior. Numerical solutions of superconducting strings with all relevant fields are presented in this paper. The field is constructed from a generalization of the usual field theory of superconducting global string, but the kinetic term consists of the Dirac Born Infeld (DBI). Some changes in the characteristic of the superconducting string DBI from the usual superconducting string case have been observed. The observation includes physical mechanism of all related fields.

  20. 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.

  1. The Dirac Operator on Generalized Taub-NUT Spaces

    NASA Astrophysics Data System (ADS)

    Moroianu, Andrei; Moroianu, Sergiu

    2011-08-01

    We find sufficient conditions for the absence of harmonic L 2 spinors on spin manifolds constructed as cone bundles over a compact Kähler base. These conditions are fulfilled for certain perturbations of the Euclidean metric, and also for the generalized Taub-NUT metrics of Iwai-Katayama, thus proving a conjecture of Vişinescu and the second author.

  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. Dirac oscillator and nonrelativistic Snyder-de Sitter algebra

    NASA Astrophysics Data System (ADS)

    Stetsko, M. M.

    2015-01-01

    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.

  4. Strong topological metal material with multiple Dirac cones

    NASA Astrophysics Data System (ADS)

    Ji, Huiwen; Pletikosić, I.; Gibson, Q. D.; Sahasrabudhe, Girija; Valla, T.; Cava, R. J.

    2016-01-01

    We report a new, cleavable, strong topological metal, Zr2Te2P , which has the same tetradymite-type crystal structure as the topological insulator B i2T e2Se . 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 Bi O2 . 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. Strong topological metal material with multiple Dirac cones

    DOE PAGESBeta

    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 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

  7. 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.…

  8. Decay of Dirac hair around a dilaton black hole

    SciTech Connect

    Gibbons, Gary W.; Rogatko, Marek

    2008-02-15

    The intermediate and late-time behavior of a massive Dirac field in the background of static spherically symmetric dilaton black hole solutions is investigated. The intermediate asymptotic behavior of a massive Dirac field depends on the mass parameter as well as the wave number of the mode, while the late-time behavior has a power-law decay rate independent of both.

  9. 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.

  10. Floquet-Engineered Valleytronics in Dirac Systems

    NASA Astrophysics Data System (ADS)

    Seradjeh, Babak; Kundu, Arijit; Fertig, Herbert

    Valley degrees of freedom offer a potential resource for quantum information processing if they can be effectively controlled. We discuss an optical approach to this problem in which intense light breaks electronic symmetries of a two-dimensional Dirac material. The resulting quasienergy structures may then differ for different valleys, so that the Floquet physics of the system can be exploited to produce highly polarized valley currents. This physics can be utilized to realize a valley valve whose behavior is determined optically. We propose a concrete way to achieve such valleytronics in graphene as well as in a simple model of an inversion-symmetry broken Dirac material, such as monolayer transition-metal dichalcogenides. Simulating the system numerically, we find that the effect is robustness against moderate disorder and small deviations in optical parameters. We also study designs for coherent manipulation of valley degrees of freedom suitable for quantum information processing. This work was supported in part by the NSF through Grant Nos. DMR-1350663 and DMR-1506460, the US-Israel Binational Science Foundation, and by Indiana University.

  11. Quasi-Dirac neutrinos at the LHC

    NASA Astrophysics Data System (ADS)

    Anamiati, G.; Hirsch, M.; Nardi, E.

    2016-10-01

    Lepton number violation is searched for at the LHC using same-sign leptons plus jets. The standard lore is that the ratio of same-sign lepton to opposite-sign lepton events, R ll , is equal to R ll = 1 ( R ll = 0) for Majorana (Dirac) neutrinos. We clarify under which conditions the ratio R ll can assume values different from 0 and 1, and we argue that the precise value 0 < R ll < 1 is controlled by the mass splitting versus the width of the quasi-Dirac resonances. A measurement of R ll = 0 , 1 would then contain valuable information about the origin of neutrino masses. We consider as an example the inverse seesaw mechanism in a left-right symmetric scenario, which is phenomenologically particularly interesting since all the heavy states in the high energy completion of the model could be within experimental reach. A prediction of this scenario is a correlation between the values of R ll and the ratio between the rates for heavy neutrino decays into standard model gauge bosons, and into three body final states ljj mediated by off-shell W R exchange.

  12. Dirac particle, gravity, and inertial effects

    NASA Astrophysics Data System (ADS)

    Huang, Justin C.

    Dirac's equation with gravity for a noninertial observer is derived using local coordinate methods. Calculations for the equation are carried out to second order in the local coordinates. For easy application to interference experiments, the Schrödinger form of the Dirac equation with a well defined Hamiltonian in the local coordinates is presented. The presence of gravitational weighting factors in the scalar product lead to hermitian and antihermitian sectors for the Hamiltonian. The antihermitian part depends directly on the curvature and vanishes for zero curvature. The hermitian part which is important for the determination of phases is studied in detail and the nonrelativistic case is obtained by the application of three successive Foldy-Wouthuysen transformations. The results also give local currents and interactions which have pure inertial, pure gravity and mixed sectors. The pure inertial terms are the ones obtained by Hehl and Ni. The pure gravity and mixed sectors have contributions which are electric, magnetic and double magnetic in character. The focus is on the curvature contributions. Some are well within reach of the anticipated accuracy of atomic interferometers currently under consideration and other terms may follow if improvements can be made.

  13. 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.

  14. Abnormal Dirac point shift in graphene field-effect transistors

    NASA Astrophysics Data System (ADS)

    Wang, Shaoqing; Jin, Zhi; Huang, Xinnan; Peng, Songang; Zhang, Dayong; Shi, Jingyuan

    2016-09-01

    The shift of Dirac point in graphene devices is of great importance, influencing the reliability and stability. Previous studies show the Dirac point shifts slightly to be more positive when the drain bias increases. Here, an abnormal shift of Dirac point is observed in monolayer graphene field effect transistors by investigating the transfer curves under various drain biases. The voltage of Dirac point shifts positively at first and then decreases rapidly when the channel electric field exceeds some threshold. The negative Dirac point shift is attributed to holes injection into oxide layer and captured by the oxide traps under high channel electric field. This can also be demonstrated through a simple probability model and the graphene Raman spectra before and after the DC measurement.

  15. Photoinduced Chern insulating states in semi-Dirac materials

    NASA Astrophysics Data System (ADS)

    Saha, Kush

    2016-08-01

    Two-dimensional (2D) semi-Dirac materials are characterized by a quadratic dispersion in one direction and a linear dispersion along the orthogonal direction. We study the topological phase transition in such 2D systems in the presence of an electromagnetic field. We show that a Chern insulating state emerges in a semi-Dirac system with two gapless Dirac nodes in the presence of light. In particular, we show that the intensity of a circularly polarized light can be used as a knob to generate topological states with nonzero Chern number. In addition, for fixed intensity and frequency of the light, a semi-Dirac system with two gapped Dirac nodes with trivial band topology can reveal the topological transition as a function of polarization of the light.

  16. 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.

  17. Z2 and Chiral Anomalies in Topological Dirac Semimetals

    NASA Astrophysics Data System (ADS)

    Burkov, Anton A.; Kim, Yong Baek

    2016-09-01

    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 Z2 anomaly, is a consequence of the fact that the Dirac nodes in topological Dirac semimetals carry a Z2 topological charge. The Z2 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 Na3Bi .

  18. Spin-foam fermions: PCT symmetry, Dirac determinant and correlation functions

    NASA Astrophysics Data System (ADS)

    Han, Muxin; Rovelli, Carlo

    2013-04-01

    We discuss fermion coupling in the framework of spin-foam quantum gravity. We analyze the gravity-fermion spin-foam model and its fermion correlation functions. We show that there is a spin-foam analogue of PCT symmetry for the fermion fields on a spin-foam model, which is proved for spin-foam fermion correlation functions. We compute the determinant of the Dirac operator for the fermions, where two presentations of the Dirac determinant are given in terms of diagram expansions. We compute the fermion correlation functions and show that they can be given by Feynman diagrams on the spin-foams, where the Feynman propagators can be represented by a discretized path integral of a world-line action along the edges of the underlying 2-complex.

  19. 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.

  20. Separability of a modified Dirac equation in a five-dimensional rotating, charged black hole in string theory

    SciTech Connect

    Wu Shuangqing

    2009-08-15

    The aim of this paper is to investigate the separability of a spin-1/2 spinor field in a five-dimensional rotating, charged black hole constructed by Cvetic and Youm in string theory, in the case when three U(1) charges are set equal. This black hole solution represents a natural generalization of the famous four-dimensional Kerr-Newman solution to five dimensions with the inclusion of a Chern-Simons term to the Maxwell equation. It is shown that the usual Dirac equation cannot be separated by variables in this general spacetime with two independent angular momenta. However if one supplements an additional counterterm into the usual Dirac operator, then the modified Dirac equation for the spin-1/2 spinor particles is separable in this rotating, charged Einstein-Maxwell-Chern-Simons black hole background geometry. A first-order symmetry operator that commutes with the modified Dirac operator has exactly the same form as that previously found in the uncharged Myers-Perry black hole case. It is expressed in terms of a rank-three totally antisymmetric tensor and its covariant derivative. This tensor obeys a generalized Killing-Yano equation and its square is a second-order symmetric Staeckel-Killing tensor admitted by the five-dimensional rotating, charged black hole spacetime.

  1. 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

  2. Dirac node arcs in PtSn4

    DOE PAGESBeta

    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 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. 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.

  4. Bosonic Analogue of Dirac Composite Fermi Liquid

    NASA Astrophysics Data System (ADS)

    Mross, David F.; Alicea, Jason; Motrunich, Olexei I.

    2016-09-01

    We introduce a particle-hole-symmetric metallic state of bosons in a magnetic field at odd-integer filling. This state hosts composite fermions whose energy dispersion features a quadratic band touching and corresponding 2 π Berry flux protected by particle-hole and discrete rotation symmetries. We also construct an alternative particle-hole symmetric state—distinct in the presence of inversion symmetry—without Berry flux. As in the Dirac composite Fermi liquid introduced by Son [Phys. Rev. X 5, 031027 (2015)], breaking particle-hole symmetry recovers the familiar Chern-Simons theory. We discuss realizations of this phase both in 2D and on bosonic topological insulator surfaces, as well as signatures in experiments and simulations.

  5. Negative Energies in the Dirac Equation

    NASA Astrophysics Data System (ADS)

    Dvoeglazov, Valeriy V.

    2016-04-01

    It is easy to check that both algebraic equation Det(hat p - m) = 0 and Det(hat p + m) = 0 for u- and v- 4-spinors have solutions with p0 = ± {E_p} = ± √ {{{{p}}^2} + {m^2}}. The same is true for higher-spin equations. Meanwhile, every book considers the equality p0=Ep for both u- and v- spinors of the (1/2, 0)⊕(0, 1/2) representation only, thus applying the Dirac-Feynman-Stueckelberg procedure for elimination of the negative-energy solutions. The recent Ziino works (and, independently, the articles of several others) show that the Fock space can be doubled. We reconsider this possibility on the quantum field level for both s=1/2 and higher-spin particles.

  6. On regularizations of the Dirac delta distribution

    NASA Astrophysics Data System (ADS)

    Hosseini, Bamdad; Nigam, Nilima; Stockie, John M.

    2016-01-01

    In this article we consider regularizations of the Dirac delta distribution with applications to prototypical elliptic and hyperbolic partial differential equations (PDEs). We study the convergence of a sequence of distributions SH to a singular term S as a parameter H (associated with the support size of SH) shrinks to zero. We characterize this convergence in both the weak-* topology of distributions and a weighted Sobolev norm. These notions motivate a framework for constructing regularizations of the delta distribution that includes a large class of existing methods in the literature. This framework allows different regularizations to be compared. The convergence of solutions of PDEs with these regularized source terms is then studied in various topologies such as pointwise convergence on a deleted neighborhood and weighted Sobolev norms. We also examine the lack of symmetry in tensor product regularizations and effects of dissipative error in hyperbolic problems.

  7. Massive mesons in Weyl-Dirac theory

    NASA Astrophysics Data System (ADS)

    Mirabotalebi, S.; Ahmadi, F.; Salehi, H.

    2008-01-01

    In order to study the mass generation of the vector fields in the framework of a conformal invariant gravitational model, the Weyl-Dirac theory is considered. The mass of the Weyl’s meson fields plays a principal role in this theory, it connects basically the conformal and gauge symmetries. We estimate this mass by using the large-scale characteristics of the observed universe. To do this we firstly specify a preferred conformal frame as a cosmological frame, then in this frame, we introduce an exact possible solution of the theory. We also study the dynamical effect of the massive vector meson fields on the trajectories of an elementary particle. We show that a local change of the cosmological frame leads to a Hamilton-Jacobi equation describing a particle with an adjustable mass. The dynamical effect of the massive vector meson field presents itself in the form of a correction term for the mass of the particle.

  8. Massive photons and Dirac monopoles: Electric condensate and magnetic confinement

    NASA Astrophysics Data System (ADS)

    Guimaraes, M. S.; Rougemont, R.; Wotzasek, C.; Zarro, C. A. D.

    2013-06-01

    We use the generalized Julia-Toulouse approach (GJTA) for condensation of topological currents (charges or defects) to argue that massive photons can coexist consistently with Dirac monopoles. The Proca theory is obtained here via GJTA as a low energy effective theory describing an electric condensate and the mass of the vector boson is responsible for generating a Meissner effect which confines the magnetic defects in monopole-antimonopole pairs connected by physical open magnetic vortices described by Dirac brane invariants, instead of Dirac strings.

  9. New Dirac equation from the view point of particle

    SciTech Connect

    Ozaydin, Fatih; Altintas, Azmi Ali; Susam, Lidya Amon; Arik, Metin; Yarman, Tolga

    2012-09-06

    According to the classical approach, especially the Lorentz Invariant Dirac Equation, when particles are bound to each other, the interaction term appears as a quantity belonging to the 'field'. In this work, as a totally new approach, we propose to alter the rest masses of the particles due to their interaction, as much as their respective contributions to the static binding energy. Thus we re-write and solve the Dirac Equation for the hydrogen atom, and amazingly, obtain practically the same numerical results for the ground states, as those obtained from the Dirac Equation.

  10. 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

  11. 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

    2016-01-01

    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. 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.

  13. Quantum field theory of photon–Dirac fermion interacting system in graphene monolayer

    NASA Astrophysics Data System (ADS)

    Nguyen, Bich Ha; Hieu Nguyen, Van

    2016-06-01

    The purpose of the present work is to elaborate quantum field theory of interacting systems comprising Dirac fermion fields in a graphene monolayer and the electromagnetic field. Since the Dirac fermions are confined in a two-dimensional plane, the interaction Hamiltonian of this system contains the projection of the electromagnetic field operator onto the plane of a graphene monolayer. Following the quantization procedure in traditional quantum electrodynamics we chose to work in the gauge determined by the weak Lorentz condition imposed on the state vectors of all physical states of the system. The explicit expression of the two-point Green function of the projection onto a graphene monolayer of a free electromagnetic field is derived. This two-point Green function and the expression of the interaction Hamiltonian together with the two-point Green functions of free Dirac fermion fields established in our previous work form the basics of the perturbation theory of the above-mentioned interacting field system. As an example, the perturbation theory is applied to the study of two-point Green functions of this interacting system of quantum fields.

  14. 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.

  15. Evolution of hot carrier dynamics in graphene with the Fermi level tuned across the Dirac point

    NASA Astrophysics Data System (ADS)

    Lin, Kuan-Chun; Li, Ming-Yang; Ling, D. C.; Chi, C. C.; Chen, Jeng-Chung

    2015-03-01

    The ultrafast dynamics of photoexcited carriers closely depends on the excitation processes pertaining to the energy band of the materials and the relevant relaxation pathway relies on the interactions between hot carriers and lattice phonons. By using ultrafast optical-pump terahertz (THz)-probe spectroscopy with an ion-gel gate to tune the Fermi energy level EF in graphene, we are able to reveal the relaxation dynamics of hot carriers at different EF. It is found that the relaxation time increases while the pump-induced differential transmission decreases as EF approaches the Dirac point. Through self-consistent model calculations, we quantitatively interpret that a temperature-dependent scattering rate is responsible for a negative photoinduced conductivity, and the relaxation transient directly manifests the Dirac spectrum dependence of the optical phonon emission and the carrier scattering rate. More interestingly, the scattering rate of hot carriers also exhibits a strong EF dependence, which is the most likely to originate from charged impurities inevitably present in graphene. The diminution of photoresponse efficiency across the Dirac point implies that the graphene-based optoelectronic devices may be operable only in the highly doped regime.

  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. 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

    2004-01-01

    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. PMID:14753977

  18. Dirac equation in low dimensions: The factorization method

    NASA Astrophysics Data System (ADS)

    Sánchez-Monroy, J. A.; Quimbay, C. J.

    2014-11-01

    We present a general approach to solve the (1 + 1) and (2 + 1) -dimensional Dirac equations in the presence of static scalar, pseudoscalar and gauge potentials, for the case in which the potentials have the same functional form and thus the factorization method can be applied. We show that the presence of electric potentials in the Dirac equation leads to two Klein-Gordon equations including an energy-dependent potential. We then generalize the factorization method for the case of energy-dependent Hamiltonians. Additionally, the shape invariance is generalized for a specific class of energy-dependent Hamiltonians. We also present a condition for the absence of the Klein paradox (stability of the Dirac sea), showing how Dirac particles in low dimensions can be confined for a wide family of potentials.

  19. RKKY interaction of magnetic impurities in Dirac and Weyl semimetals

    NASA Astrophysics Data System (ADS)

    Chang, Hao-Ran; Zhou, Jianhui; Wang, Shi-Xiong; Shan, Wen-Yu; Xiao, Di

    2015-12-01

    We theoretically study the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between magnetic impurities in both Dirac and Weyl semimetals (SMs). We find that the internode process, as well as the unique three-dimensional spin-momentum locking, has significant influences on the RKKY interaction, resulting in both a Heisenberg and an Ising term, and an additional Dzyaloshinsky-Moriya term if the inversion symmetry is absent. These interactions can lead to rich spin textures and possible ferromagnetism in Dirac and time-reversal symmetry-invariant Weyl SMs. The effect of anisotropic Dirac and Weyl nodes on the RKKY interaction is also discussed. Our results provide an alternative scheme to engineer topological SMs and shed new light on the application of Dirac and Weyl SMs in spintronics.

  20. 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.

  1. Dirac cones in transition metal doped boron nitride

    NASA Astrophysics Data System (ADS)

    Feng, Min; Shao, Bin; Cao, Xuewei; Zuo, Xu

    2015-05-01

    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.

  2. Digital quantum simulation of Dirac equation with a trapped ion

    NASA Astrophysics Data System (ADS)

    Shen, Yangchao; Zhang, Xiang; Zhang, Junhua; Casanova, Jorge; Lamata, Lucas; Solano, Enrique; Yung, Man-Hong; Zhang, Jingning; Kim, Kihwan; Department Of Physical Chemistry Collaboration

    2014-05-01

    Recently there has been growing interest in simulating relativistic effects in controllable physical system. We digitally simulate the Dirac equation in 3 +1 dimensions with a single trapped ion. We map four internal levels of 171Yb+ ion to the Dirac bispinor. The time evolution of the Dirac equation is implemented by trotter expansion. In the 3 +1 dimension, we can observe a helicoidal motion of a free Dirac particle which reduces to Zitterbewegung in 1 +1 dimension. This work was supported in part by the National Basic Research Program of China Grant 2011CBA00300, 2011CBA00301, the National Natural Science Foundation of China Grant 61033001, 61061130540. KK acknowledge the support from the recruitment program of global youth experts.

  3. 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.

  4. Observation of Dirac cone warping and chirality effects in silicene.

    PubMed

    Feng, Baojie; Li, Hui; Liu, Cheng-Cheng; Shao, Ting-Na; Cheng, Peng; Yao, Yugui; Meng, Sheng; Chen, Lan; Wu, Kehui

    2013-10-22

    We performed low temperature scanning tunneling microscopy (STM) and spectroscopy (STS) studies on the electronic properties of (√3 × √3)R30° phase of silicene on Ag(111) surface. We found the existence of Dirac Fermion chirality through the observation of -1.5 and -1.0 power law decay of quasiparticle interference (QPI) patterns. Moreover, in contrast to the trigonal warping of Dirac cone in graphene, we found that the Dirac cone of silicene is hexagonally warped, which is further confirmed by density functional calculations and explained by the unique superstructure of silicene. Our results demonstrate that the (√3 × √3)R30° phase is an ideal system to investigate the unique Dirac Fermion properties of silicene.

  5. Two-Dimensional Dirac Materials: From Graphene to Topological Insulators

    NASA Astrophysics Data System (ADS)

    Teweldebrhan, Desalegne Bekuretsion

    2011-12-01

    Silicon has been reaching physical limits as the semiconductor industry moves to smaller device feature sizes, increased integration densities and faster operation speeds. There is a strong need to engineer alternative materials, which can become foundation of new computational paradigms or lead to other applications such as efficient solid-state energy conversion. Recently discovered Dirac materials, which are characterized by the liner electron dispersion, are examples of such alternative materials. In this dissertation, I investigate two representatives of Dirac materials -- graphene and topological insulators. Specifically, I focus on the (i) effects of electron beam irradiation on graphene properties and (ii) electronic and thermal characteristics of exfoliated films of Bi2Te3-family of topological insulators. I carried out Raman investigation of changes in graphene crystal lattice induced by the low and medium energy electron-beam irradiation (5.20 keV). It was found that radiation exposures result in appearance of the disorder D band around 1345 cm-1. The dependence of the ratio of the intensities of D and G peaks, I(D)/I(G), on the irradiation dose is non-monotonic suggesting graphene.s transformation to polycrystalline and then to disordered state. By controlling the irradiation dose one can change the carrier mobility and increase the resistance at the minimum conduction point. The obtained results may lead to new methods of defect engineering of graphene properties. They also have important implications for fabrication of graphene nanodevices, which involve electron beams. Bismuth telluride and related compounds are the best thermoelectric materials known today. Recently, it was determined that they reveal the topological insulator properties. We succeeded in the first "graphene-like" exfoliation of large-area crystalline films and ribbons of Bi2Te3 with the thickness going down to a single quintuple. The presence of van der Waals gaps allowed us to

  6. Dirac equation in low dimensions: The factorization method

    SciTech Connect

    Sánchez-Monroy, J.A.; Quimbay, C.J.

    2014-11-15

    We present a general approach to solve the (1+1) and (2+1)-dimensional Dirac equations in the presence of static scalar, pseudoscalar and gauge potentials, for the case in which the potentials have the same functional form and thus the factorization method can be applied. We show that the presence of electric potentials in the Dirac equation leads to two Klein–Gordon equations including an energy-dependent potential. We then generalize the factorization method for the case of energy-dependent Hamiltonians. Additionally, the shape invariance is generalized for a specific class of energy-dependent Hamiltonians. We also present a condition for the absence of the Klein paradox (stability of the Dirac sea), showing how Dirac particles in low dimensions can be confined for a wide family of potentials. - Highlights: • The low-dimensional Dirac equation in the presence of static potentials is solved. • The factorization method is generalized for energy-dependent Hamiltonians. • The shape invariance is generalized for energy-dependent Hamiltonians. • The stability of the Dirac sea is related to the existence of supersymmetric partner Hamiltonians.

  7. Composite Dirac Liquids: Parent States for Symmetric Surface Topological Order

    NASA Astrophysics Data System (ADS)

    Mross, David F.; Essin, Andrew; Alicea, Jason

    2015-01-01

    We introduce exotic gapless states—"composite Dirac liquids"—that can appear at a strongly interacting surface of a three-dimensional electronic topological insulator. Composite Dirac liquids exhibit a gap to all charge excitations but nevertheless feature a single massless Dirac cone built from emergent electrically neutral fermions. These states thus comprise electrical insulators that, interestingly, retain thermal properties similar to those of the noninteracting topological insulator surface. A variety of novel fully gapped phases naturally descend from composite Dirac liquids. Most remarkably, we show that gapping the neutral fermions via Cooper pairing—which crucially does not violate charge conservation—yields symmetric non-Abelian topologically ordered surface phases captured in several recent works. Other (Abelian) topological orders emerge upon alternatively gapping the neutral Dirac cone with magnetism. We establish a hierarchical relationship between these descendant phases and expose an appealing connection to paired states of composite Fermi liquids arising in the half filled Landau level of two-dimensional electron gases. To controllably access these states we exploit a quasi-1D deformation of the original electronic Dirac cone that enables us to analytically address the fate of the strongly interacting surface. The algorithm we develop applies quite broadly and further allows the construction of symmetric surface topological orders for recently introduced bosonic topological insulators.

  8. Split Dirac supersymmetry: An ultraviolet completion of Higgsino dark matter

    NASA Astrophysics Data System (ADS)

    Fox, Patrick J.; Kribs, Graham D.; Martin, Adam

    2014-10-01

    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 ˜108-11 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 ≳1017 GeV. The μ 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.

  9. QUANTUM: A Wolfram Mathematica add-on for Dirac Bra-Ket Notation, Non-Commutative Algebra, and Simulation of Quantum Computing Circuits

    NASA Astrophysics Data System (ADS)

    Gómez Muñoz, J. L.; Delgado, F.

    2016-03-01

    This paper introduces QUANTUM, a free library of commands of Wolfram Mathematica that can be used to perform calculations directly in Dirac braket and operator notation. Its development started several years ago, in order to study quantum random walks. Later, many other features were included, like operator and commutator algebra, simulation and graphing of quantum computing circuits, generation and solution of Heisenberg equations of motion, among others. To the best of our knowledge, QUANTUM remains a unique tool in its use of Dirac notation, because it is used both in the input and output of the calculations. This work depicts its usage and features in Quantum Computing and Quantum Hamilton Dynamics.

  10. 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.

  11. 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. PMID:22060507

  12. 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.

  13. 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.

  14. 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.

