Topological aspect and quantum magnetoresistance of β-Ag2Te

To explain the unusual nonsaturating linear magnetoresistance observed in silver chalcogenides, the quantum scenario has been proposed based on the assumption of gapless linear energy spectrum. Here we show, by first principles calculations, that β-Ag2Te with distorted antifluorite structure is in fact a topological insulator with gapless Dirac-type surface states. The characteristic feature of this new binary topological insulator is the highly anisotropic Dirac cone, in contrast with known examples, such as Bi2Te3 and Bi2Se3. The Fermi velocity varies an order of magnitude by rotating the crystal axis.     

New generation of massless Dirac fermions in graphene under external periodic potentials

We show that new massless Dirac fermions are generated when a slowly varying periodic potential is applied to graphene. These quasiparticles, generated near the supercell Brillouin zone boundaries with anisotropic group velocity, are different from the original massless Dirac fermions. The quasiparticle wave vector (measured from the new Dirac point), the generalized pseudospin vector, and the group velocity are not collinear. We further show that with an appropriate periodic potential of triangular symmetry, there exists an energy window over which the only available states are these quasiparticles, thus providing a good system to probe experimentally the new massless Dirac fermions. The required parameters of external potentials are within the realm of laboratory conditions.     

Interaction of phonons and dirac fermions on the surface of Bi2Se3: a strong Kohn anomaly

We report the first measurements of phonon dispersion curves on the (001) surface of the strong three-dimensional topological insulator Bi2Se3. The surface phonon measurements were carried out with the aid of coherent helium beam surface scattering techniques. The results reveal a prominent signature of the exotic metallic Dirac fermion quasiparticles, including a strong Kohn anomaly. The signature is manifest in a low energy isotropic convex dispersive surface phonon branch with a frequency maximum of 1.8 THz and having a V-shaped minimum at approximately 2kF that defines the Kohn anomaly. Theoretical analysis attributes this dispersive profile to the renormalization of the surface phonon excitations by the surface Dirac fermions. The contribution of the Dirac fermions to this renormalization is derived in terms of a Coulomb-type perturbation model.     

Shubnikov-de Haas oscillations of massive Dirac fermions in a Dirac antiferromagnet SrMnSb2

We investigate the physical properties of massive Dirac fermions in SrMnSb₂ using transport, specific heat, electronic structure calculations, and Shubnikov-de Haas (SdH) oscillations. SrMnSb₂ is a candidate Dirac antiferromagnet, consisting of the MnSb layers and the distorted square net of Sb atoms with a zigzag chain structure. This structural distortion leads to gap opening at the band crossing point found in the square lattice of the sister compound SrMnBi₂ but leaves another Dirac band crossing near the Brillouin zone boundary. The small 2D Fermi surface with a light electron mass and a small Fermi energy is confirmed by the large resistivity anisotropy, the large Seebeck coefficient, and also the angle and temperature dependent SdH oscillations. The Berry phase obtained from the SdH oscillations is trivial, in contrast to the case of SrMnBi₂. The relatively large spin orbit coupling gap and the small Fermi energy in SrMnSb₂ is found to be essential to understand this contrasting behavior of the massive Dirac fermions as compared to SrMnBi₂. Our observations demonstrate that the Berry phase of the mobile electrons in SrMnSb₂ is sensitive to the Fermi level change and can be tuned by doping or deficiency.     

Statistical measures and the Klein tunneling in single-layer graphene

Statistical complexity and Fisher–Shannon information are calculated in a problem of quantum scattering, namely the Klein tunneling across a potential barrier in graphene. The treatment of electron wave functions as masless Dirac fermions allows us to compute these statistical measures. The comparison of these magnitudes with the transmission coefficient through the barrier is performed. We show that these statistical measures take their minimum values in the situations of total transparency through the barrier, a phenomenon highly anisotropic for the Klein tunneling in graphene.     

Interfacing 2D and 3D topological insulators: Bi(111) bilayer on Bi2Te3

We report the formation of a bilayer Bi(111) ultrathin film, which is theoretically predicted to be in a two-dimensional quantum spin Hall state, on a Bi(2)Te(3) substrate. From angle-resolved photoemission spectroscopy measurements and ab initio calculations, the electronic structure of the system can be understood as an overlap of the band dispersions of bilayer Bi and Bi(2)Te(3). Our results show that the Dirac cone is actually robust against nonmagnetic perturbations and imply a unique situation where the topologically protected one- and two-dimensional edge states are coexisting at the surface.     