  15. Low-Lying Dirac Eigenmodes, Topological Charge Fluctuations and the Instanton Liquid Model

    SciTech Connect

    I. Horvath; S.J. Dong; T. Draper; F.X. Lee; H.B. Thacker; J.B. Zhang

    2002-05-01

    The local structure of low-lying eigenmodes of the overlap Dirac operator is studied. It is found that these modes cannot be described as linear combinations of 't Hooft ''would-be'' zeromodes associated with instanton excitations that underly the Instanton Liquid Model. This implies that the instanton liquid scenario for spontaneous chiral symmetry breaking in QCD is not accurate. More generally, our data suggests that the vacuum fluctuations of topological charge are not effectively dominated by localized lumps of unit charge with which the topological ''would-be'' zeromodes could be associated.

  16. 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.

  17. Dirac spectrum of one-flavor QCD at θ =0 and continuity of the chiral condensate

    NASA Astrophysics Data System (ADS)

    Verbaarschot, J. J. M.; Wettig, T.

    2014-12-01

    We derive exact analytical expressions for the spectral density of the Dirac operator at fixed θ -angle in the microscopic domain of one-flavor QCD. These results are obtained by performing the sum over topological sectors using novel identities involving sums of products of Bessel functions. Because the fermion determinant is not positive definite for negative quark mass, the usual Banks-Casher relation is not valid and has to be replaced by a different mechanism first observed for QCD at nonzero chemical potential. Using the exact results for the spectral density we explain how this mechanism results in a chiral condensate that remains constant when the quark mass changes sign.

  18. 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.

  19. Dirac matrices for Chern-Simons gravity

    SciTech Connect

    Izaurieta, Fernando; Ramirez, Ricardo; Rodriguez, Eduardo

    2012-10-06

    A genuine gauge theory for the Poincare, de Sitter or anti-de Sitter algebras can be constructed in (2n- 1)-dimensional spacetime by means of the Chern-Simons form, yielding a gravitational theory that differs from General Relativity but shares many of its properties, such as second order field equations for the metric. The particular form of the Lagrangian is determined by a rank n, symmetric tensor invariant under the relevant algebra. In practice, the calculation of this invariant tensor can be reduced to the computation of the trace of the symmetrized product of n Dirac Gamma matrices {Gamma}{sub ab} in 2n-dimensional spacetime. While straightforward in principle, this calculation can become extremely cumbersome in practice. For large enough n, existing computer algebra packages take an inordinate long time to produce the answer or plainly fail having used up all available memory. In this talk we show that the general formula for the trace of the symmetrized product of 2n Gamma matrices {Gamma}{sub ab} can be written as a certain sum over the integer partitions s of n, with every term being multiplied by a numerical cofficient {alpha}{sub s}. We then give a general algorithm that computes the {alpha}-coefficients as the solution of a linear system of equations generated by evaluating the general formula for different sets of tensors B{sup ab} with random numerical entries. A recurrence relation between different coefficients is shown to hold and is used in a second, 'minimal' algorithm to greatly speed up the computations. Runtime of the minimal algorithm stays below 1 min on a typical desktop computer for up to n = 25, which easily covers all foreseeable applications of the trace formula.

  20. Negative longitudinal magnetoresistance in Dirac and Weyl metals

    NASA Astrophysics Data System (ADS)

    Burkov, A. A.

    2015-06-01

    It has recently been found that Dirac and Weyl metals are characterized by an unusual weak-field longitudinal magnetoresistance: large, negative, and quadratic in the magnetic field. This has been shown to arise from the chiral anomaly, i.e., nonconservation of the chiral charge in the presence of external electric and magnetic fields, oriented collinearly. In this paper we report on a theory of this effect in both Dirac and Weyl metals. We demonstrate that this phenomenon contains two important ingredients. One is the magnetic-field-induced coupling between the chiral and the total (or vector, in relativistic field theory terminology) charge densities. This arises from the Berry curvature and is present in principle whenever the Berry curvature is nonzero, i.e., is nonspecific to Dirac and Weyl metals. This coupling, however, leads to a large negative quadratic magnetoresistance only when the second ingredient is present, namely when the chiral charge density is a nearly conserved quantity with a long relaxation time. This property is specific to Dirac and Weyl metals and is realized only when the Fermi energy is close to Dirac or Weyl nodes, expressing an important low-energy property of these materials, emergent chiral symmetry.

  1. Two-component Dirac-like Hamiltonian for generating quantum walk on one-, two- and three-dimensional lattices

    PubMed Central

    Chandrashekar, C. M.

    2013-01-01

    From the unitary operator used for implementing two-state discrete-time quantum walk on one-, two- and three- dimensional lattice we obtain a two-component Dirac-like Hamiltonian. In particular, using different pairs of Pauli basis as position translation states we obtain three different form of Hamiltonians for evolution on one-dimensional lattice. We extend this to two- and three-dimensional lattices using different Pauli basis states as position translation states for each dimension and show that the external coin operation, which is necessary for one-dimensional walk is not a necessary requirement for a walk on higher dimensions but can serve as an additional resource to control the dynamics. The two-component Hamiltonian we present here for quantum walk on different lattices can serve as a general framework to simulate, control, and study the dynamics of quantum systems governed by Dirac-like Hamiltonian. PMID:24088731

  2. 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

  3. 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.

  4. 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′.

  5. Discrete Dirac Structures and Implicit Discrete Lagrangian and Hamiltonian Systems

    NASA Astrophysics Data System (ADS)

    Leok, Melvin; Ohsawa, Tomoki

    2010-07-01

    We present discrete analogues of Dirac structures and the Tulczyjew's triple by considering the geometry of symplectic maps and their associated generating functions. We demonstrate that this framework provides a means of deriving discrete analogues of implicit Lagrangian and Hamiltonian systems. In particular, this yields implicit nonholonomic Lagrangian and Hamiltonian integrators. We also introduce discrete Lagrange-d'Alembert-Pontryagin and Hamilton-d'Alembert variational principles, which provide an alternative derivation of the same set of integration algorithms. In addition to providing a unified treatment of discrete Lagrangian and Hamiltonian mechanics in the more general setting of Dirac mechanics, it provides a generalization of symplectic and Poisson integrators to the broader category of Dirac integrators.

  6. Simplified Dirac dark matter models and gamma-ray lines

    NASA Astrophysics Data System (ADS)

    Duerr, Michael; Fileviez Pérez, Pavel; Smirnov, Juri

    2015-10-01

    We investigate simplified dark matter models where the dark matter candidate is a Dirac fermion charged only under a new gauge symmetry. In this context one can understand dynamically the stability of the dark matter candidate and the annihilation through the new gauge boson is not velocity suppressed. We present the simplest Dirac dark matter model charged under the local B -L gauge symmetry. We discuss in great detail the theoretical predictions for the annihilation into two photons, into the standard model Higgs and a photon, and into the Z gauge boson and a photon. Our analytical results can be used for any Dirac dark matter model charged under an Abelian gauge symmetry. The numerical results are shown in the B -L dark matter model. We discuss the correlation between the constraints on the model from collider searches and dark matter experiments.

  7. Simulation of Zitterbewegung by modelling the Dirac equation in metamaterials

    NASA Astrophysics Data System (ADS)

    Ahrens, Sven; Zhu, Shi-Yao; Jiang, Jun; Sun, Yong

    2015-11-01

    Strong field processes which occur in intense laser fields are a test area for relativistic quantum field theory, but difficult to study experimentally and theoretically. Thus, modelling relativistic quantum dynamics and therewith the Dirac equation can help to understand quantum field theory. We develop a dynamic description of an effective Dirac theory in metamaterials in which the wave function is modelled by the corresponding electric and magnetic field in the metamaterial. This electromagnetic field can be probed in the experimental setup, which means that the wave function of the effective theory is directly accessible by measurement. Our model is based on a plane wave expansion which establishes the identification of Dirac spinors with single-frequency excitations of the electromagnetic field in the metamaterial. We check the validity of our relativistic quantum dynamics simulation by demonstrating the emergence of Zitterbewegung and verifying it with an analytic solution.

  8. 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.

  9. A new way of describing the Dirac bands in graphene

    NASA Astrophysics Data System (ADS)

    Kissinger, Gregory; Satpathy, Sashi

    We develop a new way of describing the electronic structure of graphene, by treating the honeycomb lattice as a network of one-dimensional quantum wires. The electrons travel as free particles along these quantum wires and interfere at the three-way junctions formed by the carbon atoms. The model generates the linearly dispersive Dirac cone band structure as well as the chiral nature of the pseudo-spin sublattice wave functions. When vacancies are incorporated, we find that it also reproduces the well known zero mode states. This simple approach might have advantages over other methods for some applications, such as in analyzing electronic transport through graphene nanoribbons. In addition, this finding suggests new ways of constructing Dirac band materials in the laboratory by nano-patterning for investigating Dirac fermions.

  10. Birefringent breakup of Dirac fermions on a square optical lattice

    SciTech Connect

    Kennett, Malcolm P.; Komeilizadeh, Nazanin; Kaveh, Kamran; Smith, Peter M.

    2011-05-15

    We introduce a lattice model for fermions in a spatially periodic magnetic field that also has spatially periodic hopping amplitudes. We discuss how this model might be realized with cold atoms in an artificial magnetic field on a square optical lattice. When there is an average flux of half a flux quantum per plaquette, the spectrum of low-energy excitations can be described by massless Dirac fermions in which the usually doubly degenerate Dirac cones split into cones with different ''speeds of light.'' These gapless birefringent Dirac fermions arise because of broken chiral symmetry in the kinetic energy term of the effective low-energy Hamiltonian. We characterize the effects of various perturbations to the low-energy spectrum, including staggered potentials, interactions, and domain-wall topological defects.

  11. Shot noise in systems with semi-Dirac points

    SciTech Connect

    Zhai, Feng; Wang, Juan

    2014-08-14

    We calculate the ballistic conductance and shot noise of electrons through a two-dimensional stripe system (width W ≫ length L) with semi-Dirac band-touching points. We find that the ratio between zero-temperature noise power and mean current (the Fano factor) is highly anisotropic. When the transport is along the linear-dispersion direction and the Fermi energy is fixed at the semi-Dirac point, the Fano factor has a universal value F = 0.179 while a minimum conductivity exists and scales with L{sup 1∕2}. Along the parabolic dispersion direction, the Fano factor at the semi-Dirac point has a contact-independent limit exceeding 0.9, which varies weakly with L due to the common-path interference of evanescent waves. Our findings suggest a way to discern the type of band-touching points.

  12. 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.

  13. 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

  14. 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.

  15. Formal analogy between the Dirac equation in its Majorana form and the discrete-velocity version of the Boltzmann kinetic equation.

    PubMed

    Fillion-Gourdeau, F; Herrmann, H J; Mendoza, M; Palpacelli, S; Succi, S

    2013-10-18

    We point out a formal analogy between the Dirac equation in Majorana form and the discrete-velocity version of the Boltzmann kinetic equation. By a systematic analysis based on the theory of operator splitting, this analogy is shown to turn into a concrete and efficient computational method, providing a unified treatment of relativistic and nonrelativistic quantum mechanics. This might have potentially far-reaching implications for both classical and quantum computing, because it shows that, by splitting time along the three spatial directions, quantum information (Dirac-Majorana wave function) propagates in space-time as a classical statistical process (Boltzmann distribution).

  16. Radiative heat transfer in 2D Dirac materials.

    PubMed

    Rodriguez-López, Pablo; Tse, Wang-Kong; Dalvit, Diego A R

    2015-06-01

    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. PMID:25965703

  17. Lorentz-Dirac force from QED for linear acceleration

    SciTech Connect

    Higuchi, Atsushi; Martin, Giles D.R.

    2004-10-15

    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 ({Dirac_h}/2{pi}){yields}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.

  18. 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.

  19. A semiclassical kinetic theory of Dirac particles and Thomas precession

    NASA Astrophysics Data System (ADS)

    Dayi, Ömer F.; Kilinçarslan, Eda

    2015-10-01

    Kinetic theory of Dirac fermions is studied within the matrix valued differential forms method. It is based on the symplectic form derived by employing the semiclassical wave packet build of the positive energy solutions of the Dirac equation. A satisfactory definition of the distribution matrix elements imposes to work in the basis where the helicity is diagonal which is also needed to attain the massless limit. We show that the kinematic Thomas precession correction can be studied straightforwardly within this approach. It contributes on an equal footing with the Berry gauge fields. In fact in equations of motion it eliminates the terms arising from the Berry gauge fields.

  20. 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.

  1. 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.

  2. Does the Dirac Cone Exist in Silicene on Metal Substrates?

    PubMed Central

    Quhe, Ruge; Yuan, Yakun; Zheng, Jiaxin; Wang, Yangyang; Ni, Zeyuan; Shi, Junjie; Yu, Dapeng; Yang, Jinbo; Lu, Jing

    2014-01-01

    Absence of the Dirac cone due to a strong band hybridization is revealed to be a common feature for epitaxial silicene on metal substrates according to our first-principles calculations for silicene on Ir, Cu, Mg, Au, Pt, Al, and Ag substrates. The destroyed Dirac cone of silicene, however, can be effectively restored with linear or parabolic dispersion by intercalating alkali metal atoms between silicene and the metal substrates, offering an opportunity to study the intriguing properties of silicene without further transfer of silicene from the metal substrates. PMID:24969493

  3. Radiative heat transfer in 2D Dirac materials

    DOE PAGESBeta

    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.

  4. Klein-Gordon and Dirac Equations with Thermodynamic Quantities

    NASA Astrophysics Data System (ADS)

    Arda, Altuğ; Tezcan, Cevdet; Sever, Ramazan

    2016-03-01

    We study the thermodynamic quantities such as the Helmholtz free energy, the mean energy and the specific heat for both the Klein-Gordon, and Dirac equations. Our analyze includes two main subsections: (1) statistical functions for the Klein-Gordon equation with a linear potential having Lorentz vector, and Lorentz scalar parts (2) thermodynamic functions for the Dirac equation with a Lorentz scalar, inverse-linear potential by assuming that the scalar potential field is strong ( A ≫ 1). We restrict ourselves to the case where only the positive part of the spectrum gives a contribution to the sum in partition function. We give the analytical results for high temperatures.

  5. 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.

  6. 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.

  7. 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.

  8. Metal-Insulator Transition of Dirac Fermions: Variational Cluster Study

    NASA Astrophysics Data System (ADS)

    Ebato, Masaki; Kaneko, Tatsuya; Ohta, Yukinori

    2015-04-01

    A comparative study is made on the metal-insulator transition of Dirac fermions in the honeycomb and π-flux Hubbard models at half filling by means of the variational cluster approximation and cluster dynamical impurity approximation. Paying particular attention to the choice of the geometry of solver clusters and the inclusion of particle-bath sites, we show that the direct transition from the Dirac semimetallic state to the antiferromagnetic Mott insulator state occurs in these models, and therefore, the spin liquid phase is absent in the intermediate region, in agreement with recent quantum-Monte-Carlo-based calculations.

  9. Transitions into the negative-energy Dirac continuum

    SciTech Connect

    Krekora, P.; Su, Q.; Grobe, R.

    2004-11-01

    We compare the predictions of the single-particle Dirac equation with quantum field theory for an electron subjected to a space and time dependent field. We demonstrate analytically and numerically that a transition into the negative-energy subspace predicted by the single-particle Dirac equation is directly associated with the degree of suppression of pair-production as described by quantum field theory. We show that the portion of the mathematical wave function that populates the negative-energy states corresponds to the difference between the positron spatial density for systems with and without an electron initially present.

  10. Does the Dirac cone exist in silicene on metal substrates?

    PubMed

    Quhe, Ruge; Yuan, Yakun; Zheng, Jiaxin; Wang, Yangyang; Ni, Zeyuan; Shi, Junjie; Yu, Dapeng; Yang, Jinbo; Lu, Jing

    2014-06-27

    Absence of the Dirac cone due to a strong band hybridization is revealed to be a common feature for epitaxial silicene on metal substrates according to our first-principles calculations for silicene on Ir, Cu, Mg, Au, Pt, Al, and Ag substrates. The destroyed Dirac cone of silicene, however, can be effectively restored with linear or parabolic dispersion by intercalating alkali metal atoms between silicene and the metal substrates, offering an opportunity to study the intriguing properties of silicene without further transfer of silicene from the metal substrates.

  11. Iterative solution of a Dirac equation with an inverse Hamiltonian method

    SciTech Connect

    Hagino, K.; Tanimura, Y.

    2010-11-15

    We solve a singe-particle Dirac equation with Woods-Saxon potentials using an iterative method in the coordinate space representation. By maximizing the expectation value of the inverse of the Dirac Hamiltonian, this method avoids the variational collapse in which an iterative solution dives into the Dirac sea. We demonstrate that this method works efficiently, reproducing the exact solutions of the Dirac equation.

  12. Quantum gravity and causal structures: Second quantization of conformal Dirac algebras

    NASA Astrophysics Data System (ADS)

    Bonezzi, R.; Corradini, O.; Latini, E.; Waldron, A.

    2015-06-01

    It is postulated that quantum gravity is a sum over causal structures coupled to matter via scale evolution. Quantized causal structures can be described by studying simple matrix models where matrices are replaced by an algebra of quantum mechanical observables. In particular, previous studies constructed quantum gravity models by quantizing the moduli of Laplace, weight, and defining-function operators on Fefferman-Graham ambient spaces. The algebra of these operators underlies conformal geometries. We extend those results to include fermions by taking an o s p (1 |2 ) "Dirac square root" of these algebras. The theory is a simple, Grassmann, two-matrix model. Its quantum action is a Chern-Simons theory whose differential is a first-quantized, quantum mechanical Becchi-Rouet-Stora-Tyutin operator. The theory is a basic ingredient for building fundamental theories of physical observables.

  13. 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.

  14. Quantum Singularity as Indicated by Klein-Gordon, Maxwell, and Dirac Fields in Quasiregular Spacetimes

    NASA Astrophysics Data System (ADS)

    Konkowski, Deborah A.; Arndt, Valerie; Helliwell, Thomas M.

    2002-04-01

    Klein-Gordon, Maxwell and Dirac fields are studied in quasiregular spacetimes, spacetimes with a classical quasiregular singularity, the mildest true classical singularity [G.F.R. Ellis and B.G. Schmidt, Gen. Rel. Grav.8, 915 (1977)]. A class of static quasiregular spacetimes possessing disclinations and dislocations [R.A. Puntigam and H.H. Soleng, Class. Quantum Grav. 14, 1129 (1997)] is shown to have field operators which are not essentially self-adjoint. This class of spacetimes includes an idealized cosmic string, i.e., a four-dimensional spacetime with a conical singularity [L.H. Ford and A. Vilenkin, J. Phys. A: Math. Gen. 14, 2353 (1981)], and a Galtsov/Letelier/Tod spacetime featuring a screw dislocation [K.P. Tod, Class. Quantum Grav. 11, 1331 (1994); D.V. Galtsov and P.S. Letelier, Phys. Rev. D47, 4273 (1993)]. The definition of G. T. Horowitz and D. Marolf [Phys. Rev. D52, 5670 (1995)] for a quantum-mechanically singular spacetime as one in which the spatial-derivative operator in the Klein-Gordon equation for a massive scalar field is not essentially self-adjoint is extended in the case of quasiregular spacetimes to include Maxwell and Dirac fields. Therefore, the class of static quasiregular spacetimes under consideration is quantum-mechanically singular independent of the type of test field.

  15. The asymptotics of an eigenfunction-correlation determinant for Dirac-δ perturbations

    NASA Astrophysics Data System (ADS)

    Gebert, Martin

    2015-07-01

    We prove the exact asymptotics of the scalar product of the ground states of two non-interacting Fermi gases confined to a 3-dimensional ball BL of radius L in the thermodynamic limit, where the underlying one-particle operators differ by a Dirac-δ perturbation. More precisely, we show the algebraic decay of the correlation determinant |det|(< φ)j L, ψk L > j , k = 1 , … , N 2 = L - ζ ( E ) + o ( 1 ) , as N, L → ∞ and N / |B L| → ρ > 0 , where φj L and ψk L denote the lowest-energy eigenfunctions of the finite-volume one-particle Schrödinger operators. The decay exponent is given in terms of the s-wave scattering phase shift ζ ( E ) ≔ /1 π 2 δ 2 ( √{ E } ) . For an attractive Dirac-δ perturbation, we conclude that the decay exponent /1 π 2 ↑arcsin↑ |T ( E ) / 2| HS 2 found in the work of Gebert et al. [J. Spect. Theory (to be published); e-print arXiv:1407.2512] does not provide a sharp upper bound on the decay of the correlation determinant.

  16. 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.

  17. 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.

  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. High energy scattering of Dirac particles on smooth potentials

    NASA Astrophysics Data System (ADS)

    Han, Nguyen Suan; Dung, Le Anh; Xuan, Nguyen Nhu; Thang, Vu Toan

    2016-08-01

    The derivation of the Glauber type representation for the high energy scattering amplitude of particles of spin 1/2 is given within the framework of the Dirac equation in the Foldy-Wouthuysen (FW) representation and two-component formalism. The differential cross-sections on the Yukawa and Gaussian potentials are also considered and discussed.

  20. Dark matter with Dirac and Majorana gaugino masses

    SciTech Connect

    Belanger, G.; Benakli, K.; Goodsell, M.; Moura, C.; Pukhov, A. E-mail: kbenakli@lpthe.jussieu.fr E-mail: moura@lpthe.jussieu.fr

    2009-08-01

    We consider the minimal supersymmetric extension of the Standard Model allowing both Dirac and Majorana gauginos. The Dirac masses are obtained by pairing up extra chiral multiplets: a singlet S for U(1){sub Y}, a triplet T for SU(2){sub w} and an octet O{sub g} for SU(3){sub c} with the respective gauginos. The electroweak symmetry breaking sector is modified by the couplings of the new fields S and T to the Higgs doublets. We discuss two limits: i) both the adjoint scalars are decoupled with the main effect being the modification of the Higgs quartic coupling; ii) the singlet remaining light, and due to its direct coupling to sfermions, providing a new contribution to the soft masses and inducing new decay/production channels. We discuss the LSP in this scenario; after mentioning the possibility that it may be a Dirac gravitino, we focus on the case where it is identified with the lightest neutralino, and exhibit particular values of the parameter space where the relic density is in agreement with WMAP data. This is illustrated for different scenarios where the LSP is either a bino (in which case it can be a Dirac fermion) or bino-higgsino/wino mixtures. We also point out in each case the peculiarity of the model with respect to dark matter detection experiments.

  1. 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.

  2. 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.

  3. 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.

  4. 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…

  5. 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.

  6. Band structures in transmission coefficients generated by Dirac comb potentials

    NASA Astrophysics Data System (ADS)

    Dharani, M.; Shastry, C. S.

    2016-11-01

    Using the threshold conditions and bound state energies investigated earlier by us as a critical input we systematically study the nature of band formation in the transmission coefficient generated by Dirac comb potentials having equispaced (i) attractive, (ii) repulsive and (iii) alternating attractive and repulsive delta terms having same strength and confined within a fixed range. We find that positions of the peaks of transmission coefficient generated by a combination of one attractive and one repulsive delta terms having same strength and separated by gap a is independent of the potential strength and coincide with the energy eigenvalues of 1D box of range a. We further study analytically and numerically the transmission across Dirac comb potentials containing two or three delta terms and these results are useful in the analysis of the transmission in the general case. In the case of Dirac comb potentials containing Na attractive delta terms we find that the nature of the first band and higher bands of the transmission coefficient are different, and if such a potential generates Nb number of bound states, the first band in the transmission coefficient generated by the potential has NT1 =Na -Nb peaks. In the case of higher bands generated by delta comb potential having N delta terms each band has N - 1 peaks. Further we systematically study the behavior of band gaps and band spread as a function of potential strength and number of terms in the Dirac comb. The results obtained by us provide a relation between bound state spectrum, number of delta terms in the Dirac comb and the band pattern which can be explored for potential applications.

  7. 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.

  8. 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.

  9. 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. PMID:26490643

  10. Dirac single particle and plasmon excitations in topological insulators

    NASA Astrophysics Data System (ADS)

    Lupi, Stefano

    Topological Insulators (TIs), like Bi2Se3 and Bi2Te3, are one of the most intriguing issues at focus in Condensed Matter Physics. TIs exhibit a band gap in the bulk like ordinary insulators, but have intrinsic 2D conducting states on their edge and surface. This means that the topology, associated with the electronic wavefunctions of the system, changes discontinuously when passing from the bulk to the surface. The edge states arise from a strong spin-orbit coupling, and they are backscattering protected, i.e. not sensitive to disorder (except that coming from magnetic impurities). Such as graphene, TIs surface charge transport is carried out by Dirac fermions, with a very high surface carrier density (n >= 1013 cm-2) , compared to typical values on metal surfaces. Apart single particle excitations, Dirac fermions in TIs sustain exotic plasmonic (collective) modes whose properties of tunability and temperature dependence can be used for photonics applications at the nanoscale. Moreover, unlike plasmons in metals, Dirac plasmons in TIs are expected to be strongly affected by an external magnetic field B due to fact that the cyclotron frequency is comparable to the the plasmon frequency, in particular when plasmons are engineered in the terahertz region of the electromagnetic spectrum. In this talk, after a general review on the properties of Topological Insulators, I will discuss the terahertz linear response of Dirac plasmons in TIs and their behavior under a strong magnetic field up to 30 T. The appearance of strong non-linear optical effects, when the THz electric field reaches values on the order of 1 MV/cm, will be also discussed. In the second part of the talk, I will discuss the sub-ps dynamics of Dirac single-particle and collective excitations as measured by optical-pump THz-probe experiments. Both the steady state and time-resolved experiments provide a unifying picture of single particle and collective electronic excitations in Topological Insulators.

  11. The Invertible Double of Elliptic Operators

    NASA Astrophysics Data System (ADS)

    Booss-Bavnbek, Bernhelm; Lesch, Matthias

    2009-02-01

    First, we review the Dirac operator folklore about basic analytic and geometrical properties of operators of Dirac type on compact manifolds with smooth boundary and on closed partitioned manifolds and show how these properties depend on the construction of a canonical invertible double and are related to the concept of the Calderón projection. Then we summarize a recent construction of a canonical invertible double for general first order elliptic differential operators over smooth compact manifolds with boundary. We derive a natural formula for the Calderón projection which yields a generalization of the famous Cobordism Theorem. We provide a list of assumptions to obtain a continuous variation of the Calderón projection under smooth variation of the coefficients. That yields various new spectral flow theorems. Finally, we sketch a research program for confining, respectively closing, the last remaining gaps between the geometric Dirac operator type situation and the general linear elliptic case.

  12. Stability of solitary waves in the nonlinear Dirac equation with arbitrary nonlinearity.

    PubMed

    Shao, Sihong; Quintero, Niurka R; Mertens, Franz G; Cooper, Fred; Khare, Avinash; Saxena, Avadh

    2014-09-01

    We consider the nonlinear Dirac equation in 1 + 1 dimension with scalar-scalar self interaction g(2)/κ+1(̅ΨΨ)(κ+1) and with mass m. Using the exact analytic form for rest frame solitary waves of the form Ψ(x,t)=ψ(x)e(-iωt) for arbitrary κ, we discuss the validity of various approaches to understanding stability that were successful for the nonlinear Schrödinger equation. In particular we study the validity of a version of Derrick's theorem and the criterion of Bogolubsky as well as the Vakhitov-Kolokolov criterion, and find that these criteria yield inconsistent results. Therefore, we study the stability by numerical simulations using a recently developed fourth-order operator splitting integration method. For different ranges of κ we map out the stability regimes in ω. We find that all stable nonlinear Dirac solitary waves have a one-hump profile, but not all one-hump waves are stable, while all waves with two humps are unstable. We also find that the time t(c), it takes for the instability to set in, is an exponentially increasing function of ω and t(c) decreases monotonically with increasing κ. PMID:25314512

  13. Floquet analysis of pulsed Dirac systems: a way to simulate rippled graphene

    NASA Astrophysics Data System (ADS)

    Mishra, Tridev; Guha Sarkar, Tapomoy; Bandyopadhyay, Jayendra N.

    2015-09-01

    The low energy continuum limit of graphene is effectively known to be modeled using the Dirac equation in (2 + 1) dimensions. We consider the possibility of using a modulated high frequency periodic driving of a two-dimensional system (optical lattice) to simulate properties of rippled graphene. We suggest that the Dirac Hamiltonian in a curved background space can also be effectively simulated by a suitable driving scheme in an optical lattice. The time dependent system yields, in the approximate limit of high frequency pulsing, an effective time independent Hamiltonian that governs the time evolution, except for an initial and a final kick. We use a specific form of 4-phase pulsed forcing with suitably tuned choice of modulating operators to mimic the effects of curvature. The extent of curvature is found to be directly related to ω-1 the time period of the driving field at the leading order. We apply the method to engineer the effects of curved background space. We find that the imprint of curvilinear geometry modifies the electronic properties, such as LDOS, significantly. We suggest that this method shall be useful in studying the response of various properties of such systems to non-trivial geometry without requiring any actual physical deformations.

  14. Correspondence between classical and Dirac-Pauli spinors in view of the Foldy-Wouthuysen transformation

    NASA Astrophysics Data System (ADS)

    Chen, Tsung-Wei; Chiou, Dah-Wei

    2014-03-01

    The classical dynamics for a charged spin particle is governed by the Lorentz force equation for orbital motion and by the Thomas-Bargmann-Michel-Telegdi (T-BMT) equation for spin precession. In static and homogeneous electromagnetic fields, it has been shown that the Foldy-Wouthuysen (FW) transform of the Dirac-Pauli Hamiltonian, which describes the relativistic quantum theory for a spin-1/2 particle, is consistent with the classical Hamiltonian (with both the orbital and spin parts) up to the order of 1/m14 (m is the particle's mass) in the low-energy and weak-field limit. In this paper, we extend this correspondence to the case of inhomogeneous fields. Regardless of the field gradient (e.g. Stern-Gerlach) force, the T-BMT equation is unaltered and thus the classical Hamiltonian remains the same, but subtleties arise and need to be clarified. For the relativistic quantum theory, we apply Eriksen's method to obtain the exact FW transformations for the two special cases, which in conjunction strongly suggest that, in the weak-field limit, the FW transformed Dirac-Pauli Hamiltonian (except for the Darwin term) is in agreement with the classical Hamiltonian in a manner that classical variables correspond to quantum operators via a specific Weyl ordering. Meanwhile, the Darwin term is shown to have no classical correspondence.

  15. Examining the equivalence of Bakamjian-Thomas mass operators in different forms of dynamics

    SciTech Connect

    Polyzou, W. N.

    2010-12-15

    We discus the proof of the equivalence of relativistic quantum mechanical models based on the generalized Bakamjian-Thomas construction in all of Dirac's forms of dynamics. Explicit representations of the equivalent mass operators are given in all three of Dirac's forms of dynamics.

  16. Relativistic Definition of Spin Operators

    NASA Astrophysics Data System (ADS)

    Ryder, Lewis H.

    2002-12-01

    Some years ago Mashhoon [1] made the highly interesting suggestion that there existed a coupling of spin with rotations, just as there exists such a coupling with orbital angular momentum, as seen in the Sagnac effect, for example. Spin being essentially a quantum phenomenon, the obvious place to look for this was by studying the Dirac equation, and Hehl and Ni, in such an investigation [2], indeed found a coupling term of just the type Mashhoon had envisaged. Part of their procedure, however, was to take the nonrelativistic limit, and this was done by performing appropriate Foldy-Wouthuysen (FW) transformations. In the nonrelativistic limit, it is well-known that the spin operators for Dirac particles are in essence the Pauli matrices; but it is also well-known, and indeed was part of the motivation for Foldy and Wouthuysen's paper, that for fully-fledged Dirac particles the (4×4 generalisation of the) Pauli matrices do not yield satisfactory spin operators, since spin defined in this way would not be conserved. The question therefore presented itself: is there a relativistic spin operator for Dirac particles, such that in the relativistic, as well as the nonrelativistic, régime a Mashhoon spin-rotation coupling exists?...

  17. 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.

  18. Phase diagram of the Dirac spectrum at nonzero chemical potential

    SciTech Connect

    Osborn, J. C.; Splittorff, K.; Verbaarschot, J. J. M.

    2008-11-15

    The Dirac spectrum of QCD with dynamical fermions at nonzero chemical potential is characterized by three regions: a region with a constant eigenvalue density, a region where the eigenvalue density shows oscillations that grow exponentially with the volume and the remainder of the complex plane where the eigenvalue density is zero. In this paper we derive the phase diagram of the Dirac spectrum from a chiral Lagrangian. We show that the constant eigenvalue density corresponds to a pion condensed phase while the strongly oscillating region is given by a kaon condensed phase. The normal phase with nonzero chiral condensate but vanishing Bose condensates coincides with the region of the complex plane where there are no eigenvalues.

  19. 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.

  20. Quantum oscillations in Weyl and Dirac semimetal ultrathin films

    NASA Astrophysics Data System (ADS)

    Bulmash, Daniel; Qi, Xiao-Liang

    2016-02-01

    We show that a Weyl or Dirac semimetal thin film with a strong in-plane magnetic field becomes a two-dimensional Fermi liquid with interesting properties. The Fermi surface in this system is strongly anisotropic, which originates from a combination of chiral bulk channels and Fermi arcs. The area enclosed by the Fermi surface depends strongly on the in-plane magnetic field component parallel to the Weyl/Dirac node splitting, which leads to unusual behavior in quantum oscillations when the magnetic field is tilted out of the plane. We estimate the oscillation frequencies and the regimes where such effects could be seen in Cd3As2 , Na3Bi , and TaAs.

  1. Dynamical class of a two-dimensional plasmonic Dirac system

    NASA Astrophysics Data System (ADS)

    Silva, Érica de Mello

    2015-10-01

    A current goal in plasmonic science and technology is to figure out how to manage the relaxational dynamics of surface plasmons in graphene since its damping constitutes a hinder for the realization of graphene-based plasmonic devices. In this sense we believe it might be of interest to enlarge the knowledge on the dynamical class of two-dimensional plasmonic Dirac systems. According to the recurrence relations method, different systems are said to be dynamically equivalent if they have identical relaxation functions at all times, and such commonality may lead to deep connections between seemingly unrelated physical systems. We employ the recurrence relations approach to obtain relaxation and memory functions of density fluctuations and show that a two-dimensional plasmonic Dirac system at long wavelength and zero temperature belongs to the same dynamical class of standard two-dimensional electron gas and classical harmonic oscillator chain with an impurity mass.

  2. Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals.

    PubMed

    Bradlyn, Barry; Cano, Jennifer; Wang, Zhijun; Vergniory, M G; Felser, C; Cava, R J; Bernevig, B Andrei

    2016-08-01

    In quantum field theory, we learn that fermions come in three varieties: Majorana, Weyl, and Dirac. Here, we show that in solid-state systems this classification is incomplete, and we find several additional types of crystal symmetry-protected free fermionic excitations. We exhaustively classify linear and quadratic three-, six-, and eight-band crossings stabilized by space group symmetries in solid-state systems with spin-orbit coupling and time-reversal symmetry. Several distinct types of fermions arise, differentiated by their degeneracies at and along high-symmetry points, lines, and surfaces. Some notable consequences of these fermions are the presence of Fermi arcs in non-Weyl systems and the existence of Dirac lines. Ab initio calculations identify a number of materials that realize these exotic fermions close to the Fermi level. PMID:27445310

  3. 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.

  4. 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.

  5. 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.

  6. 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.

    2016-09-01

    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.

  7. Entwined paths, difference equations, and the Dirac equation

    SciTech Connect

    Ord, G.N.; Mann, R.B.

    2003-02-01

    Entwined space-time paths are bound pairs of trajectories which are traversed in opposite directions with respect to macroscopic time. In this paper, we show that ensembles of entwined paths on a discrete space-time lattice are simply described by coupled difference equations which are discrete versions of the Dirac equation. There is no analytic continuation, explicit or forced, involved in this description. The entwined paths are ''self-quantizing.'' We also show that simple classical stochastic processes that generate the difference equations as ensemble averages are stable numerically and converge at a rate governed by the details of the stochastic process. This result establishes the Dirac equation in one dimension as a phenomenological equation describing an underlying classical stochastic process, in the same sense that the diffusion and telegraph equations are phenomenological descriptions of stochastic processes.

  8. 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.

  9. Topological charges of three-dimensional Dirac semimetals with rotation symmetry

    NASA Astrophysics Data System (ADS)

    Yang, Bohm-Jung; Morimoto, Takahiro; Furusaki, Akira

    2015-10-01

    In general, the stability of a band crossing point indicates the presence of a quantized topological number associated with it. In particular, the recent discovery of three-dimensional Dirac semimetals in Na3Bi and Cd3As2 demonstrates that a Dirac point with fourfold degeneracy can be stable as long as certain crystalline symmetries are supplemented in addition to the time-reversal and inversion symmetries. However, the topological charges associated with Na3Bi and Cd3As2 are not clarified yet. In this work, we identify the topological charge of three-dimensional Dirac points. It is found that although the simultaneous presence of the time-reversal and inversion symmetries forces the net chiral charge to vanish, a Dirac point can carry another quantized topological charge when an additional rotation symmetry is considered. Two different classes of Dirac semimetals are identified depending on the nature of the rotation symmetries. First, the conventional symmorphic rotational symmetry which commutes with the inversion gives rise to the class I Dirac semimetals having a pair of Dirac points on the rotation axes. Since the topological charges of each pair of Dirac points have the opposite sign, a pair creation or a pair annihilation is required to change the number of Dirac points in the momentum space. On the other hand, the class II Dirac semimetals possess a single isolated Dirac point at a time-reversal invariant momentum, which is protected by a screw rotation. The nonsymmorphic nature of screw rotations allows the anticommutation relation between the rotation and inversion symmetries, which enables to circumvent the doubling of the number of Dirac points and create a single Dirac point at the Brillouin zone boundary.

  10. 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.

  11. 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.

  12. Axial Anomaly, Dirac Sea, and the Chiral Magnetic Effect

    SciTech Connect

    Kharzeev, D.E.

    2010-05-26

    Gribov viewed the axial anomaly as a manifestation of the collective motion of Dirac fermions with arbitrarily high momenta in the vacuum. In the presence of an external magnetic field and a chirality imbalance, this collective motion becomes directly observable in the form of the electric current - this is the chiral magnetic effect (CME). I give an elementary introduction into the physics of CME, and discuss the experimental status and recent developments.

  13. Hawking radiation of Dirac particles from black strings

    NASA Astrophysics Data System (ADS)

    Ahmed, Jamil; Saifullah, K.

    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.

  14. 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.

  15. Kondo effect and STM spectroscopy of Dirac electrons in graphene

    NASA Astrophysics Data System (ADS)

    Sengupta, Krishnendu

    2011-03-01

    We show that graphene, whose low-energy quasiparticles display Dirac like behavior, may exhibit a two-channel Kondo effect in the presence of magnetic impurities. We present a large N analysis for a generic spin S local moment coupled to Dirac electrons in graphene and demonstrate that the corresponding Kondo temperature can be tuned by an experimentally controllable applied gate voltage. We also study the STM spectra of these Dirac electrons in the presence of such impurities and demonstrate that such spectra depend qualitatively on the position of the impurity atom in the graphene matrix. More specifically, for impurity atoms atop the hexagon center, the zero-bias tunneling conductance, as measured by a STM, shows a peak; for those atop a graphene site, it shows a dip. We provide a qualitative theoretical explanation of this phenomenon and show that this unconventional behavior is a consequence of conservation/breaking of pseudospin symmetry of the Dirac quasiparticles by the impurity. We also predict that tuning the Fermi energy to zero by a gate voltage would not lead to qualitative change in the shape of the conductance spectra when the impurity is atop the hexagon center. A similar tuning of the Fermi energy for the impurity atop a site, however, would lead to a change in the tunneling conductance from a dip to a peak via an antiresonance. We discuss some recent experiments on a doped graphene sample that seem to have qualitative agreement with our theory and suggest further experiments to test our predictions. DST, India.

  16. Berry Curvature and Chiral Plasmons in Massive Dirac Materials

    NASA Astrophysics Data System (ADS)

    Song, Justin; Rudner, Mark

    2015-03-01

    In the semiclassical model of carrier dynamics, quasiparticles are described as nearly free electrons with modified characteristics modified characteristics such as effective masses which may differ significantly from those of an electron in vacuum. In addition to being influenced by external electric and magnetic fields, the trajectories of electrons in topological materials are also affected by the presence of an interesting quantum mechanical field - the Berry curvature - which is responsible for a number of anomalous transport phenomena recently observed in Dirac materials including G/hBN, and MoS2. Here we discuss how Berry curvature can affect the collective behavior of electrons in these systems. In particular, we show that the collective electronic excitations in metallic massive Dirac materials can feature a chirality even in the absence of an applied magnetic field. The chirality of these plasmons arises from the Berry curvature of the massive Dirac bands. The corresponding dispersion is split between left- and right-handed modes. We also discuss experimental manifestations.

  17. MPI support in the DIRAC Pilot Job Workload Management System

    NASA Astrophysics Data System (ADS)

    Tsaregorodtsev, A.; Hamar, V.

    2012-12-01

    Parallel job execution in the grid environment using MPI technology presents a number of challenges for the sites providing this support. Multiple flavors of the MPI libraries, shared working directories required by certain applications, special settings for the batch systems make the MPI support difficult for the site managers. On the other hand the workload management systems with Pilot Jobs became ubiquitous although the support for the MPI applications in the Pilot frameworks was not available. This support was recently added in the DIRAC Project in the context of the GISELA Latin American Grid Initiative. Special services for dynamic allocation of virtual computer pools on the grid sites were developed in order to deploy MPI rings corresponding to the requirements of the jobs in the central task queue of the DIRAC Workload Management System. Pilot Jobs using user space file system techniques install the required MPI software automatically. The same technique is used to emulate shared working directories for the parallel MPI processes. This makes it possible to execute MPI jobs even on the sites not supporting them officially. Reusing so constructed MPI rings for execution of a series of parallel jobs increases dramatically their efficiency and turnaround. In this contribution we describe the design and implementation of the DIRAC MPI Service as well as its support for various types of MPI libraries. Advantages of coupling the MPI support with the Pilot frameworks are outlined and examples of usage with real applications are presented.

  18. Two-vortex structure of electron, nonlocality and Dirac equation

    NASA Astrophysics Data System (ADS)

    Tiwari, S. C.

    2012-02-01

    The dimensionless electromagnetic coupling constant α=e2/planckc may have three interpretations: as the well-known ratio between the electron charge radius e2/mc2 and the Compton wavelength of an electron λc=planck/mc, as the ratio of two angular momenta since the Planck constant has the dimension of angular momentum and as the ratio of two flux quanta e and hc/e . The anomalous part of the electron magnetic moment together with the unified picture of the three interpretations of α is suggested to have deep physical significance. The electric charge is proposed to be a new quantum of flux that leads to a new model of the electron envisaging a two-vortex structure. In analogy with quantum conditions, we postulate sub-quantum conditions applicable in a region of the order of λc replacing planck by a universal constant f=e2/2πc and we apply it to the Dirac equation in internal space that gives rise to the anomalous magnetic moment of an electron. The Dirac spinor and two-spinor representations for the vortex structure of an electron in the single-particle Dirac framework are discussed. The role of sub-quantum rules and internal variables in developing the present ideas is also discussed. A critical discussion of past attempts at giving fundamental importance to magnetism and flux quantum is presented in order to delineate the new ideas in the present work.

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

    PubMed

    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 [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. PMID:27436895

  20. Dirac-bracket structure in multidimensional mode conversion

    NASA Astrophysics Data System (ADS)

    Brizard, A. J.; Tracy, E. R.; Kaufman, A. N.; Johnston, D.; Zobin, N.

    2012-05-01

    The intersection of two (2 n - 1)-dimensional dispersion manifolds Da and Db in the 2 n-dimensional ray phase space P yields a (2 n - 2)-dimensional conversion manifold M≡Da∩Db that naturally possesses a Dirac-bracket structure that is inherited from the canonical Poisson bracket on ray phase space. The canonical symplectic two-form Ω ≡ Ω∥ + Ω⊥, defined on the 2 n-dimensional tangent plane TP≡TM⊕(TM)⊥, can thus be decomposed into the Dirac two-form Ω∥ on the (2 n - 2)-dimensional tangent plane TM at a conversion point z0∈M, and the symplectic two-form Ω⊥ on its orthogonal 2-dimensional complement (TM)⊥. These two symplectic two-forms are introduced in our analysis of multidimensional mode conversion, where their respective geometrical roles are defined. We note that since the Dirac-bracket structure Ω∥ vanishes identically when n = 1, it represents a new structure in multidimensional ( n > 1) mode conversion theory.

  1. Dirac structures in Lagrangian mechanics Part II: Variational structures

    NASA Astrophysics Data System (ADS)

    Yoshimura, Hiroaki; Marsden, Jerrold E.

    2006-12-01

    Part I of this paper introduced the notion of implicit Lagrangian systems and their geometric structure was explored in the context of Dirac structures. In this part, we develop the variational structure of implicit Lagrangian systems. Specifically, we show that the implicit Euler-Lagrange equations can be formulated using an extended variational principle of Hamilton called the Hamilton-Pontryagin principle. This variational formulation incorporates, in a natural way, the generalized Legendre transformation, which enables one to treat degenerate Lagrangian systems. The definition of this generalized Legendre transformation makes use of natural maps between iterated tangent and cotangent spaces. Then, we develop an extension of the classical Lagrange-d'Alembert principle called the Lagrange-d'Alembert-Pontryagin principle for implicit Lagrangian systems with constraints and external forces. A particularly interesting case is that of nonholonomic mechanical systems that can have both constraints and external forces. In addition, we define a constrained Dirac structure on the constraint momentum space, namely the image of the Legendre transformation (which, in the degenerate case, need not equal the whole cotangent bundle). We construct an implicit constrained Lagrangian system associated with this constrained Dirac structure by making use of an Ehresmann connection. Two examples, namely a vertical rolling disk on a plane and an L- C circuit are given to illustrate the results.

  2. 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).

  3. Dirac-like plasmons in Ag nanopillar honeycomb lattices

    NASA Astrophysics Data System (ADS)

    Peng, Siying; Brenny, Benjamin; Hellstrom, Sondra; Coenen, Toon; Polman, Albert; Atwater, Harry

    2015-03-01

    Surface plasmons in honeycomb lattices of Ag nanoparticles exhibit Dirac-like band structures, similar to the electronic band structure of graphene. Full wave simulations for an infinite honeycomb lattice of silver nano-pillars reveal hybridization of localized plasmonic modes between two neighboring pillars and the consequent formation of bonding and anti-bonding modes that are energetically degenerate at Dirac points. Electromagnetic simulations reveal the existence of plasmonic edge states in finite width nanoribbons of the honeycomb nanoparticle lattice. Nanoscale architecture of the honeycomb lattice may provide a new way to control plasmon propagation by selective excitation of directional surface plasmon edge states without backscattering. Experimentally, we have utilized cathodoluminescence (CL) spectroscopy to study angular emission patterns and construct band structures of the silver pillars in honeycomb lattices. In our initial CL measurement, silver pillars in honeycomb lattices, we have observed strong radiation patterns near the Brillouin zone edge, integrated over an interval of wavelength centered on the wavelength of the Dirac points.

  4. Non-Grassmann mechanical model of the Dirac equation

    SciTech Connect

    Deriglazov, A. A.; Zamudio, G. P.; Castro, P. S.; Rizzuti, B. F.

    2012-12-15

    We construct a new example of the spinning-particle model without Grassmann variables. The spin degrees of freedom are described on the base of an inner anti-de Sitter space. This produces both {Gamma}{sup {mu}} and {Gamma}{sup {mu}{nu}}-matrices in the course of quantization. Canonical quantization of the model implies the Dirac equation. We present the detailed analysis of both the Lagrangian and the Hamiltonian formulations of the model and obtain the general solution to the classical equations of motion. Comparing Zitterbewegung of the spatial coordinate with the evolution of spin, we ask on the possibility of space-time interpretation for the inner space of spin. We enumerate similarities between our analogous model of the Dirac equation and the two-body system subject to confining potential which admits only the elliptic orbits of the order of de Broglie wavelength. The Dirac equation dictates the perpendicularity of the elliptic orbits to the direction of center-of-mass motion.

  5. Nonlinear excitations in strongly coupled Fermi-Dirac plasmas

    NASA Astrophysics Data System (ADS)

    Akbari-Moghanjoughi, M.

    2012-04-01

    In this paper, we use the conventional quantum hydrodynamics (QHD) model in combination with the Sagdeev pseudopotential method to explore the effects of Thomas-Fermi nonuniform electron distribution, Coulomb interactions, electron exchange, and ion correlation on the large-amplitude nonlinear soliton dynamics in Fermi-Dirac plasmas. It is found that in the presence of strong interactions, significant differences in nonlinear wave dynamics of Fermi-Dirac plasmas in the two distinct regimes of nonrelativistic and relativistic degeneracies exist. Furthermore, it is remarked that first-order corrections due to such interactions (which are proportional to the fine-structure constant) are more significant on soliton characteristics (particularly the amplitude) in the nonrelativistic plasma degeneracy regime rather than the relativistic one. In the relativistic degeneracy regime, however, these effects become less important and the electron quantum-tunneling and Pauli-exclusion dominate the nonlinear wave dynamics. Hence, application of non-interacting Fermi-Dirac QHD model to study the nonlinear wave dynamics in quantum plasmas, such as in compact stars is most appropriate for the relativistic degeneracy regime rather than nonrelativistic one.

  6. 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.

  7. 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

  8. 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

  9. 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.

  10. 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.

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

    PubMed

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

    2015-02-01

    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.

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

    PubMed Central

    Hou, Jing-Min; Chen, Wei

    2015-01-01

    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. PMID:26639178

  13. 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.

  14. 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.

  15. Universal quantum criticality in Hubbard models with massless Dirac dispersion

    NASA Astrophysics Data System (ADS)

    Otsuka, Yuichi; Yunoki, Seiji; Sorella, Sandro

    We investigate the metal-insulator transition of two-dimensional interacting electrons with massless Dirac-like dispersion, describe by the Hubbard models on two geometrically different lattices: honeycomb and π-flux square lattices. By performing large-scale quantum Monte Carlo simulations followed by careful finite-size scaling analyses, we find that the transition from semi-metallic to antiferromagnetic insulating phases is continuous and evaluate the critical exponents with a high degree of accuracy for the corresponding universality class, which is described in the continuous limit by the Gross-Neveu model. We furthermore discuss the fate of the quasiparticle weight and the Fermi velocity across this transition.

  16. Discussion of a Known Spherical Basis for Dirac Wave Functions

    NASA Astrophysics Data System (ADS)

    Scheid, Werner

    2013-03-01

    The paper considers the free spherical Dirac equation with a boundary condition at r = R which is a slight extension of the original boundary condition of the MIT bag model. We discuss the basis states and apply them for a diagonalization of Coulomb potentials. The obtained results agree quite well with the lowest bound states with κ = -1, +1 and -2 and their expectation values √ {< r2>}. There appear basis states with energies -mc2 < E < mc2 under certain circumstances of the boundary condition. These states are concentrated at the boundary.

  17. Universal spin Hall conductance fluctuations in chaotic Dirac quantum dots

    NASA Astrophysics Data System (ADS)

    Vasconcelos, T. C.; Ramos, J. G. G. S.; Barbosa, A. L. R.

    2016-03-01

    We present complete analytical and numerical results that demonstrate the anomalous universal fluctuations of the spin Hall conductance in chiral materials such as graphene and topological insulators. We investigate both the corresponding fluctuations, the universal fractionated and the universal quantized, and also the open channel orbital number crossover between the two regimes. In particular, we show that the Wigner-Dyson symmetries do not properly describe such conductances and the preponderant role of the chiral classes on the Dirac quantum dots. The results are analytical and solve outstanding issues.

  18. Ultrafast exciton-polariton scattering towards the Dirac points

    NASA Astrophysics Data System (ADS)

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

    2016-03-01

    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.