Geodesic Motions in Euclidean Taub-NUT Spinning Spaces

We investigate the geodesic motions of pseudo-classical spin- \frac12\frac{1}{2} point particles in the Euclidean Taub-NUT space. We derive the constants of motion from the solutions of the generalized Killing equations for spinning spaces and exploiting those the motion of pseudo-classical Dirac fermions are analyzed on a cone and plane.     

Localization, Dirac fermions and Onsager universality

Disordered systems exhibiting exponential localization are mapped to anisotropic spin chains with localization length being related to the anisotropy of the spin model. This relates localization phenomenon in fermions to the rotational symmetry breaking in the critical spin chains. One of the intriguing consequence is that the statement of Onsager universality in spin chains implies universality of the localized fermions where the fluctuations in localized wave functions are universal. We further show that the fluctuations about localized nonrelativistic fermions describe relativistic fermions. This provides a new approach to understand the absence of localization in disordered Dirac fermions. We investigate how disorder affects well known universality of the spin chains by examining the multifractal exponents. Finally, we examine the effects of correlations on the localization characteristics of relativistic fermions. Received 28 September 2001 / Received in final form 30 November 2001 Published online 2 October 2002 RID="a" ID="a"e-mail: isatija@nickel.nist.gov     

Theory of magnetic oscillations in Weyl semimetals

Weyl semimetals are a new class of Dirac material that possesses bulk energy nodes in three dimensions, in contrast to two dimensional graphene. In this paper, we study a Weyl semimetal subject to an applied magnetic field. We find distinct behavior that can be used to identify materials containing three dimensional Dirac fermions. We derive expressions for the density of states, electronic specific heat, and the magnetization. We focus our attention on the quantum oscillations in the magnetization. We find phase shifts in the quantum oscillations that distinguish the Weyl semimetal from conventional three dimensional Schrödinger fermions, as well as from two dimensional Dirac fermions. The density of states as a function of energy displays a sawtooth pattern which has its origin in the dispersion of the three dimensional Landau levels. At the same time, the spacing in energy of the sawtooth spike goes like the square root of the applied magnetic field which reflects the Dirac nature of the fermions. These features are reflected in the specific heat and magnetization. Finally, we apply a simple model for disorder and show that this tends to damp out the magnetic oscillations in the magnetization at small fields.     

Quantum electrodynamics with anisotropic scaling: Heisenberg-Euler action and Schwinger pair production in the bilayer graphene

We discuss quantum electrodynamics emerging in the vacua with anisotropic scaling. Systems with anisotropic scaling were suggested by Hořava in relation to the quantum theory of gravity. In such vacua, the space and time are not equivalent, and moreover they obey different scaling laws, called the anisotropic scaling. Such anisotropic scaling takes place for fermions in bilayer graphene, where if one neglects the trigonal warping effects the massless Dirac fermions have quadratic dispersion. This results in the anisotropic quantum electrodynamics, in which electric and magnetic fields obey different scaling laws. Here we discuss the Heisenberg-Euler action and Schwinger pair production in such anisotropic QED.     

Three-dimensional topological insulator in a magnetic field: chiral side surface states and quantized Hall conductance

Low energy excitation of surface states of a three-dimensional topological insulator (3DTI) can be described by Dirac fermions. By using a tight-binding model, the transport properties of the surface states in a uniform magnetic field are investigated. It is found that chiral surface states parallel to the magnetic field are responsible for the quantized Hall (QH) conductance (2n + 1)e2/h multiplied by the number of Dirac cones. Due to the two-dimensional nature of the surface states, the robustness of the QH conductance against impurity scattering is determined by the oddness and evenness of the Dirac cone number. An experimental setup for transport measurement is proposed.     

Spectra of massive and massless QCD dirac operators: A novel link

We show that integrable structure of chiral random matrix models incorporating global symmetries of QCD Dirac operators (labeled by the Dyson index beta = 1,2, and 4) leads to emergence of a connection relation between the spectral statistics of massive and massless Dirac operators. This novel link established for beta-fold degenerate massive fermions is used to explicitly derive (and prove the random matrix universality of) statistics of low-lying spectra of QCD Dirac operators in the presence of SU(2) massive fermions in the fundamental representation ( beta = 1) and SU(N(c)>/=2) massive adjoint fermions ( beta = 4). Comparison with available lattice data for SU(2) dynamical staggered fermions reveals a good agreement.     