  19. Entanglement of Dirac fields in an expanding spacetime

    SciTech Connect

    Fuentes, Ivette; Mann, Robert B.; Martin-Martinez, Eduardo; Moradi, Shahpoor

    2010-08-15

    We study the entanglement generated between Dirac modes in a 2-dimensional conformally flat Robertson-Walker universe. We find radical qualitative differences between the bosonic and fermionic entanglement generated by the expansion. The particular way in which fermionic fields get entangled encodes more information about the underlying spacetime than the bosonic case, thereby allowing us to reconstruct the parameters of the history of the expansion. This highlights the importance of bosonic/fermionic statistics to account for relativistic effects on the entanglement of quantum fields.

  20. 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.

  1. Spin-polarized gapped Dirac spectrum of unsupported silicene

    NASA Astrophysics Data System (ADS)

    Podsiadły-Paszkowska, A.; Krawiec, M.

    2016-06-01

    We study effects of the spin-orbit interaction and the atomic reconstruction of silicene on its electronic spectrum. As an example we consider unsupported silicene pulled off from Pb(111) substrate. Using first principles density functional theory we show that the inversion symmetry broken arrangement of atoms and the spin-orbit interaction generate a spin-polarized electronic spectrum with an energy gap in the Dirac cone. These findings are particularly interesting in view of the quantum anomalous and quantum valley Hall effects and should be observable in weakly interacting silicene-substrate systems.

  2. On the Pauli-Weisskopf anti-Dirac paper

    NASA Astrophysics Data System (ADS)

    Dittrich, Walter

    2015-03-01

    We review in this article the role which the work of Pauli and Weisskopf played in formulating a quantum field theory of spinless particles. To make our computations as transparent as possible, we offer a physicist's derivation of the Klein-Gordon-Fock equation. Since invariant functions play a significant part in our paper, we will discuss them in great detail. We emphasize Pauli's and Weisskopf's view that Dirac's hole theory is totally obsolete in formulating a consistent quantum field theory, be it for scalar or spinor particles. As an important example we present the calculation for producing charged scalar particles in an external electric field.

  3. 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. PMID:26886717

  4. 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.

  5. Helical Spin Order from Topological Dirac and Weyl Semimetals

    SciTech Connect

    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.

  6. 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.

  7. Scanning tunneling spectroscopy study of the Dirac spectrum of germanene.

    PubMed

    Walhout, C J; Acun, A; Zhang, L; Ezawa, M; Zandvliet, H J W

    2016-07-20

    The temperature dependence of the density of states of germanene, synthesized on Ge/Pt crystals, has been investigated with scanning tunneling spectroscopy. After correction for thermal broadening, a virtually perfect V-shaped density of states, which is a hallmark of a two-dimensional Dirac system, has been found. In an attempt to directly measure the energy dispersion relation via quasiparticle interference we have recorded spatial maps of the differential conductivity near the edges and defects of germanene. Unfortunately, we did not find any sign of Friedel oscillations. The absence of these Friedel oscillations hints to the occurrence of Klein tunneling. PMID:27227390

  8. Surface conduction of topological Dirac electrons in bulk insulating Bi2Se3

    NASA Astrophysics Data System (ADS)

    Fuhrer, Michael

    2013-03-01

    The three dimensional strong topological insulator (STI) is a new phase of electronic matter which is distinct from ordinary insulators in that it supports on its surface a conducting two-dimensional surface state whose existence is guaranteed by topology. I will discuss experiments on the STI material Bi2Se3, which has a bulk bandgap of 300 meV, much greater than room temperature, and a single topological surface state with a massless Dirac dispersion. Field effect transistors consisting of thin (3-20 nm) Bi2Se3 are fabricated from mechanically exfoliated from single crystals, and electrochemical and/or chemical gating methods are used to move the Fermi energy into the bulk bandgap, revealing the ambipolar gapless nature of transport in the Bi2Se3 surface states. The minimum conductivity of the topological surface state is understood within the self-consistent theory of Dirac electrons in the presence of charged impurities. The intrinsic finite-temperature resistivity of the topological surface state due to electron-acoustic phonon scattering is measured to be ~60 times larger than that of graphene largely due to the smaller Fermi and sound velocities in Bi2Se3, which will have implications for topological electronic devices operating at room temperature. As samples are made thinner, coherent coupling of the top and bottom topological surfaces is observed through the magnitude of the weak anti-localization correction to the conductivity, and, in the thinnest Bi2Se3 samples (~ 3 nm), in thermally-activated conductivity reflecting the opening of a bandgap.

  9. Huygens’ principle for hyperbolic operators and integrable hierarchies

    NASA Astrophysics Data System (ADS)

    Chalub, Fabio A. C. C.; Zubelli, Jorge P.

    2006-01-01

    We show that the stationary solutions of the canonical AKNS hierarchy of nonlinear evolution equations yield perturbations of Dirac operators that satisfy a strict form of Huygens’ principle. Namely, the domain of dependence of such Dirac operators at any given point y is contained in the light-cone’s hypersurface issued from y. By the canonical AKNS hierarchy we mean that the differential polynomials defining the flows are isobaric with respect to certain weights. The method we employ is of interest by itself. Indeed, we consider the Riesz kernels associated to a given hyperbolic differential operator and expand the fundamental solution of perturbations of this operator in a series in such Riesz kernels. Using the coefficients of this Hadamard type expansion we introduce a family of vector fields. For the D’Alembertian such vector field family corresponds to the KdV hierarchy and for the Dirac operators they include the AKNS one.

  10. On the electronic viscosity of a Dirac fluid in deformed graphene

    NASA Astrophysics Data System (ADS)

    Sergeenkov, Sergei; Ausloos, Marcel

    2016-03-01

    We discuss the properties of the electronic viscosity of a Dirac fluid in deformed graphene by introducing a strain ? and a velocity gradient ?, as equivalent to a pseudo-magnetic ? and a pseudo-electric ? field respectively into the Dirac equation. It is thereby analytically established that the dynamic shear viscosity coefficient ? substantially decreases with the applied strain as ?, reaching as much as ? for ?.

  11. 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.

  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. Can neutrino-electron scattering tell us whether neutrinos are Dirac or Majorana particles

    SciTech Connect

    Kayser, B.

    1988-04-01

    There has recently been interest in the possibility that neutrino-electron scattering experiments could determine whether neutrinos are Dirac or Majorana particles by providing information on their electromagnetic structure. We try to explain why studies of neutrino electromagnetic structure actually cannot distinguish between Dirac and Majorana neutrinos. 9 refs.

  14. 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

  15. Baryon spectrum analysis using Dirac's covariant constraint dynamics

    NASA Astrophysics Data System (ADS)

    Whitney, Joshua F.; Crater, Horace W.

    2014-01-01

    We present a relativistic quark model for the baryons that combines three related relativistic formalisms. The three-body constraint formalism of Sazdjian is used to recast three relativistic two-body equations for the three pairs of interacting quarks into a single relativistically covariant three-body equation for the bound state energies, having a Schrodinger-like structure. The two-body equations are the two-body Dirac equations of constraint dynamics derived by Crater and Van Alstine for combined world vector and scalar interactions providing the necessary spin dependent and spin independent interaction terms. The minimal quasipotential formalism of Todorov is used to provide an invariant framework for the vector and scalar dynamics used in the two-body Dirac equations into which is inserted a local simplified version of the Richardson potential. The spectral results are analyzed and compared to experiment using a best fit method and several different algorithms, including a gradient approach, and a Monte Carlo method.

  16. Presymmetry in the Standard Model with adulterated Dirac neutrinos

    NASA Astrophysics Data System (ADS)

    Matute, Ernesto A.

    2015-08-01

    Recently we proposed a model for light Dirac neutrinos in which two right-handed (RH) neutrinos per generation are added to the particles of the Standard Model (SM), implemented with the symmetry of fermionic contents. The ordinary one is decoupled via the high scale type-I seesaw mechanism, while the extra pairs off with its left-handed (LH) partner. The symmetry of lepton and quark contents was merely used as a guideline to the choice of parameters because it is not a proper symmetry. Here we argue that the underlying symmetry to take for this correspondence is presymmetry, the hidden electroweak symmetry of the SM extended with RH neutrinos defined by transformations which exchange lepton and quark bare states with the same electroweak charges and no Majorana mass terms in the underlying Lagrangian. It gives a topological character to fractional charges, relates the number of families to the number of quark colors, and now guarantees the great disparity between the couplings of the two RH neutrinos. Thus, Dirac neutrinos with extremely small masses appear as natural predictions of presymmetry, satisfying the ’t Hooft’s naturalness conditions in the extended seesaw where the extra RH neutrinos serve to adulterate the mass properties in the low scale effective theory, which retains without extensions the gauge and Higgs sectors of the SM. However, the high energy threshold for the seesaw implies new physics to stabilize the quantum corrections to the Higgs boson mass in agreement with the naturalness requirement.

  17. Dirac Cellular Automaton from Split-step Quantum Walk

    NASA Astrophysics Data System (ADS)

    Mallick, Arindam; Chandrashekar, C. M.

    2016-05-01

    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.

  18. 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.

  19. Answering Dirac's Challenge: Practical Quantum Mechanics for Materials

    NASA Astrophysics Data System (ADS)

    Chelikowsky, James

    2012-10-01

    Over eight decades ago, after the invention of quantum mechanics, P. A. M. Dirac made the following observation: ``The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems...'' The creation of ``approximate practical methods'' in response to Dirac's challenge has included the one electron picture, density functional theory and the pseudopotential concept. The combination of such methods in conjunction with contemporary computational platforms and new algorithms offer the possibility of predicting properties of materials solely on the basis of the atomic species present. I will give an overview of progress in this field with an emphasis on materials at the nanoscale.

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

    SciTech Connect

    Akbari-Moghanjoughi, M.

    2011-07-15

    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.

  1. Optical properties of Dirac electrons in a parabolic well.

    PubMed

    Kim, S C; Lee, J W; Yang, S-R Eric

    2013-09-01

    A single electron transitor may be fabricated using qunatum dots. A good model for the confinement potential of a quantum dot is a parabolic well. Here we consider such a parabolic dot made of graphene. Recently, we found counter intuitively that resonant quasi-boundstates of both positive and negative energies exist in the energy spectrum. The presence of resonant quasi-boundstates of negative energies is a unique property of massless Dirac fermions. As magnetic field B gets smaller the energy width of these states become broader and for sufficiently weak value of B resonant quasi-bound states disappear into a quasi-continuum. In the limit of small B resonant and nonresonant states transform into discrete anomalous states with a narrow probability density peak inside the well and another broad peak under the potential barrier. In this paper we compute the optical strength between resonant quasi-bound states as a function of B, and investigate how the signature of resonant quasi-bound states of Dirac electrons may appear in optical measurements.

  2. Einstein - Cartan - Dirac theory in the low-energy limit

    NASA Astrophysics Data System (ADS)

    Singh, P.; Ryder, L. H.

    1997-12-01

    We look for manifestations of the effects of torsion in the low-energy limit in the context of Einstein - Cartan - Dirac theory (or any theory of gravity in which the torsion tensor is purely axial). To proceed, we introduce the mathematical law governing the transport of orthonormal bases or tetrads in a spacetime with torsion. This law is applied to compute the metric and connection in a rotating and accelerating frame, or laboratory. A spin-0264-9381/14/12/031/img1 particle is placed in this rotating and accelerating frame and the low-energy limit of the Dirac equation is taken by means of the Foldy - Wouthuysen transformation. In addition to obtaining the Bonse - Wroblewski phase shift due to acceleration, Sagnac-type effects, rotation - spin couplings of the Mashhoon type, redshift of the kinetic energy and the spin - orbit coupling term of Hehl and Ni, we also obtain several interesting and significant terms as a consequence of introducing torsion into spacetime. We give a detailed interpretation of these additional terms and discuss their observability in the light of current well-known experimental techniques.

  3. 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.

  4. 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.

  5. Two-dimensional gas of massless Dirac fermions in graphene.

    PubMed

    Novoselov, K S; Geim, A K; Morozov, S V; Jiang, D; Katsnelson, M I; Grigorieva, I V; Dubonos, S V; Firsov, A A

    2005-11-10

    Quantum electrodynamics (resulting from the merger of quantum mechanics and relativity theory) has provided a clear understanding of phenomena ranging from particle physics to cosmology and from astrophysics to quantum chemistry. The ideas underlying quantum electrodynamics also influence the theory of condensed matter, but quantum relativistic effects are usually minute in the known experimental systems that can be described accurately by the non-relativistic Schrödinger equation. Here we report an experimental study of a condensed-matter system (graphene, a single atomic layer of carbon) in which electron transport is essentially governed by Dirac's (relativistic) equation. The charge carriers in graphene mimic relativistic particles with zero rest mass and have an effective 'speed of light' c* approximately 10(6) m s(-1). Our study reveals a variety of unusual phenomena that are characteristic of two-dimensional Dirac fermions. In particular we have observed the following: first, graphene's conductivity never falls below a minimum value corresponding to the quantum unit of conductance, even when concentrations of charge carriers tend to zero; second, the integer quantum Hall effect in graphene is anomalous in that it occurs at half-integer filling factors; and third, the cyclotron mass m(c) of massless carriers in graphene is described by E = m(c)c*2. This two-dimensional system is not only interesting in itself but also allows access to the subtle and rich physics of quantum electrodynamics in a bench-top experiment.

  6. Dirac spectra of two-dimensional QCD-like theories

    NASA Astrophysics Data System (ADS)

    Kieburg, Mario; Verbaarschot, Jacobus J. M.; Zafeiropoulos, Savvas

    2014-10-01

    We analyze Dirac spectra of two-dimensional QCD-like theories both in the continuum and on the lattice and classify them according to random matrix theories sharing the same global symmetries. The classification is different from QCD in four dimensions because the antiunitary symmetries do not commute with γ5. Therefore, in a chiral basis, the number of degrees of freedom per matrix element are not given by the Dyson index. Our predictions are confirmed by Dirac spectra from quenched lattice simulations for QCD with two or three colors with quarks in the fundamental representation as well as in the adjoint representation. The universality class of the spectra depends on the parity of the number of lattice points in each direction. Our results show an agreement with random matrix theory that is qualitatively similar to the agreement found for QCD in four dimensions. We discuss the implications for the Mermin-Wagner-Coleman theorem and put our results in the context of two-dimensional disordered systems.

  7. Massless Dirac particles in the vacuum C-metric

    NASA Astrophysics Data System (ADS)

    Bini, Donato; Bittencourt, Eduardo; Geralico, Andrea

    2015-11-01

    We study the behavior of massless Dirac particles in the vacuum C-metric spacetime, representing the nonlinear superposition of the Schwarzschild black hole solution and the Rindler flat spacetime associated with uniformly accelerated observers. Under certain conditions, the C-metric can be considered as a unique laboratory to test the coupling between intrinsic properties of particles and fields with the background acceleration in the full (exact) strong-field regime. The Dirac equation is separable by using, e.g., a spherical-like coordinate system, reducing the problem to one-dimensional radial and angular parts. Both radial and angular equations can be solved exactly in terms of general Heun functions. We also provide perturbative solutions to first order in a suitably defined acceleration parameter, and compute the acceleration-induced corrections to the particle absorption rate as well as to the angle-averaged cross section of the associated scattering problem in the low-frequency limit. Furthermore, we show that the angular eigenvalue problem can be put in one-to-one correspondence with the analogous problem for a Kerr spacetime, by identifying a map between these ‘acceleration’ harmonics and Kerr spheroidal harmonics. Finally, in this respect we discuss the nature of the coupling between intrinsic spin and spacetime acceleration in comparison with the well known Kerr spin-rotation coupling.

  8. The Talbot Effect for two-dimensional massless Dirac fermions

    NASA Astrophysics Data System (ADS)

    Walls, Jamie D.; Hadad, Daniel

    2016-05-01

    A monochromatic beam of wavelength λ transmitted through a periodic one-dimensional diffraction grating with lattice constant d will be spatially refocused at distances from the grating that are integer multiples of . This self-refocusing phenomena, commonly referred to as the Talbot effect, has been experimentally demonstrated in a variety of systems ranging from optical to matter waves. Theoretical predictions suggest that the Talbot effect should exist in the case of relativistic Dirac fermions with nonzero mass. However, the Talbot effect for massless Dirac fermions (mDfs), such as those found in monolayer graphene or in topological insulator surfaces, has not been previously investigated. In this work, the theory of the Talbot effect for two-dimensional mDfs is presented. It is shown that the Talbot effect for mDfs exists and that the probability density of the transmitted mDfs waves through a periodic one-dimensional array of localized scatterers is also refocused at integer multiples of zT. However, due to the spinor nature of the mDfs, there are additional phase-shifts and amplitude modulations in the probability density that are most pronounced for waves at non-normal incidence to the scattering array.

  9. 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.

  10. The Talbot Effect for two-dimensional massless Dirac fermions

    PubMed Central

    Walls, Jamie D.; Hadad, Daniel

    2016-01-01

    A monochromatic beam of wavelength λ transmitted through a periodic one-dimensional diffraction grating with lattice constant d will be spatially refocused at distances from the grating that are integer multiples of . This self-refocusing phenomena, commonly referred to as the Talbot effect, has been experimentally demonstrated in a variety of systems ranging from optical to matter waves. Theoretical predictions suggest that the Talbot effect should exist in the case of relativistic Dirac fermions with nonzero mass. However, the Talbot effect for massless Dirac fermions (mDfs), such as those found in monolayer graphene or in topological insulator surfaces, has not been previously investigated. In this work, the theory of the Talbot effect for two-dimensional mDfs is presented. It is shown that the Talbot effect for mDfs exists and that the probability density of the transmitted mDfs waves through a periodic one-dimensional array of localized scatterers is also refocused at integer multiples of zT. However, due to the spinor nature of the mDfs, there are additional phase-shifts and amplitude modulations in the probability density that are most pronounced for waves at non-normal incidence to the scattering array. PMID:27221604

  11. 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.

  12. High Field Magnetoresistance of Graphene at the Dirac Point

    NASA Astrophysics Data System (ADS)

    Checkelsky, Joseph; Li, Lu; Ong, N. P.

    2008-03-01

    The longitudinal and Hall resistance of graphene near the charge neutral point have been studied down to low temperature (20 mK) in high magnetic field (20 T). At issue is the nature of the ground state in the vicinity of the Dirac point in high magnetic fields. In samples in which the offset voltage is small, we observe a highly unusual approach to an insulating state as the field increases. In samples with μ> 0.5 T-1 and V0< 3 V, the resistance at the Dirac point R0 increases divergently to Mφ in fields of 14-20 T at temperatures T < 2 K. This divergent behavior is suppressed in samples with large V0. Surprisingly, this rise shows little temperature dependence below 2 K. The acute dependence on magnetic field and accompanying lack of activated behavior with temperature provides evidence for an unusual cross-over or transition to the insulating state. Implications for theoretical models including gapless edge modes and Quantum Hall Ferromagnetism will be discussed in the context of these results.

  13. Aneesur Rahman Prize for Computational Physics Lecture: Addressing Dirac's Challenge

    NASA Astrophysics Data System (ADS)

    Chelikowsky, James

    2013-03-01

    After the invention of quantum mechanics, P. A. M. Dirac made the following observation: ``The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems...'' The creation of ``approximate practical methods'' in response to Dirac's challenge has included the one electron picture, density functional theory and the pseudopotential concept. The combination of such methods in conjunction with contemporary computational platforms and new algorithms offer the possibility of predicting properties of materials solely from knowledge of the atomic species present. I will give an overview of progress in this field with an emphasis on materials at the nanoscale. Support from the Department of Energy and the National Science Foundation is acknowledged.

  14. 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.

  15. 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

  16. 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.

  17. Multiple Scattering of Dirac Fermions in Two Dimensions

    NASA Astrophysics Data System (ADS)

    Asmar, Mahmoud M.; Ulloa, Sergio E.

    2014-03-01

    The low energy dispersion of electrons in graphene-as well as surface states of three dimensional topological insulators- are characterized by a linear dispersion, leading to interesting dynamical properties. The presence of potential scattering centers, such as impurities in real samples or artificially created gated regions, also reflect the ``massless'' nature of electrons in these materials. The study of Dirac fermion scattering from single potential obstacles is made possible through partial wave methods. In the case of closely-spaced potential obstacles (high defect concentration), one should consider multiple scattering effects. Using separation of variables, Graf's addition rules, and far field matching, one can generalize the partial wave method to the case of many scatterers, and obtain physical observables for such problem. We present our study of the scattering problem of Dirac fermions from multiple potential obstacles, with focus on the two-center problem. We discuss the dependence of the differential cross section on the separation, and different potential shifts caused by these obstacles, and compare these results with the differential cross section for a single scattering center. We also study the minimal conditions that allow the observation of Klein tunneling. Supported by MWN/CIAM-NSF and AvH.

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

    SciTech Connect

    Berredo-Peixoto, G. de; Shapiro, I.L.; Souza, C.A. de; Freidel, L. E-mail: lfreidel@perimeterinstitute.ca E-mail: abrahaocleber@gmail.com

    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 → ∞)

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

    PubMed

    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

  20. Magnetic Torque Anomaly in the Quantum Limit of Weyl and Dirac Semimetals

    NASA Astrophysics Data System (ADS)

    Nair, Nityan L.; Moll, Philip J. W.; Potter, Andrew C.; Ramshaw, Brad; Modic, Kimberly; Riggs, Scott; Zeng, Bin; Ghimire, Nirmal; Bauer, Eric; Kealhofer, Robert; Li, Zhenglu; Louie, Steven; Ronning, Filip; Analytis, James G.

    Three dimensional Dirac and Weyl semimetals, characterized by bulk quasiparticles that behave as massless, linearly dispersing Dirac or Weyl fermions, have excited physicists with their unique topological properties and potential for applications. The experimental signatures of Weyl or Dirac fermions, however, are often subtle and indirect, especially in systems where they coexist with trivial electrons. Here, we report a novel method by which these topological systems can be unambiguously experimentally identified. Magnetic torque measurements were performed on the Weyl semimetal NbAs in high magnetic field, showing a large anomaly upon entering the quantum limit. The torque exhibits a striking sign reversal, corresponding to a change in the magnetic anisotropy that is a direct result of the topological properties of the charge carriers. This result can be generalized to other Dirac and Weyl semimetal systems and establishes quantum limit torque measurements as a simple and direct experimental method of distinguishing topologically non-trivial Weyl and Dirac systems from trivial semiconductors.

  1. 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

  2. Magnetic Kronig-Penney-type graphene superlattices: finite energy Dirac points with anisotropic velocity renormalization.

    PubMed

    Qui Le, V; Huy Pham, C; Lien Nguyen, V

    2012-08-29

    We study the energy band structure of magnetic graphene superlattices with delta-function magnetic barriers and zero average magnetic field. The dispersion relation obtained using the T-matrix approach shows the emergence of an infinite number of Dirac-like points at finite energies, while the original Dirac point is still located at the same place as that for pristine graphene. The carrier group velocity at the original Dirac point is isotropically renormalized, but at finite energy Dirac points it is generally anisotropic. An asymmetry in the width between the wells and the barriers of the periodic potential induces a shift of the original Dirac point in the zero-energy plane, keeping the velocity renormalization isotropic.

  3. 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

    2016-01-01

    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

  4. 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.

  5. 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.

  6. Higher-degree Dirac currents of twistor and Killing spinors in supergravity theories

    NASA Astrophysics Data System (ADS)

    Açık, Özgür; Ertem, Ümit

    2015-09-01

    We show that higher degree Dirac currents of twistor and Killing spinors correspond to the hidden symmetries of the background spacetime which are generalizations of conformal Killing and Killing vector fields respectively. They are the generalizations of one-form Dirac currents to higher degrees which are used in constructing the bosonic supercharges in supergravity theories. In the case of Killing spinors, we find that the equations satisfied by the higher degree Dirac currents are related to Maxwell-like and Duffin-Kemmer-Petiau equations. Correspondence between the Dirac currents and harmonic forms for parallel and pure spinor cases is determined. We also analyze the supergravity twistor and Killing spinor cases in ten and eleven-dimensional supergravity theories and find that although different inner product classes induce different involutions on spinors, the higher degree Dirac currents still correspond to the hidden symmetries of the spacetime.

  7. 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.

  8. Dual Dirac Liquid on the Surface of the Electron Topological Insulator

    NASA Astrophysics Data System (ADS)

    Wang, Chong; Senthil, T.

    2015-10-01

    We discuss a non-Fermi liquid gapless metallic surface state of the topological band insulator. It has an odd number of gapless Dirac fermions coupled to a noncompact U (1 ) gauge field. This can be viewed as a vortex dual to the conventional Dirac fermion surface state. This surface duality is a reflection of a bulk dual description discussed recently for the gauged topological insulator. All the other known surface states can be conveniently accessed from the dual Dirac liquid, including the surface quantum Hall state, the Fu-Kane superconductor, the gapped symmetric topological order and the "composite Dirac liquid." We also discuss the physical properties of the dual Dirac liquid and its connection to the half-filled Landau level.

  9. 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

  10. 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.

  11. 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.

  12. 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.

  13. 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

  14. 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

  15. Searching for an equation: Dirac, Majorana and the others

    NASA Astrophysics Data System (ADS)

    Esposito, S.

    2012-06-01

    We review the non-trivial issue of the relativistic description of a quantum mechanical system that, contrary to a common belief, kept theoreticians busy from the end of 1920s to (at least) mid 1940s. Starting by the well-known works by Klein-Gordon and Dirac, we then give an account of the main results achieved by a variety of different authors, ranging from de Broglie to Proca, Majorana, Fierz-Pauli, Kemmer, Rarita-Schwinger and many others. A particular interest comes out for the general problem of the description of particles with arbitrary spin, introduced (and solved) by Majorana as early as 1932, and later reconsidered, within a different approach, by Dirac in 1936 and by Fierz-Pauli in 1939. The final settlement of the problem in 1945 by Bhabha, who came back to the general ideas introduced by Majorana in 1932, is discussed as well, and, by making recourse also to unpublished documents by Majorana, we are able to reconstruct the line of reasoning behind the Majorana and the Bhabha equations, as well as its evolution. Intriguingly enough, such an evolution was identical in the two authors, the difference being just the period of time required for that: probably few weeks in one case (Majorana), while more than ten years in the other one (Bhabha), with the contribution of several intermediate authors. The important unpublished contributions by Majorana anticipated later results obtained, in a more involved way, by de Broglie (1934) and by Duffin and Kemmer (1938-9), and testify the intermediate steps in the line of reasoning that led to the paper published in 1932 by Majorana, while Bhabha took benefit of the corresponding (later) published literature. Majorana's paper of 1932, in fact, contrary to the more complicated Dirac-Fierz-Pauli formalism, resulted to be very difficult to fully understand (probably for its pregnant meaning and latent physical and mathematical content): as is clear from his letters, even Pauli (who suggested its reading to Bhabha) took

  16. Dirac equation with an ultraviolet cutoff and a quantum walk

    SciTech Connect

    Sato, Fumihito; Katori, Makoto

    2010-01-15

    The weak convergence theorems of the one- and two-dimensional simple quantum walks, SQW{sup (d)},d=1,2, show a striking contrast to the classical counterparts, the simple random walks, SRW{sup (d)}. In the SRW{sup (d)}, the distribution of position X(t) of the particle starting from the origin converges to the Gaussian distribution in the diffusion scaling limit, in which the time scale T and spatial scale L both go to infinity as the ratio L/sq root(T) is kept finite. On the other hand, in the SQW{sup (d)}, the ratio L/T is kept to define the pseudovelocity V(t)=X(t)/t, and then all joint moments of the components V{sub j}(t),1<=j<=d, of V(t) converge in the T=L->infinity limit. The limit distributions have novel structures such that they are inverted-bell shaped and their supports are bounded. In the present paper we claim that these properties of the SQW{sup (d)} can be explained by the theory of relativistic quantum mechanics. We show that the Dirac equation with a proper ultraviolet cutoff can provide a quantum walk model in three dimensions, where the walker has a four-component qubit. We clarify that the pseudovelocity V(t) of the quantum walker, which solves the Dirac equation, is identified with the relativistic velocity. Since the quantum walker should be a tardyon, not a tachyon, |V(t)|Dirac equation, we obtain the limit distributions of pseudovelocities for the lower dimensional quantum walks. We show that the obtained limit distributions for the one- and two-dimensional systems have common features with those of SQW{sup (1)} and SQW{sup (2)}.

  17. 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".

  18. 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

    2016-01-01

    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 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. PMID:27466151

  19. Dirac and Weyl rings in three-dimensional cold-atom optical lattices

    NASA Astrophysics Data System (ADS)

    Xu, Yong; Zhang, Chuanwei

    2016-06-01

    Recently three-dimensional topological quantum materials with gapless energy spectra have attracted considerable interest in many branches of physics. Besides the celebrated example, Dirac and Weyl points which possess gapless point structures in the underlying energy dispersion, the topologically protected gapless spectrum, can also occur along a ring, named Dirac and Weyl nodal rings. Ultracold atomic gases provide an ideal platform for exploring new topological materials with designed symmetries and dispersion. However, whether Dirac and Weyl rings can exist in the single-particle spectrum of cold atoms remains elusive. Here we propose a realistic model for realizing Dirac and Weyl rings in the single-particle band dispersion of a cold-atom optical lattice. Our scheme is based on a previously experimentally implemented Raman coupling setup for realizing spin-orbit coupling. Without the Zeeman field, the model preserves both pseudo-time-reversal and inversion symmetries, allowing Dirac rings. The Dirac rings split into Weyl rings with a Zeeman field that breaks the pseudo-time-reversal symmetry. We examine the superfluidity of attractive Fermi gases in this model and also find Dirac and Weyl rings in the quasiparticle spectrum.

  20. 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

  1. 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.

  2. 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.

  3. 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. PMID:27093586

  4. 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.

  5. Quenched dynamics of superconducting Dirac fermions on honeycomb lattice

    NASA Astrophysics Data System (ADS)

    Lu, Ming; Xie, X. C.; X. C. Xie's group Team

    We study the BCS paring dynamics for the superconducting Dirac fermions on honeycomb lattice after a sudden quench of pairing strength. We observe two distinct phases, one is the synchronized phase with undamped oscillations of paring amplitude; the other phase has the paring amplitude oscillates from positive to negative. The exact phase transition point is given by investigating the integrability of the system. Different from the previous work on normal superconducting fermions, which has three distinct phases, our results shows the absence of the Landau damped phase and over damped phase. Moreover, we present a linear analysis in the weakly quenched regime, showing that in a rather long time scale, the dynamics can be approximated as the periodic oscillation with 2Δ∞ angular frequency along with the logarithmic decay of the pairing amplitude, in contrast of the t - 1 / 2 decay for the normal fermions, namely the Landau damped phase. The presenter's advisor.

  6. Accurate solution of the Dirac equation on Lagrange meshes.

    PubMed

    Baye, Daniel; Filippin, Livio; Godefroid, Michel

    2014-04-01

    The Lagrange-mesh method is an approximate variational method taking the form of equations on a grid because of the use of a Gauss quadrature approximation. With a basis of Lagrange functions involving associated Laguerre polynomials related to the Gauss quadrature, the method is applied to the Dirac equation. The potential may possess a 1/r singularity. For hydrogenic atoms, numerically exact energies and wave functions are obtained with small numbers n+1 of mesh points, where n is the principal quantum number. Numerically exact mean values of powers -2 to 3 of the radial coordinate r can also be obtained with n+2 mesh points. For the Yukawa potential, a 15-digit agreement with benchmark energies of the literature is obtained with 50 or fewer mesh points.

  7. Dirac's Covariant Constraint Dynamics Applied to the Baryon Spectrum

    NASA Astrophysics Data System (ADS)

    Whitney, Joshua; Crater, Horace

    2010-02-01

    A baryon is a hadron containing three quarks in a combination of up, down, strange, charm, or bottom. For prediction of the baryon energy spectrum, a baryon is modeled as a three-body system with the interacting forces coming from a set of two-body potentials that depend on the distance between the quarks, the spin-spin and spin-orbit angular momentum coupling terms, and a tensor term. Techniques and equations are derived from Todorov's work on constraint dynamics and the quasi-potential equation together with Two Body Dirac equations developed by Crater and Van Alstine, and adapted to this specific problem by further use of Sazdjian's N-body constraints dynamics for general confined systems. Baryon spectroscopy results are presented and compared with experiment. Typically, a best fit method is used in the analyses that employ several different algorithms, including a gradient approach, Monte Carlo modeling, and simulated annealing methods. )

  8. 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.

  9. States of the Dirac Equation in Confining Potentials

    SciTech Connect

    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 Schroedinger 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.

  10. 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.

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

    PubMed

    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

  12. Probing Resonances of the Dirac Equation with Complex Momentum Representation.

    PubMed

    Li, Niu; Shi, Min; Guo, Jian-You; Niu, Zhong-Ming; Liang, Haozhao

    2016-08-01

    Resonance plays critical roles in the formation of many physical phenomena, and several methods have been developed for the exploration of resonance. In this work, we propose a new scheme for resonance by solving the Dirac equation in the complex momentum representation, in which the resonant states are exposed clearly in the complex momentum plane and the resonance parameters can be determined precisely without imposing unphysical parameters. Combined with the relativistic mean-field theory, this method is applied to probe the resonances in ^{120}Sn with the energies, widths, and wave functions being obtained. Compared to other methods, this method is not only very effective for narrow resonances, but also can be reliably applied to broad resonances. PMID:27541464

  13. 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

  14. Anomalous conductivity tensor in the Dirac semimetal Na3Bi

    NASA Astrophysics Data System (ADS)

    Xiong, Jun; Kushwaha, Satya; Krizan, Jason; Liang, Tian; Cava, R. J.; Ong, N. P.

    2016-04-01

    Na3Bi is a Dirac semimetal with protected nodes that may be sensitive to the breaking of time-reversal invariance in a magnetic field B. We report experiments which reveal that both the conductivity and resistivity tensors exhibit robust anomalies in B. The resistivity ρxx is B-linear up to 35 T, while the Hall angle exhibits an unusual profile approaching a step function. The conductivities σxx and σxy share identical power-law dependences at large B. We propose that these significant deviations from conventional transport result from an unusual sensitivity of the transport lifetime to B. The transport features are compared with those in Cd3As2.

  15. The Einstein-Brillouin Action Quantization for Dirac Fermions

    NASA Astrophysics Data System (ADS)

    Onorato, P.

    The Einstein-Brillouin-Keller semiclassical quantization and the topological Maslov index are used to compute the electronic structure of carbon based nanostructures with or without transverse magnetic field. The calculation is based on the Dirac Fermions approach in the limit of strong coupling for the pseudospin. The electronic bandstructure for carbon nanotubes and graphene nanoribbons are discussed, focusing on the role of the chirality and of the unbonded edges configuration respectively. The effects of a transverse uniform magnetic field are analyzed, the different kinds of classical trajectories are discussed and related to the corresponding energies. The development is concise, transparent, and involves only elementary integral calculus and provides a conceptual and intuitive introduction to the quantum nature of carbon nanostructures.

  16. 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.

  17. Chirality Quantum Phase Transition in Noncommutative Dirac Oscillator

    NASA Astrophysics Data System (ADS)

    Wang, Shao-Hua; Hou, Yu-Long; Wang, Qing; Long, Zheng-Wen; Jing, Jian

    2014-12-01

    The charged Dirac oscillator on a noncommutative plane coupling to a uniform perpendicular magnetic held is studied in this paper. We map the noncommutative plane to a commutative one by means of Bopp shift and study this problem on the commutative plane. We find that this model can be mapped onto a quantum optics model which contains Anti—Jaynes—Cummings (AJC) or Jaynes—Cummings (JC) interactions when a dimensionless parameter ζ (which is the function of the intensity of the magnetic held) takes values in different regimes. Furthermore, this model behaves as experiencing a chirality quantum phase transition when the dimensionless parameter ζ approaches the critical point. Several evidences of the chirality quantum phase transition are presented. We also study the non-relativistic limit of this model and find that a similar chirality quantum phase transition takes place in its non-relativistic limit.

  18. 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.

  19. Solitary waves in the nonlinear Dirac equation with arbitrary nonlinearity.

    PubMed

    Cooper, Fred; Khare, Avinash; Mihaila, Bogdan; Saxena, Avadh

    2010-09-01

    We consider the nonlinear Dirac equations (NLDE's) in 1+1 dimension with scalar-scalar self interaction g{2}/k+1(ΨΨ){k+1} , as well as a vector-vector self interaction g{2}/k+1(Ψγ{μ}ΨΨγ{μ}Ψ){1/2(k+1)} . We find the exact analytic form for solitary waves for arbitrary k and find that they are a generalization of the exact solutions for the nonlinear Schrödinger equation (NLSE) and reduce to these solutions in a well defined nonrelativistic limit. We perform the nonrelativistic reduction and find the 1/2m correction to the NLSE, valid when |ω-m|<2m , where ω is the frequency of the solitary wave in the rest frame. We discuss the stability and blowup of solitary waves assuming the modified NLSE is valid and find that they should be stable for k<2 . PMID:21230200

  20. Landauer conductance and twisted boundary conditions for Dirac fermions

    NASA Astrophysics Data System (ADS)

    Ryu, Shinsei; Mudry, Christopher; Furusaki, Akira; Ludwig, Andreas

    2007-03-01

    We apply the generating function technique developed by Nazarov to the computation of the density of transmission eigenvalues for a finite graphene sheet in which a two-dimensional freely propagating massless Dirac fermion is realized. By modeling ideal leads attached to the sample as a conformal invariant boundary condition, we relate the generating function for the density of transmission eigenvalues to the twisted chiral partition functions of fermionic (c=1) and bosonic (c=-1) conformal field theories. We also discuss the scaling behavior of the ac Kubo conductivity and compare its different dc limits with results obtained from the Landauer conductance. Finally, we show that the disorder averaged Einstein conductivity is an analytic function of the disorder strength, with vanishing first-order correction, for a tight-binding model on the honeycomb lattice with weak real-valued and nearest-neighbor random hopping.

  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. Probing Resonances of the Dirac Equation with Complex Momentum Representation

    NASA Astrophysics Data System (ADS)

    Li, Niu; Shi, Min; Guo, Jian-You; Niu, Zhong-Ming; Liang, Haozhao

    2016-08-01

    Resonance plays critical roles in the formation of many physical phenomena, and several methods have been developed for the exploration of resonance. In this work, we propose a new scheme for resonance by solving the Dirac equation in the complex momentum representation, in which the resonant states are exposed clearly in the complex momentum plane and the resonance parameters can be determined precisely without imposing unphysical parameters. Combined with the relativistic mean-field theory, this method is applied to probe the resonances in 120120 with the energies, widths, and wave functions being obtained. Compared to other methods, this method is not only very effective for narrow resonances, but also can be reliably applied to broad resonances.

  3. 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.

  4. Chiral gauge theories and a dirac neutrino - Dark matter connection

    NASA Astrophysics Data System (ADS)

    Hernandez, Daniel

    2016-06-01

    It is proposed that all light fermionic degrees of freedom, including the Standard Model (SM) fermions and all possible light beyond-the-standard model fields, are chiral with respect to some spontaneously broken abelian gauge symmetry. A new gauge symmetry U(1)ν is required if light fermionic new states are to exist. Anomaly cancellations mandate the existence of several new fields with nontrivial U(1)ν charges. A general technique to write down chiral-fermions-only models that are at least anomaly-free under a U(1) gauge symmetry is described. A concrete example that provides a Dark Matter candidate and leads to parametrically small Dirac neutrino masses is further developed.

  5. 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.

  6. 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.

  7. 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.

  8. On the nature of an emergent symmetry in QCD with low-lying Dirac modes removed

    NASA Astrophysics Data System (ADS)

    Cohen, Thomas D.

    2016-02-01

    Remarkable symmetry properties appear to arise in lattice calculations of correlation functions in which the lowest-lying eigenmodes of the Dirac operator in quark propagators are removed by hand. The Banks-Casher relation ties the chiral condensate to the density of low-lying modes; thus, it is plausible that removal of such modes could lead to a regime where spontaneous chiral symmetry breaking does not occur. Surprising, a pattern of identical correlation functions was observed that is larger than can be explained by a restoration of chiral symmetry. This suggests that a larger symmetry—one that is not present in the QCD Lagrangian—emerges when these modes are removed. Previously it was argued that this emergent symmetry was SU(4). However, when the low-lying modes are removed, the correlation functions of sources in the SU(4) 15-plet of spin-1 mesons appear to coincide with the correlation function of the SU(4) singlet. A natural explanation for this is an emergent symmetry larger than SU(4). In this work, it is shown that there exists no continuous symmetry whose generators in the field theory are spatial integrals of local operators that can account for the full pattern of identical correlation functions unless the apparent coincidence of the singlet channel with the 15-plet is accidental.

  9. Bloch-Zener oscillations across a merging transition of Dirac points.

    PubMed

    Lim, Lih-King; Fuchs, Jean-Noël; Montambaux, Gilles

    2012-04-27

    Bloch oscillations are a powerful tool to investigate spectra with Dirac points. By varying band parameters, Dirac points can be manipulated and merged at a topological transition toward a gapped phase. Under a constant force, a Fermi sea initially in the lower band performs Bloch oscillations and may Zener tunnel to the upper band mostly at the location of the Dirac points. The tunneling probability is computed from the low-energy universal Hamiltonian describing the vicinity of the merging. The agreement with a recent experiment on cold atoms in an optical lattice is very good.

  10. The interaction Lagrangian for two spin 1/2 elementary Dirac particles

    SciTech Connect

    Rivas, Martin

    2007-06-13

    It has been recently shown that the spacetime symmetry group of a Dirac particle is larger than the Poincare group. It also contains spacetime dilations and local rotations. In the quantum representation it becomes WxSU(2), where W is the Weyl group (Poincare group including spacetime dilations) and SU(2) is the unitary representation of the local rotation group. In this work we obtain the interaction Lagrangian for two Dirac particles, which is invariant under this enlarged spacetime group. We analyze the interaction between two Dirac particles, and show that it is possible the existence of metastable bound states for particles of the same charge, provided some initial conditions are fulfilled.

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

    NASA Astrophysics Data System (ADS)

    Li, Lijun; Wang, Kefeng; Graf, D.; Wang, Limin; Wang, Aifeng; Petrovic, C.

    2016-03-01

    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.

  13. Dirac: A campaign of experiments to study physics and chemistry at ultrahigh magnetic fields

    SciTech Connect

    Solem, J.C.; Fowler, C.M.; Goettee, J.D.; Rickel, D.; Campbell, L.J.; Veeser, L.

    1996-12-01

    We present an overview of the Dirac experimental campaign conducted at Los Alamos in spring of 1996. The name was chosen in recognition of P.A.M. Dirac`s monumental contributions to quantum theory, which affected every aspect of the science we planned to investigate. We show how the various collaborations were put together, discuss some of the difficulties of collecting data in rapidly changing magnetic fields, describe the motivation, packaging, and integration of experiments, and give an exceedingly preliminary discussion of some of the results.

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

    DOE PAGESBeta

    Li, Lijun; Wang, Kefeng; Graf, D.; Wang, Limin; Wang, Aifeng; Petrovic, C.

    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.

  15. 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.

  16. Ultrafast terahertz dynamics of hot Dirac-electron surface scattering in the topological insulator Bi2Se3

    NASA Astrophysics Data System (ADS)

    Sim, Sangwan; Brahlek, Matthew; Koirala, Nikesh; Cha, Soonyoung; Oh, Seongshik; Choi, Hyunyong

    2014-04-01

    Two-dimensional surface-scattering dynamics are central in the physics of topological insulators. Numerous electrical and optical measurements have evidenced that the origins of novel optoelectronic response can be traced back to Dirac surface-electron dynamics. Intrinsic surface dynamics, however, remain elusive because these experiments cannot access the frequencies of the surface-scattering rate. Time-resolved terahertz spectroscopy is the only apparatus for directly probing the collective response of low-energy electronic transitions. Here, by utilizing ultrafast optical-pump terahertz-probe spectroscopy, we discovered anomalous characteristics of the surface-scattering dynamics. Upon photoexcitation, the surface-scattering rate is increased and results in negative dynamic conductance at low temperature. Surprisingly, the differential changes of the surface-scattering rate are strongly reduced by photoexcited electrons at elevated temperature. We find that this nontrivial surface-electron dynamics is due to opening a carrier-relaxation channel from bulk to the surface state—one distinct characteristic of topological insulators. Our observations reveal unexpected surface dynamics of hot Dirac electrons, providing experimental a priori knowledge toward ultrafast optoelectronic operations.

  17. 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)

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. Dynamical merging of Dirac points in the periodically driven Kitaev honeycomb model

    NASA Astrophysics Data System (ADS)

    Bhattacharya, Utso; Dasgupta, Sayak; Dutta, Amit

    2016-10-01

    We study the effect of a half wave rectified sinusoidal electromagnetic (EM) wave on the Kitaev honeycomb model with an additional magneto-electric coupling term arising due to induced polarization of the bonds. Within the framework of Floquet analysis, we show that merging of a pair of Dirac points in the gapless region of the Kitaev model leading to a semi-Dirac spectrum is indeed possible by externally varying the amplitude and the phase of the EM field.

  3. Darboux partners of pseudoscalar Dirac potentials associated with exceptional orthogonal polynomials

    SciTech Connect

    Schulze-Halberg, Axel; Roy, Barnana

    2014-10-15

    We introduce a method for constructing Darboux (or supersymmetric) pairs of pseudoscalar and scalar Dirac potentials that are associated with exceptional orthogonal polynomials. Properties of the transformed potentials and regularity conditions are discussed. As an application, we consider a pseudoscalar Dirac potential related to the Schrödinger model for the rationally extended radial oscillator. The pseudoscalar partner potentials are constructed under the first- and second-order Darboux transformations.

  4. Computational relativistic quantum dynamics and its application to relativistic tunneling and Kapitza-Dirac scattering

    NASA Astrophysics Data System (ADS)

    Bauke, Heiko; Klaiber, Michael; Yakaboylu, Enderalp; Hatsagortsyan, Karen Z.; Ahrens, Sven; Müller, Carsten; Keitel, Christoph H.

    2013-05-01

    Computational methods are indispensable to study the quantum dynamics of relativistic light-matter interactions in parameter regimes where analytical methods become inapplicable. We present numerical methods for solving the time-dependent Dirac equation and the time-dependent Klein-Gordon equation and their implementation on high performance graphics cards. These methods allow us to study tunneling from hydrogen-like highly charged ions in strong laser fields and Kapitza-Dirac scattering in the relativistic regime.

  5. Dirac and scalar particles tunnelling from topological massive warped-AdS3 black hole

    NASA Astrophysics Data System (ADS)

    Gecim, G.; Sucu, Y.

    2015-06-01

    We investigate the Dirac and scalar particles tunnelling as a radiation of Warped AdS3 black holes in Topological Massive Gravity. Using Hamilton-Jacobi method, we discuss tunnelling probability and Hawking temperature of the spin-1/2 and spin-0 particles for the black hole. We observe the tunnelling probability and Hawking temperature to be same for the spin-1/2 and spin-0. We show that the tunnelling process may occur, for both Dirac and scalar particles.

  6. Decay of Dirac massive hair in the background of a spherical black hole

    SciTech Connect

    Moderski, Rafal; Rogatko, Marek

    2008-06-15

    The intermediate and late-time behavior of massive Dirac hair in the static spherically general black hole spacetime is studied. It is revealed that the intermediate asymptotic pattern of decay of massive Dirac spinor hair is dependent on the mass of the field under consideration as well as the multiple number of the wave mode. The long-lived oscillatory tail observed at timelike infinity in the considered background decays slowly as t{sup -5/6}.

  7. Zeeman splitting and dynamical mass generation in Dirac semimetal ZrTe5

    PubMed Central

    Liu, Yanwen; Yuan, Xiang; Zhang, Cheng; Jin, Zhao; Narayan, Awadhesh; Luo, Chen; Chen, Zhigang; Yang, Lei; Zou, Jin; Wu, Xing; Sanvito, Stefano; Xia, Zhengcai; Li, Liang; Wang, Zhong; Xiu, Faxian

    2016-01-01

    Dirac semimetals have attracted extensive attentions in recent years. It has been theoretically suggested that many-body interactions may drive exotic phase transitions, spontaneously generating a Dirac mass for the nominally massless Dirac electrons. So far, signature of interaction-driven transition has been lacking. In this work, we report high-magnetic-field transport measurements of the Dirac semimetal candidate ZrTe5. Owing to the large g factor in ZrTe5, the Zeeman splitting can be observed at magnetic field as low as 3 T. Most prominently, high pulsed magnetic field up to 60 T drives the system into the ultra-quantum limit, where we observe abrupt changes in the magnetoresistance, indicating field-induced phase transitions. This is interpreted as an interaction-induced spontaneous mass generation of the Dirac fermions, which bears resemblance to the dynamical mass generation of nucleons in high-energy physics. Our work establishes Dirac semimetals as ideal platforms for investigating emerging correlation effects in topological matters. PMID:27515493

  8. Zeeman splitting and dynamical mass generation in Dirac semimetal ZrTe5

    NASA Astrophysics Data System (ADS)

    Liu, Yanwen; Yuan, Xiang; Zhang, Cheng; Jin, Zhao; Narayan, Awadhesh; Luo, Chen; Chen, Zhigang; Yang, Lei; Zou, Jin; Wu, Xing; Sanvito, Stefano; Xia, Zhengcai; Li, Liang; Wang, Zhong; Xiu, Faxian

    2016-08-01

    Dirac semimetals have attracted extensive attentions in recent years. It has been theoretically suggested that many-body interactions may drive exotic phase transitions, spontaneously generating a Dirac mass for the nominally massless Dirac electrons. So far, signature of interaction-driven transition has been lacking. In this work, we report high-magnetic-field transport measurements of the Dirac semimetal candidate ZrTe5. Owing to the large g factor in ZrTe5, the Zeeman splitting can be observed at magnetic field as low as 3 T. Most prominently, high pulsed magnetic field up to 60 T drives the system into the ultra-quantum limit, where we observe abrupt changes in the magnetoresistance, indicating field-induced phase transitions. This is interpreted as an interaction-induced spontaneous mass generation of the Dirac fermions, which bears resemblance to the dynamical mass generation of nucleons in high-energy physics. Our work establishes Dirac semimetals as ideal platforms for investigating emerging correlation effects in topological matters.

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

    PubMed

    Wang, Z F; Liu, Feng

    2015-07-10

    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 sp(3) dangling bonds form a honeycomb superstructure on the Si(111) surface that results in an anisotropic Dirac band with a group velocity (∼10(6)  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.

  10. Zeeman splitting and dynamical mass generation in Dirac semimetal ZrTe5.

    PubMed

    Liu, Yanwen; Yuan, Xiang; Zhang, Cheng; Jin, Zhao; Narayan, Awadhesh; Luo, Chen; Chen, Zhigang; Yang, Lei; Zou, Jin; Wu, Xing; Sanvito, Stefano; Xia, Zhengcai; Li, Liang; Wang, Zhong; Xiu, Faxian

    2016-01-01

    Dirac semimetals have attracted extensive attentions in recent years. It has been theoretically suggested that many-body interactions may drive exotic phase transitions, spontaneously generating a Dirac mass for the nominally massless Dirac electrons. So far, signature of interaction-driven transition has been lacking. In this work, we report high-magnetic-field transport measurements of the Dirac semimetal candidate ZrTe5. Owing to the large g factor in ZrTe5, the Zeeman splitting can be observed at magnetic field as low as 3 T. Most prominently, high pulsed magnetic field up to 60 T drives the system into the ultra-quantum limit, where we observe abrupt changes in the magnetoresistance, indicating field-induced phase transitions. This is interpreted as an interaction-induced spontaneous mass generation of the Dirac fermions, which bears resemblance to the dynamical mass generation of nucleons in high-energy physics. Our work establishes Dirac semimetals as ideal platforms for investigating emerging correlation effects in topological matters. PMID:27515493

  11. DBSR_HF: A B-spline Dirac-Hartree-Fock program

    NASA Astrophysics Data System (ADS)

    Zatsarinny, Oleg; Froese Fischer, Charlotte

    2016-05-01

    A B-spline version of a general Dirac-Hartree-Fock program is described. The usual differential equations are replaced by a set of generalized eigenvalue problems of the form (Ha -εa B) Pa = 0, where Ha and B are the Hamiltonian and overlap matrices, respectively, and Pa is the two-component relativistic orbit in the B-spline basis. A default universal grid allows for flexible adjustment to different nuclear models. When two orthogonal orbitals are both varied, the energy must also be stationary with respect to orthonormal transformations. At such a stationary point the off-diagonal Lagrange multipliers may be eliminated through projection operators. The self-consistent field procedure exhibits excellent convergence. Several atomic states can be considered simultaneously, including some configuration-interaction calculations. The program provides several options for the treatment of Breit interaction and QED corrections. The information about atoms up to Z = 104 is stored by the program. Along with a simple interface through command-line arguments, this information allows the user to run the program with minimal initial preparations.