Graphene-like physics in optical lattices

Graphene has attracted enormous attention over the past years in condensed matter physics. The most interesting feature of graphene is that its low-energy excitations are relativistic Dirac fermions. Such feature is the origin of many topological properties in graphene-like physics. On the other hand, ultracold quantum gas trapped in an optical lattice has become a unique setting for quantum simulation of condensed matter physics. Here, we mainly review our recent work on quantum simulation of graphene-like physics with ultracold atoms trapped in a honeycomb or square optical lattice, including the simulation of Dirac fermions and quantum Hall effect with and without Landau levels. We also present the related experimental advances.     

Interacting random Dirac fermions in superconducting cuprates

We study the effects of quasiparticle interactions on disorder-induced localization of Dirac-like nodal excitations in superconducting high- Tc cuprates. As suggested by the experimental angle-resolved photoemission spectroscopy and terahertz conductivity data in Bi2Sr2CaCu2O(8+delta), we focus on the interactions mediated by the order parameter fluctuations near an incipient second pairing transition d --> d + is(id'). We find interaction corrections to the density of states, specific heat, and conductivity as well as phase and energy relaxation rates and assess the applicability of the recent localization scenarios for noninteracting random Dirac fermions to the cuprates.     

Parisi-Sourlas fermions from Ramond superstring

We show that the zero energy limit of the Ramond superstring naturally describes Dirac fermions with an OSP(D + 1,1¦2) or Parisi-Sourlas supersymmetry, and establish an equivalence between ordinary Dirac fermions and a massive (0 + 1)-dimensional supergravity theory.     

Chaotic spin precession in anisotropic universes and fermionic dark matter

We consider the precession of a Dirac particle spin in some anisotropic Bianchi universes. This effect is present already in the Bianchi-I universe. In the Bianchi-IX universe it acquires the chaotic character due to the stochasticity of the oscillatory approach to the cosmological singularity. The related helicity flip of fermions in the veryearly Universe may produce the sterile particles contributing to dark matter.     

Band structures of bilayer graphene superlattices

We formulate a low energy effective Hamiltonian to study superlattices in bilayer graphene (BLG) using a minimal model which supports quadratic band touching points. We show that a one dimensional (1D) periodic modulation of the chemical potential or the electric field perpendicular to the layers leads to the generation of zero-energy anisotropic massless Dirac fermions and finite energy Dirac points with tunable velocities. The electric field superlattice maps onto a coupled chain model comprised of "topological" edge modes. 2D superlattice modulations are shown to lead to gaps on the mini-Brillouin zone boundary but do not, for certain symmetries, gap out the quadratic band touching point. Such potential variations, induced by impurities and rippling in biased BLG, could lead to subgap modes which are argued to be relevant to understanding transport measurements.     

Qualitative analysis of trapped Dirac fermions in graphene

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.     

Sub-Poissonian shot noise in graphene

We calculate the mode-dependent transmission probability of massless Dirac fermions through an ideal strip of graphene (length L, width W, no impurities or defects) to obtain the conductance and shot noise as a function of Fermi energy. We find that the minimum conductivity of order e2/h at the Dirac point (when the electron and hole excitations are degenerate) is associated with a maximum of the Fano factor (the ratio of noise power and mean current). For short and wide graphene strips the Fano factor at the Dirac point equals 1/3, 3 times smaller than for a Poisson process. This is the same value as for a disordered metal, which is remarkable since the classical dynamics of the Dirac fermions is ballistic.     

Fragility of surface states and robustness of topological order in Bi2Se3 against oxidation

Topological surface states are protected against local perturbations, but this protection does not extend to chemical reaction over the whole surface, as demonstrated by theoretical studies of the oxidation of Bi(2)Se(3) and its effects on the surface spin polarization and current. While chemisorption of O(2) largely preserves the topological surface states, reaction with atomic O removes the original surface states and yields two new sets of surface states. One set forms a regular Dirac cone but is topologically trivial. The other set, while topologically relevant, forms an unusual rounded Dirac cone. The details are governed by the hybridization interaction at the interface.