  12. Full Parallel Implementation of an All-Electron Four-Component Dirac-Kohn-Sham Program.

    PubMed

    Rampino, Sergio; Belpassi, Leonardo; Tarantelli, Francesco; Storchi, Loriano

    2014-09-01

    A full distributed-memory implementation of the Dirac-Kohn-Sham (DKS) module of the program BERTHA (Belpassi et al., Phys. Chem. Chem. Phys. 2011, 13, 12368-12394) is presented, where the self-consistent field (SCF) procedure is replicated on all the parallel processes, each process working on subsets of the global matrices. The key feature of the implementation is an efficient procedure for switching between two matrix distribution schemes, one (integral-driven) optimal for the parallel computation of the matrix elements and another (block-cyclic) optimal for the parallel linear algebra operations. This approach, making both CPU-time and memory scalable with the number of processors used, virtually overcomes at once both time and memory barriers associated with DKS calculations. Performance, portability, and numerical stability of the code are illustrated on the basis of test calculations on three gold clusters of increasing size, an organometallic compound, and a perovskite model. The calculations are performed on a Beowulf and a BlueGene/Q system.

  13. Full Parallel Implementation of an All-Electron Four-Component Dirac-Kohn-Sham Program.

    PubMed

    Rampino, Sergio; Belpassi, Leonardo; Tarantelli, Francesco; Storchi, Loriano

    2014-09-01

    A full distributed-memory implementation of the Dirac-Kohn-Sham (DKS) module of the program BERTHA (Belpassi et al., Phys. Chem. Chem. Phys. 2011, 13, 12368-12394) is presented, where the self-consistent field (SCF) procedure is replicated on all the parallel processes, each process working on subsets of the global matrices. The key feature of the implementation is an efficient procedure for switching between two matrix distribution schemes, one (integral-driven) optimal for the parallel computation of the matrix elements and another (block-cyclic) optimal for the parallel linear algebra operations. This approach, making both CPU-time and memory scalable with the number of processors used, virtually overcomes at once both time and memory barriers associated with DKS calculations. Performance, portability, and numerical stability of the code are illustrated on the basis of test calculations on three gold clusters of increasing size, an organometallic compound, and a perovskite model. The calculations are performed on a Beowulf and a BlueGene/Q system. PMID:26588521

  14. General solution of the Dirac equation for quasi-two-dimensional electrons

    NASA Astrophysics Data System (ADS)

    Eremko, Alexander; Brizhik, Larissa; Loktev, Vadim

    2016-06-01

    The general solution of the Dirac equation for quasi-two-dimensional electrons confined in an asymmetric quantum well, is found. The energy spectrum of such a system is exactly calculated using special unitary operator and is shown to depend on the electron spin polarization. This solution contains free parameters, whose variation continuously transforms one known particular solution into another. As an example, two different cases are considered in detail: electron in a deep and in a strongly asymmetric shallow quantum well. The effective mass renormalized by relativistic corrections and Bychkov-Rashba coefficients are analytically obtained for both cases. It is demonstrated that the general solution transforms to the particular solutions, found previously (Eremko et al., 2015) with the use of spin invariants. The general solution allows to establish conditions at which a specific (accompanied or non-accompanied by Rashba splitting) spin state can be realized. These results can prompt the ways to control the spin degree of freedom via the synthesis of spintronic heterostructures with the required properties.

  15. Efficient iterative method for solving the Dirac-Kohn-Sham density functional theory

    SciTech Connect

    Lin, Lin; Shao, Sihong; E, Weinan

    2012-11-06

    We present for the first time an efficient iterative method to directly solve the four-component Dirac-Kohn-Sham (DKS) density functional theory. Due to the existence of the negative energy continuum in the DKS operator, the existing iterative techniques for solving the Kohn-Sham systems cannot be efficiently applied to solve the DKS systems. The key component of our method is a novel filtering step (F) which acts as a preconditioner in the framework of the locally optimal block preconditioned conjugate gradient (LOBPCG) method. The resulting method, dubbed the LOBPCG-F method, is able to compute the desired eigenvalues and eigenvectors in the positive energy band without computing any state in the negative energy band. The LOBPCG-F method introduces mild extra cost compared to the standard LOBPCG method and can be easily implemented. We demonstrate our method in the pseudopotential framework with a planewave basis set which naturally satisfies the kinetic balance prescription. Numerical results for Pt$_{2}$, Au$_{2}$, TlF, and Bi$_{2}$Se$_{3}$ indicate that the LOBPCG-F method is a robust and efficient method for investigating the relativistic effect in systems containing heavy elements.

  16. Negative magnetoresistance in Dirac semimetal Cd3As2

    PubMed Central

    Li, Hui; He, Hongtao; Lu, Hai-Zhou; Zhang, Huachen; Liu, Hongchao; Ma, Rong; Fan, Zhiyong; Shen, Shun-Qing; Wang, Jiannong

    2016-01-01

    A large negative magnetoresistance (NMR) is anticipated in topological semimetals in parallel magnetic fields, demonstrating the chiral anomaly, a long-sought high-energy-physics effect, in solid-state systems. Recent experiments reveal that the Dirac semimetal Cd3As2 has the record-high mobility and positive linear magnetoresistance in perpendicular magnetic fields. However, the NMR has not yet been unveiled. Here we report the observation of NMR in Cd3As2 microribbons in parallel magnetic fields up to 66% at 50 K and visible at room temperatures. The NMR is sensitive to the angle between magnetic and electrical fields, robust against temperature and dependent on the carrier density. The large NMR results from low carrier densities in our Cd3As2 samples, ranging from 3.0 × 1017 cm−3 at 300 K to 2.2 × 1016 cm−3 below 50 K. We therefore attribute the observed NMR to the chiral anomaly. In perpendicular magnetic fields, a positive linear magnetoresistance up to 1,670% at 14 T and 2 K is also observed. PMID:26744088

  17. Quantum Fisher and skew information for Unruh accelerated Dirac qubit

    NASA Astrophysics Data System (ADS)

    Banerjee, Subhashish; Alok, Ashutosh Kumar; Omkar, S.

    2016-08-01

    We develop a Bloch vector representation of the Unruh channel for a Dirac field mode. This is used to provide a unified, analytical treatment of quantum Fisher and skew information for a qubit subjected to the Unruh channel, both in its pure form as well as in the presence of experimentally relevant external noise channels. The time evolution of Fisher and skew information is studied along with the impact of external environment parameters such as temperature and squeezing. The external noises are modelled by both purely dephasing phase damping and the squeezed generalised amplitude damping channels. An interesting interplay between the external reservoir temperature and squeezing on the Fisher and skew information is observed, in particular, for the action of the squeezed generalised amplitude damping channel. It is seen that for some regimes, squeezing can enhance the quantum information against the deteriorating influence of the ambient environment. Similar features are also observed for the analogous study of skew information, highlighting a similar origin of the Fisher and skew information.

  18. Finitely many Dirac-delta interactions on Riemannian manifolds

    SciTech Connect

    Altunkaynak, Baris; Erman, Fatih; Turgut, O. Teoman

    2006-08-15

    This work is intended as an attempt to study the nonperturbative renormalization of bound state problem of finitely many Dirac-delta interactions on Riemannian manifolds, S{sup 2}, H{sup 2}, and H{sup 3}. We formulate the problem in terms of a finite dimensional matrix, called the characteristic matrix {phi}. The bound state energies can be found from the characteristic equation {phi}(-{nu}{sup 2})A=0. The characteristic matrix can be found after a regularization and renormalization by using a sharp cut-off in the eigenvalue spectrum of the Laplacian, as it is done in the flat space, or using the heat kernel method. These two approaches are equivalent in the case of compact manifolds. The heat kernel method has a general advantage to find lower bounds on the spectrum even for compact manifolds as shown in the case of S{sup 2}. The heat kernels for H{sup 2} and H{sup 3} are known explicitly, thus we can calculate the characteristic matrix {phi}. Using the result, we give lower bound estimates of the discrete spectrum.

  19. Dirac Node Lines in Pure Alkali Earth Metals.

    PubMed

    Li, Ronghan; Ma, Hui; Cheng, Xiyue; Wang, Shoulong; Li, Dianzhong; Zhang, Zhengyu; Li, Yiyi; Chen, Xing-Qiu

    2016-08-26

    Beryllium is a simple alkali earth metal, but has been the target of intensive studies for decades because of its unusual electron behavior at surfaces. The puzzling aspects include (i) severe deviations from the description of the nearly free-electron picture, (ii) an anomalously large electron-phonon coupling effect, and (iii) giant Friedel oscillations. The underlying origins for such anomalous surface electron behavior have been under active debate, but with no consensus. Here, by means of first-principles calculations, we discover that this pure metal system, surprisingly, harbors the Dirac node line (DNL) that in turn helps to rationalize many of the existing puzzles. The DNL is featured by a closed line consisting of linear band crossings, and its induced topological surface band agrees well with previous photoemission spectroscopy observations on the Be (0001) surface. We further reveal that each of the elemental alkali earth metals of Mg, Ca, and Sr also harbors the DNL and speculate that the fascinating topological property of the DNL might naturally exist in other elemental metals as well. PMID:27610865

  20. Dirac Node Lines in Pure Alkali Earth Metals.

    PubMed

    Li, Ronghan; Ma, Hui; Cheng, Xiyue; Wang, Shoulong; Li, Dianzhong; Zhang, Zhengyu; Li, Yiyi; Chen, Xing-Qiu

    2016-08-26

    Beryllium is a simple alkali earth metal, but has been the target of intensive studies for decades because of its unusual electron behavior at surfaces. The puzzling aspects include (i) severe deviations from the description of the nearly free-electron picture, (ii) an anomalously large electron-phonon coupling effect, and (iii) giant Friedel oscillations. The underlying origins for such anomalous surface electron behavior have been under active debate, but with no consensus. Here, by means of first-principles calculations, we discover that this pure metal system, surprisingly, harbors the Dirac node line (DNL) that in turn helps to rationalize many of the existing puzzles. The DNL is featured by a closed line consisting of linear band crossings, and its induced topological surface band agrees well with previous photoemission spectroscopy observations on the Be (0001) surface. We further reveal that each of the elemental alkali earth metals of Mg, Ca, and Sr also harbors the DNL and speculate that the fascinating topological property of the DNL might naturally exist in other elemental metals as well.

  1. A Programmable Cellular-Automata Polarized Dirac Vacuum

    NASA Astrophysics Data System (ADS)

    Osoroma, Drahcir S.

    2013-09-01

    We explore properties of a `Least Cosmological Unit' (LCU) as an inherent spacetime raster tiling or tessellating the unique backcloth of Holographic Anthropic Multiverse (HAM) cosmology as an array of programmable cellular automata. The HAM vacuum is a scale-invariant HD extension of a covariant polarized Dirac vacuum with `bumps' and `holes' typically described by extended electromagnetic theory corresponding to an Einstein energy-dependent spacetime metric admitting a periodic photon mass. The new cosmology incorporates a unique form of M-Theoretic Calabi-Yau-Poincaré Dodecadedral-AdS5-DS5space (PDS) with mirror symmetry best described by an HD extension of Cramer's Transactional Interpretation when integrated also with an HD extension of the de Broglie-Bohm-Vigier causal interpretation of quantum theory. We incorporate a unique form of large-scale additional dimensionality (LSXD) bearing some similarity to that conceived by Randall and Sundrum; and extend the fundamental basis of our model to the Unified Field, UF. A Sagnac Effect rf-pulsed incursive resonance hierarchy is utilized to manipulate and ballistically program the geometric-topological properties of this putative LSXD space-spacetime network. The model is empirically testable; and it is proposed that a variety of new technologies will arise from ballistic programming of tessellated LCU vacuum cellular automata.

  2. Dirac semimetal thin films in in-plane magnetic fields

    PubMed Central

    Siu, Zhuo Bin; Jalil, Mansoor B. A.; Tan, Seng Ghee

    2016-01-01

    In this work we study the effects of in-plane magnetic fields on thin films of the Dirac Semimetal (DSM) Na3Bi where one of the in-plane directions is perpendicular to the k-separation between the two Weyl nodes that exist for each spin orientation. We show numerically that the states localized near the surfaces of these thin films are related to the Fermi arc states in semi-infinite slabs. Due to the anisotropy between the two in-plane directions, the application of a magnetic field along these directions have differing effects. A field parallel to the k space separation between the Weyl nodes leads to a broadening of the surface state band and the formation of an energy plateau, while a perpendicular field shifts the energy where the hole and particle bands meet upwards, and sharpens the tips of the bands. We illustrate the effects of these changes to the dispersion relation by studying the transmission from a source segment without a magnetic field to a drain segment with a field, with the field and interface at various in-plane directions. PMID:27721387

  3. Dirac semimetal thin films in in-plane magnetic fields

    NASA Astrophysics Data System (ADS)

    Siu, Zhuo Bin; Jalil, Mansoor B. A.; Tan, Seng Ghee

    2016-10-01

    In this work we study the effects of in-plane magnetic fields on thin films of the Dirac Semimetal (DSM) Na3Bi where one of the in-plane directions is perpendicular to the k-separation between the two Weyl nodes that exist for each spin orientation. We show numerically that the states localized near the surfaces of these thin films are related to the Fermi arc states in semi-infinite slabs. Due to the anisotropy between the two in-plane directions, the application of a magnetic field along these directions have differing effects. A field parallel to the k space separation between the Weyl nodes leads to a broadening of the surface state band and the formation of an energy plateau, while a perpendicular field shifts the energy where the hole and particle bands meet upwards, and sharpens the tips of the bands. We illustrate the effects of these changes to the dispersion relation by studying the transmission from a source segment without a magnetic field to a drain segment with a field, with the field and interface at various in-plane directions.

  4. Thermoelectric and thermospintronic transport in Dirac material-based nanostructures

    NASA Astrophysics Data System (ADS)

    Chang, Po-Hao

    The growing need for power due to the rapid developments of the technologies has urged both engineers and scientists to study more sustainable types of energy. On the other hand, the improvement of our abilities although enable us, for example, to double the number of transistors in a dense integrated circuit approximately every two years (Moore's law), comes with side effect due to overheating. Taking advantage of thermoelectric effect has thus become one of the obvious solutions for the problems. But due to the poor efficiency of electricity-heat conversion, there are still challenges to be overcome in order to fully utilize the idea. In the past few years, the realization of graphene along with the discoveries of topological insulators (TI) which are both considered as Dirac material (DM) have offer alternative routs for improving the energy conversion efficiency through different approaches as well as novel quantum effects of materials themselves for investigation. The aim of this thesis is to present contributions to improving the efficiency of thermoelectric conversion as well as analyzing spin transport phenomena that occur in nano-devices. This thesis spans the areas of thermoelectric (TE) effect, spin-Seebeck effect (SSE) and the spin transport on the 3D topological insulator (TI). The different methods have been applied ranging from tight-binding (TB) approximation to density function theory (DFT) combined with non-equilibrium function (NEGF) techniques.

  5. Dirac Node Lines in Pure Alkali Earth Metals

    NASA Astrophysics Data System (ADS)

    Li, Ronghan; Ma, Hui; Cheng, Xiyue; Wang, Shoulong; Li, Dianzhong; Zhang, Zhengyu; Li, Yiyi; Chen, Xing-Qiu

    2016-08-01

    Beryllium is a simple alkali earth metal, but has been the target of intensive studies for decades because of its unusual electron behavior at surfaces. The puzzling aspects include (i) severe deviations from the description of the nearly free-electron picture, (ii) an anomalously large electron-phonon coupling effect, and (iii) giant Friedel oscillations. The underlying origins for such anomalous surface electron behavior have been under active debate, but with no consensus. Here, by means of first-principles calculations, we discover that this pure metal system, surprisingly, harbors the Dirac node line (DNL) that in turn helps to rationalize many of the existing puzzles. The DNL is featured by a closed line consisting of linear band crossings, and its induced topological surface band agrees well with previous photoemission spectroscopy observations on the Be (0001) surface. We further reveal that each of the elemental alkali earth metals of Mg, Ca, and Sr also harbors the DNL and speculate that the fascinating topological property of the DNL might naturally exist in other elemental metals as well.

  6. Enhanced inflation in the Dirac-Born-Infeld framework

    SciTech Connect

    Chimento, Luis P.; Richarte, Martin G.; Lazkoz, Ruth

    2011-03-15

    We consider the Einstein equations within the Dirac-Born-Infield (DBI) scenario for a spatially flat Friedmann-Robertson-Walker (FRW) spacetime without a cosmological constant. We derive the inflationary scenario by applying the symmetry transformations which preserve the form of the Friedmann and conservation equations. These form invariance transformations generate a symmetry group parametrized by the Lorentz factor {gamma}. We explicitly obtain an inflationary scenario by the cooperative effect of adding energy density into the Friedmann equation. For the case of a constant Lorentz factor, and under the slow roll assumption, we find the transformation rules for the scalar and tensor power spectra of perturbations as well as their ratio under the action of the form invariance symmetry group. Within this case and due to its relevance for the inflationary paradigm, we find the general solution of the dynamical equations for a DBI field driven by an exponential potential and show a broad set of inflationary solutions. The general solution can be split into three subsets and all these behave asymptotically as a power-law solution at early and at late times.

  7. Spin Hall Conductivity and Spin Chern Number for Dirac Systems

    NASA Astrophysics Data System (ADS)

    Yunt, Elif; Dayi, Omer Faruk

    A semiclassical differential form formalism of the spin Hall effect for Dirac systems is presented. In this formalism, space coordinates and momenta are usual dynamical variables, whereas spin is not a dynamical degree of freedom. Spin depicts itself in the matrix-valuedness of equations of motion. We demonstrate that the main contribution to the spin Hall conductivity is given by the spin Chern number whether the spin is conserved or not at the quantum level. We illustrated the formulation within the Kane-Mele model of graphene in the absence and in the presence of the Rashba spin-orbit coupling term. Kane-Mele Model of graphene, which incorporates intrinsic spin-orbit interaction, constitutes the first example of a two dimensional topological insulator. We established the anomalous Hall conductivity as well as the spin Hall conductivity from the term linear in the electric field and the Berry curvature in the the anamolous velocity term. In a basis where the component of spin under consideration is diagonal this term is diagonal. We argue that this semiclassical procedure of calculating the spin Hall conductivity can be generalized to any dimension.

  8. The leptonic Dirac CP-violating phase from sum rules

    NASA Astrophysics Data System (ADS)

    Girardi, I.; Petcov, S. T.; Titov, A. V.

    2016-05-01

    In the reference 3-neutrino mixing scheme with three light massive neutrinos, CP-violating effects in neutrino oscillations can be caused by the Dirac CP-violating phase δ present in the unitary neutrino mixing matrix U. Using the fact that U = U†eUv , where Ue and Uv are unitary matrices arising from the diagonalisation, respectively, of the charged lepton and neutrino mass matrices, we consider in a systematic way forms of Ue and Uv allowing us to express δ as a function of the neutrino mixing angles present in U and the angles contained in Uv. After obtaining sum rules for cos δ, we consider several forms of Uv dictated by, or associated with, symmetries, such as tri-bimaximal, bimaximal, etc., for which the angles in Uv are fixed. For each of these forms and forms of Ue allowing to reproduce the measured values of the neutrino mixing angles, we construct the likelihood function for cos δ, using the prospective uncertainties in the determination of the mixing angles. Our results show that the measurement of δ along with improvement of the precision on the neutrino mixing angles can provide unique information about the possible existence of a new fundamental symmetry in the lepton sector.

  9. Correlated Dirac particles and superconductivity on the honeycomb lattice

    NASA Astrophysics Data System (ADS)

    Wu, Wei; Scherer, Michael M.; Honerkamp, Carsten; Le Hur, Karyn

    2013-03-01

    We investigate the properties of the nearest-neighbor singlet pairing and the emergence of d-wave superconductivity in the doped honeycomb lattice considering the limit of large interactions and the t-J1-J2 model. First, by applying a renormalized mean-field procedure as well as slave-boson theories which account for the proximity to the Mott-insulating state, we confirm the emergence of d-wave superconductivity, in agreement with earlier works. We show that a small but finite J2 spin coupling between next-nearest neighbors stabilizes d-wave symmetry compared to the extendeds-wave scenario. At small hole doping, to minimize the energy and to gap the whole Fermi surface or all the Dirac points, the superconducting ground state is characterized by a d+id singlet pairing assigned to one valley and a d-id singlet pairing to the other, which then preserves time-reversal symmetry. The slightly doped situation is distinct from the heavily doped case (around 3/8 and 5/8 filling) supporting a pure chiral d+id symmetry and breaking time-reversal symmetry. Then, we apply the functional renormalization group and study in more detail the competition between antiferromagnetism and superconductivity in the vicinity of half filling. We discuss possible applications to strongly correlated compounds with copper hexagonal planes such as In3Cu2VO9. Our findings are also relevant to the understanding of exotic superfluidity with cold atoms.

  10. Dirac-fermionic dark matter in U(1)X models

    NASA Astrophysics Data System (ADS)

    Alves, Alexandre; Berlin, Asher; Profumo, Stefano; Queiroz, Farinaldo S.

    2015-10-01

    We study a number of U(1)X models featuring a Dirac fermion dark matter particle. We perform a comprehensive analysis which includes the study of corrections to the muon magnetic moment, dilepton searches with LHC data, as well as direct and indirect dark matter detection constraints. We consider four different coupling structures, namely U(1) B-L , U(1) d-u , U(1)universal, and U{(1)}_{10+overline{5}} , all motivated by compelling extensions to the standard model. We outline the viable and excluded regions of parameter space using a large set of probes. Our key findings are that (i) the combination of direct detection and collider constraints rule out dark matter particle masses lighter than ˜ 1 TeV, unless rather suppressed Z '-fermion couplings exist, and that (ii) for several of the models under consideration, collider constraints rule out Z ' masses up to ˜ 3 TeV. Lastly, we show that we can accommodate the recent Diboson excess reported by ATLAS collaboration within the U(1) d- u model.

  11. Bound state solution of Dirac equation for Hulthen plus trigonometric Rosen Morse non-central potential using Romanovski polynomial

    SciTech Connect

    Suparmi, A. Cari, C.; Angraini, L. M.

    2014-09-30

    The bound state solutions of Dirac equation for Hulthen and trigonometric Rosen Morse non-central potential are obtained using finite Romanovski polynomials. The approximate relativistic energy spectrum and the radial wave functions which are given in terms of Romanovski polynomials are obtained from solution of radial Dirac equation. The angular wave functions and the orbital quantum number are found from angular Dirac equation solution. In non-relativistic limit, the relativistic energy spectrum reduces into non-relativistic energy.

  12. Three-dimensional Dirac cone carrier dynamics in Na3Bi and Cd3As2

    NASA Astrophysics Data System (ADS)

    Jenkins, G. S.; Lane, C.; Barbiellini, B.; Sushkov, A. B.; Carey, R. L.; Liu, Fengguang; Krizan, J. W.; Kushwaha, S. K.; Gibson, Q.; Chang, Tay-Rong; Jeng, Horng-Tay; Lin, Hsin; Cava, R. J.; Bansil, A.; Drew, H. D.

    2016-08-01

    Optical measurements and band structure calculations are reported on three-dimensional Dirac materials. The electronic properties associated with the Dirac cone are identified in the reflectivity spectra of Cd3As2 and Na3Bi single crystals. In Na3Bi , the plasma edge is found to be strongly temperature dependent due to thermally excited free carriers in the Dirac cone. The thermal behavior provides an estimate of the Fermi level EF=25 meV and the z -axis Fermi velocity vz=0.3 eV Å associated with the heavy bismuth Dirac band. At high energies above the Γ -point Lifshitz gap energy, a frequency- and temperature-independent ɛ2 indicative of Dirac cone interband transitions translates into an ab-plane Fermi velocity of 3 eV Å. The observed number of IR phonons rules out the P 63/m m c space-group symmetry but is consistent with the P 3 ¯c 1 candidate symmetry. A plasmaron excitation is discovered near the plasmon energy that persists over a broad range of temperature. The optical signature of the large joint density of states arising from saddle points at Γ is strongly suppressed in Na3Bi , consistent with band structure calculations that show the dipole transition-matrix elements to be weak due to the very small s -orbital character of the Dirac bands. In Cd3As2 , a distinctive peak in reflectivity due to the logarithmic divergence in ɛ1 expected at the onset of Dirac cone interband transitions is identified. The center frequency of the peak shifts with temperature quantitatively consistent with a linear dispersion and a carrier density of n =1.3 ×1017cm-3 . The peak width gives a measure of the Fermi-velocity anisotropy of 10 % , indicating a nearly spherical Fermi surface. The line shape gives an upper bound estimate of 7 meV for the potential fluctuation energy scale.

  13. Geometrization of the physics with teleparallelism. II. Towards a fully geometric Dirac equation

    NASA Astrophysics Data System (ADS)

    Vargas, José G.; Torr, Douglas G.; Lecompte, Alvaro

    1992-04-01

    In an accompanying paper (I), it is shown that the basic equations of the theory of Lorentzian connections with teleparallelism (TP) acquire standard forms of physical field equations upon removal of the constraints represented by the Bianchi identities. A classical physical theory results that supersedes general relativity and Maxwell-Lorentz electrodynamics if the connection is viewed as Finslerian. The theory also encompasses a short-range, strong, classical interaction. It has, however, an open end, since the source side of the torsion field equation is not geometric. In this paper, Kaehler's partial geometrization of the Dirac equation is taken as a starting point for the development of fully geometric Dirac equations via the correspondence principle given in I. For this purpose, Kaehler's calculus (where the spinors are differential forms) is generalized so that it also applies when the torsion is not zero. The point is then made that the forms can take values in tangent Clifford algebras rather than in tensor algebras. The basic “Eigenschaft” of the Kaehler calculus also is examined from the physical perspective of dimensional analysis. Geometric Dirac equations of great structural simplicity are finally inferred from the standard Dirac equation by using the aforementioned correspondence principle. The realm of application of the Dirac theory is thus enriched in principle, though only at an abstract level at this point: the standard spinors, which are scalar-valued forms in the Kaehler version of that theory, become Clifford-valued. In addition, the geometrization of the Dirac equation implies a geometrization of the Dirac current. When this current is replaced in the field equations for the torsion, the theory of Paper I becomes fully geometric.

  14. Quantum field as a quantum cellular automaton: The Dirac free evolution in one dimension

    SciTech Connect

    Bisio, Alessandro; D’Ariano, Giacomo Mauro; Tosini, Alessandro

    2015-03-15

    We present a quantum cellular automaton model in one space-dimension which has the Dirac equation as emergent. This model, a discrete-time and causal unitary evolution of a lattice of quantum systems, is derived from the assumptions of homogeneity, parity and time-reversal invariance. The comparison between the automaton and the Dirac evolutions is rigorously set as a discrimination problem between unitary channels. We derive an exact lower bound for the probability of error in the discrimination as an explicit function of the mass, the number and the momentum of the particles, and the duration of the evolution. Computing this bound with experimentally achievable values, we see that in that regime the QCA model cannot be discriminated from the usual Dirac evolution. Finally, we show that the evolution of one-particle states with narrow-band in momentum can be efficiently simulated by a dispersive differential equation for any regime. This analysis allows for a comparison with the dynamics of wave-packets as it is described by the usual Dirac equation. This paper is a first step in exploring the idea that quantum field theory could be grounded on a more fundamental quantum cellular automaton model and that physical dynamics could emerge from quantum information processing. In this framework, the discretization is a central ingredient and not only a tool for performing non-perturbative calculation as in lattice gauge theory. The automaton model, endowed with a precise notion of local observables and a full probabilistic interpretation, could lead to a coherent unification of a hypothetical discrete Planck scale with the usual Fermi scale of high-energy physics. - Highlights: • The free Dirac field in one space dimension as a quantum cellular automaton. • Large scale limit of the automaton and the emergence of the Dirac equation. • Dispersive differential equation for the evolution of smooth states on the automaton. • Optimal discrimination between the

  15. Large linear magnetoresistance in a new Dirac material BaMnBi2

    NASA Astrophysics Data System (ADS)

    Wang, Yi-Yan; Yu, Qiao-He; Xia, Tian-Long

    2016-10-01

    Dirac semimetal is a class of materials that host Dirac fermions as emergent quasi-particles. Dirac cone-type band structure can bring interesting properties such as quantum linear magnetoresistance and large mobility in the materials. In this paper, we report the synthesis of high quality single crystals of BaMnBi2 and investigate the transport properties of the samples. BaMnBi2 is a metal with an antiferromagnetic transition at T N = 288 K. The temperature dependence of magnetization displays different behavior from CaMnBi2 and SrMnBi2, which suggests the possible different magnetic structure of BaMnBi2. The Hall data reveals electron-type carriers and a mobility μ(5 K) = 1500 cm2/V·s. Angle-dependent magnetoresistance reveals the quasi-two-dimensional (2D) Fermi surface in BaMnBi2. A crossover from semiclassical MR ˜ H 2 dependence in low field to MR ˜ H dependence in high field, which is attributed to the quantum limit of Dirac fermions, has been observed in magnetoresistance. Our results indicate the existence of Dirac fermions in BaMnBi2. Project supported by the National Natural Science Foundation of China (Grant No. 11574391), the Fundamental Research Funds for the Central Universities, and the Research Funds of Renmin University of China (Grant No. 14XNLQ07).

  16. Observation of Dirac-like semi-metallic phase in NdSb

    NASA Astrophysics Data System (ADS)

    Neupane, Madhab; Mofazzel Hosen, M.; Belopolski, Ilya; Wakeham, Nicholas; Dimitri, Klauss; Dhakal, Nagendra; Zhu, Jian-Xin; Zahid Hasan, M.; Bauer, Eric D.; Ronning, Filip

    2016-06-01

    The search of new topological phases of matter is one of the new directions in condensed matter physics. Recent experimental realizations of Dirac semimetal phases pave the way to look for other exotic phases of matter in real materials. Here we present a systematic angle-resolved photoemission spectroscopy (ARPES) study of NdSb, a potential candidate for hosting a Dirac semi-metal phase. Our studies reveal two hole-like Fermi surface pockets present at the zone center (Γ ) point as well as two elliptical electron-pockets present in the zone corner (X) point of the Brillouin zone (BZ). Interestingly, Dirac-like linearly dispersive states are observed about the zone corner (X) point in NdSb. Our first-principles calculations agree with the experimentally observed bands at the Γ point. Moreover, the Dirac-like state observed in NdSb may be a novel correlated state, not yet predicted in calculations. Our study opens a new direction to look for Dirac semi-metal states in other members of the rare earth monopnictide family.

  17. Dirac vs Majorana gauginos at a 100 TeV collider

    NASA Astrophysics Data System (ADS)

    di Cortona, Giovanni Grilli; Hardy, Edward; Powell, Andrew J.

    2016-08-01

    We compare the prospects for observing theories with Majorana or Dirac gauginos at a future 100 TeV proton-proton collider. Calculating the expected discovery and exclusion regions, we find that for heavy gluino masses the squark discovery reach is significantly reduced in Dirac gluino models relative to the Majorana case. However, if the squark and gluino masses are close the reach is similar in both scenarios. We also consider the electroweak fine tuning of theories observable at such a collider, and the impact of existing constraints from flavour and CP violating observables. Models with Majorana gluinos that are fine tuned to less than one part in 10, 000 can typically be discovered or excluded, and Dirac models with tuning of one part in 1, 000 can be probed. The flavour structure of Majorana models is highly constrained if they have observable squarks, while O(1) violation is possible in accessible Dirac models. In both cases new sources of CP violation must be very suppressed. Future collider searches can also give important information on possible dark matter candidates. We study the relation of this to indirect and direct detection searches, and find that if dark matter is a neutralino, a 100 TeV collider could probe the viable dark matter candidates in large classes of both Dirac and Majorana models.

  18. Hydrostatic pressure induced three-dimensional Dirac semimetal in black phosphorus

    NASA Astrophysics Data System (ADS)

    Gong, Peng-Lai; Liu, Da-Yong; Yang, Kai-Shuai; Xiang, Zi-Ji; Chen, Xian-Hui; Zeng, Zhi; Shen, Shun-Qing; Zou, Liang-Jian

    2016-05-01

    We present the first-principles studies on the hydrostatic pressure effect of the electronic properties of black phosphorus. We show that the energy bands crossover around the critical pressure Pc=1.23 GPa; with increasing pressure, the band reversal occurs at the Z point and evolves into 4 twofold-degenerate Dirac cones around the Z point, suggesting that pressured black phosphorus is a 3D Dirac semimetal. With further increasing pressure the Dirac cones in the Γ -Z line move toward the Γ point and evolve into two hole-type Fermi pockets, and those in the Z -M lines move toward the M point and evolve into two tiny electron-type Fermi pockets, and a band above the Z -M line sinks below EF and contributes four electron-type pockets. A clear Lifshitz transition occurs at Pc from semiconductor to 3D Dirac semimetal. Such a 3D Dirac semimetal is protected by the nonsymmorphic space symmetry of bulk black phosphorus. These suggest the bright perspective of black phosphorus for optoelectronic and electronic devices due to its easy modulation by pressure.

  19. Prediction of a strain-tunable 2D Topological Dirac semimetal in monolayers of black phosphorus

    NASA Astrophysics Data System (ADS)

    Zhang, Xiuwen; Liu, Qihang; Zunger, Alex; Theory Team

    2015-03-01

    N-dimensional Topological Nonmetals (TNM) such as N = 2D HgTe/CdTe quantum wells or N = 3D Bi2Se3 have a finite (often tiny) band gap between occupied and unoccupied bands, and show conductive Dirac cones in their N-1 dimensional geometric boundaries. On the other hand, examples of topological semimetals (TSM) are known for 3D solids (Cd3As2) where they have Dirac cones in the 3D system itself. Using density functional calculation of bands and the topological invariant Z2 we predict the existence of 2D topological Dirac semimetal in few monolayers of strain tuned black phosphorus (BP), with Dirac cones induced by band inversion. The band structures of few monolayers and bulk crystal of BP under a few percent biaxial and uniaxial strains were calculated using state-of-art electronic structure methods. The critical strain of the transition to TSM was found to decrease as the layer thickness increases. We will discuss the protection of the Dirac cones by the crystalline symmetry in the 2D TSM and the manipulation of crystalline symmetry, which induces further topological phase transitions. Supported by the NSF-DMREF-13-34170.

  20. A Matter of Principle: The Principles of Quantum Theory, Dirac's Equation, and Quantum Information

    NASA Astrophysics Data System (ADS)

    Plotnitsky, Arkady

    2015-10-01

    This article is concerned with the role of fundamental principles in theoretical physics, especially quantum theory. The fundamental principles of relativity will be addressed as well, in view of their role in quantum electrodynamics and quantum field theory, specifically Dirac's work, which, in particular Dirac's derivation of his relativistic equation of the electron from the principles of relativity and quantum theory, is the main focus of this article. I shall also consider Heisenberg's earlier work leading him to the discovery of quantum mechanics, which inspired Dirac's work. I argue that Heisenberg's and Dirac's work was guided by their adherence to and their confidence in the fundamental principles of quantum theory. The final section of the article discusses the recent work by D'Ariano and coworkers on the principles of quantum information theory, which extend quantum theory and its principles in a new direction. This extension enabled them to offer a new derivation of Dirac's equations from these principles alone, without using the principles of relativity.

  1. Designer Dirac Fermions, Topological Phases, and Gauge Fields in Molecular Graphene

    NASA Astrophysics Data System (ADS)

    Manoharan, Hari C.

    2013-03-01

    The observation of massless Dirac fermions in monolayer graphene has propelled a new area of science and technology seeking to harness charge carriers that behave relativistically within solid-state materials. Using low-temperature scanning tunneling microscopy and spectroscopy, we show the emergence of Dirac fermions in a fully tunable condensed-matter system--molecular graphene--assembled via atomic manipulation of a conventional two-dimensional electron system in a surface state. We embed, image, and tune the symmetries underlying the two-dimensional Dirac equation into these electrons by sculpting the surface potential with manipulated molecules. By distorting the effective electron hopping parameters into a Kekulé pattern, we find that these natively massless Dirac particles can be endowed with a tunable mass engendered by the associated scalar gauge field, in analogy to the Higgs field. With altered symmetry and texturing of the assembled lattices, the Dirac fermions can be dressed with gauge electric or magnetic fields such that the carriers believe they are in real fields and condense into the corresponding ground state, as confirmed by tunneling spectroscopy. Using these techniques we ultimately fabricate a quantum Hall state without breaking time-reversal symmetry, in which electrons quantize in a gauge magnetic field ramped to 60 Tesla with zero applied laboratory field. We show that these and other chiral states now possible to realize have direct analogues in topological insulators, and can be used to guide or confine charge in nontrivial ways.

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

    NASA Astrophysics Data System (ADS)

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

    2015-11-01

    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.

  3. A detailed study of nonperturbative solutions of two-body Dirac equations

    SciTech Connect

    Crater, H.W.; Becker, R.L.; Wong, C.Y.; Van Alstine, P.

    1992-12-01

    In quark model calculations of the meson spectrums fully covariant two-body Dirac equations dictated by Dirac's relativistic constraint mechanics gave a good fit to the entire meson mass spectrum for light quark mesons as well as heavy quark mesons with constituent world scalar and vector potentials depending on just one or two parameters. In this paper, we investigate the properties of these equations that made them work so well by solving them numerically for quantum electrodynamics (QED) and related field theories. The constraint formalism generates a relativistic quantum mechanics defined by two coupled Dirac equations on a sixteen component wave function which contain Lorentz covariant constituent potentials that are initially undetermined. An exact Pauli reduction leads to a second order relativistic Schroedinger-like equation for a reduced eight component wave function determined by an effective interaction -- the quasipotential. We first determine perturbatively to lowest order the relativistic quasipotential for the Schroedinger-like equation by comparing that form with one derived from the Bethe-Salpeter equation. Insertion of this perturbative information into the minimal interaction structures of the two-body Dirac equations then completely determines their interaction structures. Then we give a procedure for constructing the full sixteen component solution to our coupled first-order Dirac equations from a solution of the second order equation for the reduced wave function. Next, we show that a perturbative treatment of these equations yields the standard spectral results for QED and related interactions.

  4. Generalized virial theorem for massless electrons in graphene and other Dirac materials

    NASA Astrophysics Data System (ADS)

    Sokolik, A. A.; Zabolotskiy, A. D.; Lozovik, Yu. E.

    2016-05-01

    The virial theorem for a system of interacting electrons in a crystal, which is described within the framework of the tight-binding model, is derived. We show that, in the particular case of interacting massless electrons in graphene and other Dirac materials, the conventional virial theorem is violated. Starting from the tight-binding model, we derive the generalized virial theorem for Dirac electron systems, which contains an additional term associated with a momentum cutoff at the bottom of the energy band. Additionally, we derive the generalized virial theorem within the Dirac model using the minimization of the variational energy. The obtained theorem is illustrated by many-body calculations of the ground-state energy of an electron gas in graphene carried out in Hartree-Fock and self-consistent random-phase approximations. Experimental verification of the theorem in the case of graphene is discussed.

  5. Modified Dirac Hamiltonian for efficient quantum mechanical simulations of micron sized devices

    NASA Astrophysics Data System (ADS)

    Habib, K. M. Masum; Sajjad, Redwan N.; Ghosh, Avik W.

    2016-03-01

    Representing massless Dirac fermions on a spatial lattice poses a potential challenge known as the Fermion Doubling problem. Addition of a quadratic term to the Dirac Hamiltonian provides a possible way to circumvent this problem. We show that the modified Hamiltonian with the additional term results in a very small Hamiltonian matrix when discretized on a real space square lattice. The resulting Hamiltonian matrix is considerably more efficient for numerical simulations without sacrificing on accuracy and is several orders of magnitude faster than the atomistic tight binding model. Using this Hamiltonian and the non-equilibrium Green's function formalism, we show several transport phenomena in graphene, such as magnetic focusing, chiral tunneling in the ballistic limit, and conductivity in the diffusive limit in micron sized graphene devices. The modified Hamiltonian can be used for any system with massless Dirac fermions such as Topological Insulators, opening up a simulation domain that is not readily accessible otherwise.

  6. Few layer epitaxial germanene: a novel two-dimensional Dirac material.

    PubMed

    Dávila, María Eugenia; Le Lay, Guy

    2016-01-01

    Monolayer germanene, a novel graphene-like germanium allotrope akin to silicene has been recently grown on metallic substrates. Lying directly on the metal surfaces the reconstructed atom-thin sheets are prone to lose the massless Dirac fermion character and unique associated physical properties of free standing germanene. Here, we show that few layer germanene, which we create by dry epitaxy on a gold template, possesses Dirac cones thanks to a reduced interaction. This finding established on synchrotron-radiation-based photoemission, scanning tunneling microscopy imaging and surface electron diffraction places few layer germanene among the rare two-dimensional Dirac materials. Since germanium is currently used in the mainstream Si-based electronics, perspectives of using germanene for scaling down beyond the 5 nm node appear very promising. Other fascinating properties seem at hand, typically the robust quantum spin Hall effect for applications in spintronics and the engineering of Floquet Majorana fermions by light for quantum computing.

  7. Direct observation and temperature control of the surface Dirac gap in a topological crystalline insulator.

    PubMed

    Wojek, B M; Berntsen, M H; Jonsson, V; Szczerbakow, A; Dziawa, P; Kowalski, B J; Story, T; Tjernberg, O

    2015-10-13

    Since the advent of topological insulators hosting Dirac surface states, efforts have been made to gap these states in a controllable way. A new route to accomplish this was opened up by the discovery of topological crystalline insulators where the topological states are protected by crystal symmetries and thus prone to gap formation by structural changes of the lattice. Here we show a temperature-driven gap opening in Dirac surface states within the topological crystalline insulator phase in (Pb,Sn)Se. By using angle-resolved photoelectron spectroscopy, the gap formation and mass acquisition is studied as a function of composition and temperature. The resulting observations lead to the addition of a temperature- and composition-dependent boundary between massless and massive Dirac states in the topological phase diagram for (Pb,Sn)Se (001). Overall, our results experimentally establish the possibility to tune between massless and massive topological states on the surface of a topological system.

  8. Derivatives of the Dirac delta function by explicit construction of sequences

    NASA Astrophysics Data System (ADS)

    Boykin, Timothy B.

    2003-05-01

    Explicit sequences that approach the Dirac delta function and its derivatives are often helpful in presenting generalized functions. We present a method by which a finite difference formula may be easily converted into a sequence that approaches a derivative of the Dirac delta function in one dimension. In three dimensions, we employ a sequence for the Dirac delta function based on a uniformly charged sphere of infinitesimal radius and infinite charge density and show that the charge density of an electric dipole is (in the sense of a generalized function) equal to -(∂/∂z)δ3(r). We use this result to derive Gauss' law in a dielectric medium directly from the charge densities, without using the potentials.

  9. Narrow depression in the density of states at the Dirac point in disordered graphene

    NASA Astrophysics Data System (ADS)

    Schweitzer, L.

    2009-12-01

    The electronic properties of noninteracting particles moving on a two-dimensional bricklayer lattice are investigated numerically. In particular, the influence of disorder in form of a spatially varying random magnetic flux is studied. In addition, a strong perpendicular constant magnetic field B is considered. The density of states ρ(E) goes to zero for E→0 as in the ordered system but with a much steeper slope. This happens for both cases: at the Dirac point for B=0 and at the center of the central Landau band for finite B . Close to the Dirac point, the dependence of ρ(E) on the system size, on the disorder strength, and on the constant magnetic flux density is analyzed and fitted to an analytical expression proposed previously in connection with the thermal quantum-Hall effect. Additional short-range on-site disorder completely replenishes the indentation in the density of states at the Dirac point.

  10. Dirac leaky-wave antennas for continuous beam scanning from photonic crystals

    NASA Astrophysics Data System (ADS)

    Memarian, Mohammad; Eleftheriades, George V.

    2015-01-01

    Leaky-Wave Antennas (LWAs) enable directive and scannable radiation patterns, which are highly desirable attributes at terahertz, infrared and optical frequencies. However, a LWA is generally incapable of continuous beam scanning through broadside, due to an open stopband in its dispersion characteristic. This issue is yet to be addressed at frequencies beyond microwaves, mainly as existing microwave solutions (for example, transmission line metamaterials) are unavailable at these higher frequencies. Here we report leaky-wave radiation from the interface of a photonic crystal (PC) with a Dirac-type dispersion and air. The resulting Dirac LWA (DLWA) can radiate at broadside, chiefly owing to the closed Γ-point bandgap of the Dirac PC. Thus, the DLWA can continuously scan a directive beam over a wide range of angles by varying the frequency. These DLWAs can be designed at microwave as well as terahertz to optical frequencies, with feasible dimensions and low losses.

  11. Dirac-node arc in the topological line-node semimetal HfSiS

    NASA Astrophysics Data System (ADS)

    Takane, D.; Wang, Zhiwei; Souma, S.; Nakayama, K.; Trang, C. X.; Sato, T.; Takahashi, T.; Ando, Yoichi

    2016-09-01

    We have performed angle-resolved photoemission spectroscopy on HfSiS, which has been predicted to be a topological line-node semimetal with square Si lattice. We found a quasi-two-dimensional Fermi surface hosting bulk nodal lines, alongside the surface states at the Brillouin-zone corner exhibiting a sizable Rashba splitting and band-mass renormalization due to many-body interactions. Most notably, we discovered an unexpected Dirac-like dispersion extending one dimensionally in k space—the Dirac-node arc—near the bulk node at the zone diagonal. These novel Dirac states reside on the surface and could be related to hybridizations of bulk states, but currently we have no explanation for its origin. This discovery poses an intriguing challenge to the theoretical understanding of topological line-node semimetals.

  12. Existence of Dirac cones in the Brillouin zone of diperiodic atomic crystals according to group theory

    NASA Astrophysics Data System (ADS)

    Damljanović, V.; Gajić, R.

    2016-03-01

    We have considered non-magnetic materials with weak spin-orbit coupling, that are periodic in two non-collinear directions, and finite in the third, orthogonal direction. In some cases, the combined time-reversal and crystal symmetry of such systems, allows the existence of Dirac cones at certain points in the reciprocal space. We have investigated in a systematic way, all points of the Brillouin zone of all 80 diperiodic groups and have found sufficient conditions for the existence of s  =  1/2 Dirac fermions, with symmetry-provided band touching at the vertex of the Dirac cones. Conversely, complete linear dispersion is forbidden for orbital wave functions belonging to two-dimensional (2D) irreducible representations (irreps) of little groups that do not satisfy certain group theoretical conditions given in this paper. Our results are illustrated by a tight-binding example.

  13. Few layer epitaxial germanene: a novel two-dimensional Dirac material.

    PubMed

    Dávila, María Eugenia; Le Lay, Guy

    2016-01-01

    Monolayer germanene, a novel graphene-like germanium allotrope akin to silicene has been recently grown on metallic substrates. Lying directly on the metal surfaces the reconstructed atom-thin sheets are prone to lose the massless Dirac fermion character and unique associated physical properties of free standing germanene. Here, we show that few layer germanene, which we create by dry epitaxy on a gold template, possesses Dirac cones thanks to a reduced interaction. This finding established on synchrotron-radiation-based photoemission, scanning tunneling microscopy imaging and surface electron diffraction places few layer germanene among the rare two-dimensional Dirac materials. Since germanium is currently used in the mainstream Si-based electronics, perspectives of using germanene for scaling down beyond the 5 nm node appear very promising. Other fascinating properties seem at hand, typically the robust quantum spin Hall effect for applications in spintronics and the engineering of Floquet Majorana fermions by light for quantum computing. PMID:26860590

  14. Coexisting massive and massless Dirac fermions in quasi-freestanding bilayer graphene

    NASA Astrophysics Data System (ADS)

    Kim, Keun Su; Walter, Andrew L.; Moreschini, Luca; Seyller, Thomas; Horn, Karsten; Rotenberg, Eli; Bostwick, Aaron

    2013-03-01

    The most widely accepted theoretical model to describe charge carriers in bilayer graphene is ``massive Dirac fermions'', characterized by a nearly parabolic band pair touching each other at the Dirac energy. This electronic structure of bilayer graphene is widely believed to be unstable towards symmetry breaking either by structural distortions, such as twist and strain, or electronic interactions. In this work, we investigate quasi-freestanding bilayer graphene by angle-resolved photoemission spectroscopy, which shows an unexpected electronic spectrum, consisting of both massive and massless Dirac fermions. The latter has a unique band topology with a chiral pseudospin texture, and its origin will be discussed in terms of symmetry breaking induced by a native imperfection of bilayer graphene.

  15. Confinement of a Dirac Particle to a Hard-Wall Confining Potential Induced by Noninertial Effects

    NASA Astrophysics Data System (ADS)

    Bakke, K.

    2013-01-01

    In this contribution, we discuss the influence of noninertial effects on a Dirac particle in the Minkowski spacetime by showing that the geometry of the manifold can play the role of a hard-wall confining potential. Thus, we discuss a limit case where the relativistic bound states can be achieved in analogous way to having a Dirac particle confined to a quantum dot. We discuss the application of this mathematical model in studies of noninertial effects on condensed matter systems described by the Dirac equation, and compare the nonrelativistic limit of the energy levels with the spectrum of energy of a spin-½ particle confined to a quantum dot [E. Tsitsishvili et al., Phys. Rev. B70 (2004) 115316].

  16. Interfacial Dirac cones from alternating topological invariant superlattice structures of Bi2Se3.

    PubMed

    Song, Jung-Hwan; Jin, Hosub; Freeman, Arthur J

    2010-08-27

    When the three-dimensional topological insulators Bi2Se3 and Bi2Te3 have an interface with vacuum, i.e., a surface, they show remarkable features such as topologically protected and spin-momentum locked surface states. However, for practical applications, one often requires multiple interfaces or channels rather than a single surface. Here, for the first time, we show that an interfacial and ideal Dirac cone is realized by alternating band and topological insulators. The multichannel Dirac fermions from the superlattice structures open a new way for applications such as thermoelectric and spintronics devices. Indeed, utilizing the interfacial Dirac fermions, we also demonstrate the possible power factor improvement for thermoelectric applications. PMID:20868180

  17. Few layer epitaxial germanene: a novel two-dimensional Dirac material

    PubMed Central

    Dávila, María Eugenia; Le Lay, Guy

    2016-01-01

    Monolayer germanene, a novel graphene-like germanium allotrope akin to silicene has been recently grown on metallic substrates. Lying directly on the metal surfaces the reconstructed atom-thin sheets are prone to lose the massless Dirac fermion character and unique associated physical properties of free standing germanene. Here, we show that few layer germanene, which we create by dry epitaxy on a gold template, possesses Dirac cones thanks to a reduced interaction. This finding established on synchrotron-radiation-based photoemission, scanning tunneling microscopy imaging and surface electron diffraction places few layer germanene among the rare two-dimensional Dirac materials. Since germanium is currently used in the mainstream Si-based electronics, perspectives of using germanene for scaling down beyond the 5 nm node appear very promising. Other fascinating properties seem at hand, typically the robust quantum spin Hall effect for applications in spintronics and the engineering of Floquet Majorana fermions by light for quantum computing. PMID:26860590

  18. Leading two-loop corrections to the Higgs boson masses in SUSY models with Dirac gauginos

    NASA Astrophysics Data System (ADS)

    Braathen, Johannes; Goodsell, Mark D.; Slavich, Pietro

    2016-09-01

    We compute the two-loop {O}({α}_t{α}_s) corrections to the Higgs boson masses in supersymmetric extensions of the Standard Model with Dirac gaugino masses. We rely on the effective-potential technique, allow for both Dirac and Majorana mass terms for the gluinos, and compute the corrections in both the overline{DR} and on-shell renormalisation schemes. We give detailed results for the MDGSSM and the MRSSM, and simple approximate formulae valid in the decoupling limit for all currently-studied variants of supersymmetric models with Dirac gluinos. These results represent the first explicit two-loop calculation of Higgs boson masses in supersymmetric models beyond the MSSM and the NMSSM.

  19. Interplay of Surface and Dirac Plasmons in Topological Insulators: The Case of Bi_{2}Se_{3}.

    PubMed

    Politano, A; Silkin, V M; Nechaev, I A; Vitiello, M S; Viti, L; Aliev, Z S; Babanly, M B; Chiarello, G; Echenique, P M; Chulkov, E V

    2015-11-20

    We have investigated plasmonic excitations at the surface of Bi_{2}Se_{3}(0001) via high-resolution electron energy loss spectroscopy. For low parallel momentum transfer q_{∥}, the loss spectrum shows a distinctive feature peaked at 104 meV. This mode varies weakly with q_{∥}. The behavior of its intensity as a function of primary energy and scattering angle indicates that it is a surface plasmon. At larger momenta (q_{∥}~0.04 Å^{-1}), an additional peak, attributed to the Dirac plasmon, becomes clearly defined in the loss spectrum. Momentum-resolved loss spectra provide evidence of the mutual interaction between the surface plasmon and the Dirac plasmon of Bi_{2}Se_{3}. The proposed theoretical model accounting for the coexistence of three-dimensional doping electrons and two-dimensional Dirac fermions accurately represents the experimental observations. The results reveal novel routes for engineering plasmonic devices based on topological insulators. PMID:26636863

  20. Domain wall interactions due to vacuum Dirac field fluctuations in 2 +1 dimensions

    NASA Astrophysics Data System (ADS)

    Fosco, C. D.; Mazzitelli, F. D.

    2016-07-01

    We evaluate quantum effects due to a two-component Dirac field in 2 +1 spacetime dimensions, coupled to domain-wall-like defects with a smooth shape. We show that these effects induce nontrivial contributions to the (shape-dependent) energy of the domain walls. For a single defect, we study the divergences in the corresponding self-energy, and also consider the role of the massless zero mode—corresponding to the Callan-Harvey mechanism—by coupling the Dirac field to an external gauge field. For two defects, we show that the Dirac field induces a nontrivial, Casimir-like effect between them, and we provide an exact expression for that interaction in the case of two straight-line parallel defects. As is the case for the Casimir interaction energy, the result is finite and unambiguous.

  1. Interplay of Surface and Dirac Plasmons in Topological Insulators: The Case of Bi_{2}Se_{3}.

    PubMed

    Politano, A; Silkin, V M; Nechaev, I A; Vitiello, M S; Viti, L; Aliev, Z S; Babanly, M B; Chiarello, G; Echenique, P M; Chulkov, E V

    2015-11-20

    We have investigated plasmonic excitations at the surface of Bi_{2}Se_{3}(0001) via high-resolution electron energy loss spectroscopy. For low parallel momentum transfer q_{∥}, the loss spectrum shows a distinctive feature peaked at 104 meV. This mode varies weakly with q_{∥}. The behavior of its intensity as a function of primary energy and scattering angle indicates that it is a surface plasmon. At larger momenta (q_{∥}~0.04 Å^{-1}), an additional peak, attributed to the Dirac plasmon, becomes clearly defined in the loss spectrum. Momentum-resolved loss spectra provide evidence of the mutual interaction between the surface plasmon and the Dirac plasmon of Bi_{2}Se_{3}. The proposed theoretical model accounting for the coexistence of three-dimensional doping electrons and two-dimensional Dirac fermions accurately represents the experimental observations. The results reveal novel routes for engineering plasmonic devices based on topological insulators.

  2. Way to distinguish between Majorana and Dirac massive neutrinos in neutrino-counting reactions

    SciTech Connect

    Chhabra, T.; Ram Babu, P. 452001 )

    1992-08-01

    The question of ascertaining the Majorana and Dirac nature of heavy fourth-generation or excited neutrinos is considered model independently without assuming definite handedness. Expressions for longitudinal- and transverse-polarization asymmetries in the reaction {ital e}{sup +}{ital e{minus}}{r arrow}{ital N{bar N}}{gamma} are given in the cases when {ital N} is a Majorana or Dirac neutrino. Measurements of such asymmetries provide a way to ascertain the nature of neutrinos. For different masses of neutrinos, numerical computation of longitudinal-polarization asymmetries at definite emission angles of the photon and neutrino and at definite neutrino energy are performed. Significant differences in the cases when final neutrinos are Majorana or Dirac are observed.

  3. Dirac leaky-wave antennas for continuous beam scanning from photonic crystals.

    PubMed

    Memarian, Mohammad; Eleftheriades, George V

    2015-01-01

    Leaky-Wave Antennas (LWAs) enable directive and scannable radiation patterns, which are highly desirable attributes at terahertz, infrared and optical frequencies. However, a LWA is generally incapable of continuous beam scanning through broadside, due to an open stopband in its dispersion characteristic. This issue is yet to be addressed at frequencies beyond microwaves, mainly as existing microwave solutions (for example, transmission line metamaterials) are unavailable at these higher frequencies. Here we report leaky-wave radiation from the interface of a photonic crystal (PC) with a Dirac-type dispersion and air. The resulting Dirac LWA (DLWA) can radiate at broadside, chiefly owing to the closed Γ-point bandgap of the Dirac PC. Thus, the DLWA can continuously scan a directive beam over a wide range of angles by varying the frequency. These DLWAs can be designed at microwave as well as terahertz to optical frequencies, with feasible dimensions and low losses. PMID:25556705

  4. Emergence of massless Dirac quasiparticles in correlated hydrogenated graphene with broken sublattice symmetry

    NASA Astrophysics Data System (ADS)

    Seki, Kazuhiro; Shirakawa, Tomonori; Zhang, Qinfang; Li, Tao; Yunoki, Seiji

    2016-04-01

    Using the variational cluster approximation (VCA) and the cluster perturbation theory, we study the finite-temperature phase diagram of a half-depleted periodic Anderson model on the honeycomb lattice at half-filling for a model of graphone, i.e., single-side hydrogenated graphene. The ground state of this model is found to be ferromagnetic (FM) semimetal. The origin of this FM state is attributed to the instability of a flat band located at the Fermi energy in the noninteracting limit and is smoothly connected to the Lieb-Mattis-type ferromagnetism. The spin-wave dispersion in the FM state is linear in momentum at zero temperature but becomes quadratic at finite temperatures, implying that the FM state is fragile against thermal fluctuations. Indeed, our VCA calculations find that the paramagnetic (PM) state dominates the finite-temperature phase diagram. More surprisingly, we find that massless Dirac quasiparticles with the linear energy dispersion emerge at the Fermi energy upon introducing the electron correlation U at the impurity sites in the PM phase. The Dirac Fermi velocity is found to be highly correlated to the quasiparticle weight of the emergent massless Dirac quasiparticles at the Fermi energy and monotonically increases with U . These unexpected massless Dirac quasiparticles are also examined with the Hubbard-I approximation and the origin is discussed in terms of the spectral weight redistribution involving a large energy scale of U . Considering an effective quasiparticle Hamiltonian which reproduces the single-particle excitations obtained by the Hubbard-I approximation, we argue that the massless Dirac quasiparticles are protected by the electron correlation. Our finding therefore provides a unique example of the emergence of massless Dirac quasiparticles due to dynamical electron correlations without breaking any spatial symmetry. The experimental implications of our results for graphone as well as a graphene sheet on transition-metal substrates

  5. Fierz bilinear formulation of the Maxwell–Dirac equations and symmetry reductions

    SciTech Connect

    Inglis, Shaun Jarvis, Peter

    2014-09-15

    We study the Maxwell–Dirac equations in a manifestly gauge invariant presentation using only the spinor bilinear scalar and pseudoscalar densities, and the vector and pseudovector currents, together with their quadratic Fierz relations. The internally produced vector potential is expressed via algebraic manipulation of the Dirac equation, as a rational function of the Fierz bilinears and first derivatives (valid on the support of the scalar density), which allows a gauge invariant vector potential to be defined. This leads to a Fierz bilinear formulation of the Maxwell tensor and of the Maxwell–Dirac equations, without any reference to gauge dependent quantities. We show how demanding invariance of tensor fields under the action of a fixed (but arbitrary) Lie subgroup of the Poincaré group leads to symmetry reduced equations. The procedure is illustrated, and the reduced equations worked out explicitly for standard spherical and cylindrical cases, which are coupled third order nonlinear PDEs. Spherical symmetry necessitates the existence of magnetic monopoles, which do not affect the coupled Maxwell–Dirac system due to magnetic terms cancelling. In this paper we do not take up numerical computations. As a demonstration of the power of our approach, we also work out the symmetry reduced equations for two distinct classes of dimension 4 one-parameter families of Poincaré subgroups, one splitting and one non-splitting. The splitting class yields no solutions, whereas for the non-splitting class we find a family of formal exact solutions in closed form. - Highlights: • Maxwell–Dirac equations derived in manifestly gauge invariant tensor form. • Invariant scalar and four vector fields for four Poincaré subgroups derived, including two unusual cases. • Symmetry reduction imposed on Maxwell–Dirac equations under example subgroups. • Magnetic monopole arises for spherically symmetric case, consistent with charge quantization condition.

  6. Three Dirac points on the (110) surface of the topological insulator Bi1-xSbx

    NASA Astrophysics Data System (ADS)

    Zhu, Xie-Gang; Stensgaard, Malthe; Barreto, Lucas; Silva, Wendell Simoes e.; Ulstrup, Søren; Michiardi, Matteo; Bianchi, Marco; Dendzik, Maciej; Hofmann, Philip

    2013-10-01

    Topological insulator surfaces support metallic surface states with closed Fermi contours, encircling an odd number of Dirac points. Experimental studies have so far concentrated on surfaces with only one Dirac point, but three Dirac points can be expected for certain surface orientations of several topological insulator materials. Here we experimentally realize the Bi1-xSbx(110) surface for which an electronic structure with three Dirac points has been predicted (Teo et al 2008 Phys. Rev. B 78 045426), in contrast to the closed-packed (111) surface of the same material that supports only one Dirac point. We study the electronic structure of Bi1-xSbx(110) with angle-resolved photoemission and tight-binding calculations. We observe several metallic surface states, confirming not only the expectation that a topological insulator should be enclosed by metallic surfaces on all faces, but also the prediction of the surface state topology. Tight-binding calculations of the electronic structure are found to reproduce the expected topology of the surface states but they show one Dirac point that is not observed in the experiment, in the mirror line of the surface Brillouin zone. As in the case of Bi1-xSbx(111), this can be ascribed to an incorrect value of the mirror Chern number in the tight-binding parameters employed for the calculation. The quantitative agreement of the tight-binding calculation and the experiment is poorer than in the case of the (111) surface, something that is ascribed to the existence of dangling bonds on the (110) surface.

  7. Quantum Transport of Spin-helical Dirac Fermion Topological Surface States in Topological Insulators

    NASA Astrophysics Data System (ADS)

    Chen, Yong P.

    Three-dimensional (3D) topological insulators (TI) are a novel class of electronic materials with topologically-nontrivial band structure such that the bulk is gapped and insulating yet the surface has topologically protected gapless conducting states. Such ``topological surface states'' (TSS) give helically spin polarized Dirac fermions, and offer a promising platform to realize various other novel physics such as topological magnetoelectric effects and Majorana fermions. However, it is often challenging to unambiguously access and study the transport properties of TSS in many practical TI materials due to non-negligible bulk conducting states. I will discuss our recent experiments on high-quality ``intrinsic'' TIs with insulating bulk and surface-dominated conduction that allow us to reveal a number of characteristic transport properties of spin-helical Dirac fermion topological surface states. We have observed, for example, a thickness-independent and surface-dominated conductance (even at room temperature) in exfoliated TI thin films and well-developed ``half-integer'' Dirac fermion quantum Hall effect (QHE) arising from TSS (observed up to 40K); fully-tunable ``two-species'' Dirac fermion QHE and other intriguing states in dual gated devices where both top and bottom surfaces can be independently controlled; current-induced helical spin-polarization detected by spin sensitive transport measurements using magnetic electrodes; and in TI nanoribbons, Shubnikov-de Hass (SdH) oscillations showing gate-tunable Berry phase and ultra-relativistic Dirac mass; and a ``half-integer'' Aharonov-Bohm effect (ABE) unique to the circumferentially quantized spin helical Dirac fermion surface state modes (sub-bands), with a gate-tunable conductance oscillation and alternation between the ``half-integer'' ABE and regular ABE periodic in fermi momentum. Such TIs and related devices may enable promising future applications in spintronics, thermoelectrics and various topological

  8. Nonlinear Dirac equation solitary waves in external fields.

    PubMed

    Mertens, Franz G; Quintero, Niurka R; Cooper, Fred; Khare, Avinash; Saxena, Avadh

    2012-10-01

    We consider nonlinear Dirac equations (NLDE's) in the 1+1 dimension with scalar-scalar self-interaction g2/κ+1(Ψ[over ¯]Ψ)κ+1 in the presence of various external electromagnetic fields. We find exact solutions for special external fields and we study the behavior of solitary-wave solutions to the NLDE in the presence of a wide variety of fields in a variational approximation depending on collective coordinates which allows the position, width, and phase of these waves to vary in time. We find that in this approximation the position q(t) of the center of the solitary wave obeys the usual behavior of a relativistic point particle in an external field. For time-independent external fields, we find that the energy of the solitary wave is conserved but not the momentum, which becomes a function of time. We postulate that, similarly to the nonlinear Schrödinger equation (NLSE), a sufficient dynamical condition for instability to arise is that dP(t)/dq[over ̇](t)<0. Here P(t) is the momentum of the solitary wave, and q[over ̇] is the velocity of the center of the wave in the collective coordinate approximation. We found for our choices of external potentials that we always have dP(t)/dq[over ̇](t)>0, so, when instabilities do occur, they are due to a different source. We investigate the accuracy of our variational approximation using numerical simulations of the NLDE and find that, when the forcing term is small and we are in a regime where the solitary wave is stable, that the behavior of the solutions of the collective coordinate equations agrees very well with the numerical simulations. We found that the time evolution of the collective coordinates of the solitary wave in our numerical simulations, namely the position of the average charge density and the momentum of the solitary wave, provide good indicators for when the solitary wave first becomes unstable. When these variables stop being smooth functions of time (t), then the solitary wave starts to distort

  9. Nonlinear Dirac equation solitary waves in external fields.

    PubMed

    Mertens, Franz G; Quintero, Niurka R; Cooper, Fred; Khare, Avinash; Saxena, Avadh

    2012-10-01

    We consider nonlinear Dirac equations (NLDE's) in the 1+1 dimension with scalar-scalar self-interaction g2/κ+1(Ψ[over ¯]Ψ)κ+1 in the presence of various external electromagnetic fields. We find exact solutions for special external fields and we study the behavior of solitary-wave solutions to the NLDE in the presence of a wide variety of fields in a variational approximation depending on collective coordinates which allows the position, width, and phase of these waves to vary in time. We find that in this approximation the position q(t) of the center of the solitary wave obeys the usual behavior of a relativistic point particle in an external field. For time-independent external fields, we find that the energy of the solitary wave is conserved but not the momentum, which becomes a function of time. We postulate that, similarly to the nonlinear Schrödinger equation (NLSE), a sufficient dynamical condition for instability to arise is that dP(t)/dq[over ̇](t)<0. Here P(t) is the momentum of the solitary wave, and q[over ̇] is the velocity of the center of the wave in the collective coordinate approximation. We found for our choices of external potentials that we always have dP(t)/dq[over ̇](t)>0, so, when instabilities do occur, they are due to a different source. We investigate the accuracy of our variational approximation using numerical simulations of the NLDE and find that, when the forcing term is small and we are in a regime where the solitary wave is stable, that the behavior of the solutions of the collective coordinate equations agrees very well with the numerical simulations. We found that the time evolution of the collective coordinates of the solitary wave in our numerical simulations, namely the position of the average charge density and the momentum of the solitary wave, provide good indicators for when the solitary wave first becomes unstable. When these variables stop being smooth functions of time (t), then the solitary wave starts to distort

  10. Phases of S U (3 ) gauge theories with fundamental quarks via Dirac spectral density

    NASA Astrophysics Data System (ADS)

    Alexandru, Andrei; Horváth, Ivan

    2015-08-01

    We propose that, in S U (3 ) gauge theories with fundamental quarks, confinement can be inferred from spectral density of the Dirac operator. This stems from the proposition that its possible behaviors are exhausted by three distinct types (Fig. 1). The monotonic cases are standard and entail confinement with valence chiral symmetry breaking (A) or the lack of both (C,C'). The bimodal (anomalous) option (B) was frequently regarded as an artifact (lattice or other) in previous studies, but we show for the first time that it persists in the continuum limit, and conclude that it informs of a nonconfining phase with broken valence chiral symmetry. This generalization rests on the following. (α ) We show that bimodality in Nf=0 theory past deconfinement temperature Tc is stable with respect to removal of both infrared and ultraviolet cutoffs, indicating that anomalous phase is not an artifact. (β ) We demonstrate that transition to bimodality in Nf=0 is simultaneous with the loss of confinement: anomalous phase occurs for Tc

  11. Quantum-confinement and Structural Anisotropy result in Electrically-Tunable Dirac Cone in Few-layer Black Phosphorous

    PubMed Central

    Dolui, Kapildeb; Quek, Su Ying

    2015-01-01

    Two-dimensional (2D) materials are well-known to exhibit interesting phenomena due to quantum confinement. Here, we show that quantum confinement, together with structural anisotropy, result in an electric-field-tunable Dirac cone in 2D black phosphorus. Using density functional theory calculations, we find that an electric field, Eext, applied normal to a 2D black phosphorus thin film, can reduce the direct band gap of few-layer black phosphorus, resulting in an insulator-to-metal transition at a critical field, Ec. Increasing Eext beyond Ec can induce a Dirac cone in the system, provided the black phosphorus film is sufficiently thin. The electric field strength can tune the position of the Dirac cone and the Dirac-Fermi velocities, the latter being similar in magnitude to that in graphene. We show that the Dirac cone arises from an anisotropic interaction term between the frontier orbitals that are spatially separated due to the applied field, on different halves of the 2D slab. When this interaction term becomes vanishingly small for thicker films, the Dirac cone can no longer be induced. Spin-orbit coupling can gap out the Dirac cone at certain electric fields; however, a further increase in field strength reduces the spin-orbit-induced gap, eventually resulting in a topological-insulator-to-Dirac-semimetal transition. PMID:26129645

  12. Bound state solution of Dirac equation for 3D harmonics oscillator plus trigonometric scarf noncentral potential using SUSY QM approach

    SciTech Connect

    Cari, C. Suparmi, A.

    2014-09-30

    Dirac equation of 3D harmonics oscillator plus trigonometric Scarf non-central potential for spin symmetric case is solved using supersymmetric quantum mechanics approach. The Dirac equation for exact spin symmetry reduces to Schrodinger like equation. The relativistic energy and wave function for spin symmetric case are simply obtained using SUSY quantum mechanics method and idea of shape invariance.

  13. Scattering, GREEN’S Functions and Symmetries in a Total Space of a Dirac Monopole Fibre Bundle

    NASA Astrophysics Data System (ADS)

    Savinkov, A. G.; Ryzhov, A. B.

    The scattering wave functions and Green’s functions were found in a total space of a Dirac monopole principal bundle. Also, hidden symmetries of a charge-Dirac monopole system and those joining the states relating to different topological charges n=2eg were found.

  14. White Noise Path Integral Treatment of a Two-dimensional Dirac Oscillator in a Uniform Magnetic Field

    SciTech Connect

    Bastatas, Lyndon D.; Bornales, Jinky B.

    2008-06-18

    White noise path integral prescription is applied to solve the Dirac equation for a two-dimensional Dirac oscillator in a uniform magnetic field. The energy spectrum obtained agrees with the result obtained by Villalba and Maggiolo using the differential approach.

  15. Quantum-confinement and Structural Anisotropy result in Electrically-Tunable Dirac Cone in Few-layer Black Phosphorous.

    PubMed

    Dolui, Kapildeb; Quek, Su Ying

    2015-07-01

    Two-dimensional (2D) materials are well-known to exhibit interesting phenomena due to quantum confinement. Here, we show that quantum confinement, together with structural anisotropy, result in an electric-field-tunable Dirac cone in 2D black phosphorus. Using density functional theory calculations, we find that an electric field, E ext, applied normal to a 2D black phosphorus thin film, can reduce the direct band gap of few-layer black phosphorus, resulting in an insulator-to-metal transition at a critical field, Ec. Increasing E ext beyond Ec can induce a Dirac cone in the system, provided the black phosphorus film is sufficiently thin. The electric field strength can tune the position of the Dirac cone and the Dirac-Fermi velocities, the latter being similar in magnitude to that in graphene. We show that the Dirac cone arises from an anisotropic interaction term between the frontier orbitals that are spatially separated due to the applied field, on different halves of the 2D slab. When this interaction term becomes vanishingly small for thicker films, the Dirac cone can no longer be induced. Spin-orbit coupling can gap out the Dirac cone at certain electric fields; however, a further increase in field strength reduces the spin-orbit-induced gap, eventually resulting in a topological-insulator-to-Dirac-semimetal transition.

  16. Quantum-confinement and Structural Anisotropy result in Electrically-Tunable Dirac Cone in Few-layer Black Phosphorous

    NASA Astrophysics Data System (ADS)

    Dolui, Kapildeb; Quek, Su Ying

    2015-07-01

    Two-dimensional (2D) materials are well-known to exhibit interesting phenomena due to quantum confinement. Here, we show that quantum confinement, together with structural anisotropy, result in an electric-field-tunable Dirac cone in 2D black phosphorus. Using density functional theory calculations, we find that an electric field, Eext, applied normal to a 2D black phosphorus thin film, can reduce the direct band gap of few-layer black phosphorus, resulting in an insulator-to-metal transition at a critical field, Ec. Increasing Eext beyond Ec can induce a Dirac cone in the system, provided the black phosphorus film is sufficiently thin. The electric field strength can tune the position of the Dirac cone and the Dirac-Fermi velocities, the latter being similar in magnitude to that in graphene. We show that the Dirac cone arises from an anisotropic interaction term between the frontier orbitals that are spatially separated due to the applied field, on different halves of the 2D slab. When this interaction term becomes vanishingly small for thicker films, the Dirac cone can no longer be induced. Spin-orbit coupling can gap out the Dirac cone at certain electric fields; however, a further increase in field strength reduces the spin-orbit-induced gap, eventually resulting in a topological-insulator-to-Dirac-semimetal transition.

  17. Solution of the Dirac Equation and the Solvable Potentials in the Schrodinger Equation

    SciTech Connect

    Bakhshi, Z.; Panahi, H.

    2011-12-26

    The point canonical transformation in non-relativistic quantum mechanics is applied as an algebraic method to obtain the solutions of the Dirac equation with spherical symmetry electromagnetic potentials. We show that some of the solvable potentials in the non-relativistic quantum mechanics can be related to the Dirac equation. The spinor wave functions for some of the obtained gauge field potentials are given in terms of special functions such as Jacobi, Generalized Laguerre and Hermit polynomials. The relativistic bound states spectrum for each cases are also obtained in terms of the bound states spectrum of the solvable potentials.

  18. Quantum work statistics of charged Dirac particles in time-dependent fields.

    PubMed

    Deffner, Sebastian; Saxena, Avadh

    2015-09-01

    The quantum Jarzynski equality is an important theorem of modern quantum thermodynamics. We show that the Jarzynski equality readily generalizes to relativistic quantum mechanics described by the Dirac equation. After establishing the conceptual framework we solve a pedagogical, yet experimentally relevant, system analytically. As a main result we obtain the exact quantum work distributions for charged particles traveling through a time-dependent vector potential evolving under Schrödinger as well as under Dirac dynamics, and for which the Jarzynski equality is verified. Special emphasis is put on the conceptual and technical subtleties arising from relativistic quantum mechanics.

  19. Slow Noncollinear Coulomb Scattering in the Vicinity of the Dirac Point in Graphene.

    PubMed

    König-Otto, J C; Mittendorff, M; Winzer, T; Kadi, F; Malic, E; Knorr, A; Berger, C; de Heer, W A; Pashkin, A; Schneider, H; Helm, M; Winnerl, S

    2016-08-19

    The Coulomb scattering dynamics in graphene in energetic proximity to the Dirac point is investigated by polarization resolved pump-probe spectroscopy and microscopic theory. Collinear Coulomb scattering rapidly thermalizes the carrier distribution in k directions pointing radially away from the Dirac point. Our study reveals, however, that, in almost intrinsic graphene, full thermalization in all directions relying on noncollinear scattering is much slower. For low photon energies, carrier-optical-phonon processes are strongly suppressed and Coulomb mediated noncollinear scattering is remarkably slow, namely on a ps time scale. This effect is very promising for infrared and THz devices based on hot carrier effects. PMID:27588881

  20. Connecting Dirac and Majorana neutrino mass matrices in the minimal left-right symmetric model.

    PubMed

    Nemevšek, Miha; Senjanović, Goran; Tello, Vladimir

    2013-04-12

    Probing the origin of neutrino mass by disentangling the seesaw mechanism is one of the central issues of particle physics. We address it in the minimal left-right symmetric model and show how the knowledge of light and heavy neutrino masses and mixings suffices to determine their Dirac Yukawa couplings. This in turn allows one to make predictions for a number of high and low energy phenomena, such as decays of heavy neutrinos, neutrinoless double beta decay, electric dipole moments of charged leptons, and neutrino transition moments. We also discuss a way of reconstructing the neutrino Dirac Yukawa couplings at colliders such as the LHC.