Electron in a quantized plane-wave field and in the classical field of a longitudinal electric wave

The Dirac equation is solved for an electron moving in a quantized plane-wave field in the classical field of a longitudinal traveling electric wave propagating in one direction. Through a canonical transformation of the photon creation and annihilation operators the problem is reduced to a quasiparticle problem; the quasiparticle energy depends on the time and the coordinates.     

Axial-vector anomalies and the index theorem in charged Schwarzschild and Taub-NUT spaces

The index theorem gives a topological expression for the excess of zero-eigenvalues of positive chirality over negative chirality solutions of the Dirac equation. These solutions are derived directly from the Dirac equation in charged Euclideanized Schwarzschild and Taub-NUT spaces, and the results are compared with the predictions of the index theorem.     

Characteristics of level-spacing statistics in chaotic graphene billiards

A fundamental result in nonrelativistic quantum nonlinear dynamics is that the spectral statistics of quantum systems that possess no geometric symmetry, but whose classical dynamics are chaotic, are described by those of the Gaussian orthogonal ensemble (GOE) or the Gaussian unitary ensemble (GUE), in the presence or absence of time-reversal symmetry, respectively. For massless spin-half particles such as neutrinos in relativistic quantum mechanics in a chaotic billiard, the seminal work of Berry and Mondragon established the GUE nature of the level-spacing statistics, due to the combination of the chirality of Dirac particles and the confinement, which breaks the time-reversal symmetry. A question is whether the GOE or the GUE statistics can be observed in experimentally accessible, relativistic quantum systems. We demonstrate, using graphene confinements in which the quasiparticle motions are governed by the Dirac equation in the low-energy regime, that the level-spacing statistics are persistently those of GOE random matrices. We present extensive numerical evidence obtained from the tight-binding approach and a physical explanation for the GOE statistics. We also find that the presence of a weak magnetic field switches the statistics to those of GUE. For a strong magnetic field, Landau levels become influential, causing the level-spacing distribution to deviate markedly from the random-matrix predictions. Issues addressed also include the effects of a number of realistic factors on level-spacing statistics such as next nearest-neighbor interactions, different lattice orientations, enhanced hopping energy for atoms on the boundary, and staggered potential due to graphene-substrate interactions.     

Survival of the Dirac points in rippled graphene

We study the effects of the rippling of a graphene sheet on quasiparticle dispersion. This is achieved using a generalization to the honeycomb lattice of the momentum average approximation, which is accurate for all coupling strengths and at all energies. We show that even though the position of the Dirac points may move and the Fermi speed can be renormalized significantly, quasiparticles with very long lifetimes survive near the Dirac points even for very strong couplings.     

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.     

Random magnetic field and quasiparticle transport in the mixed state of high- Tc cuprates

By a singular gauge transformation, the quasiparticle transport in the mixed state of high- Tc cuprates is mapped into a charge-neutral Dirac moving in short-range correlated random scalar and long-range correlated vector potential. A fully quantum mechanical approach to longitudinal and transverse thermal conductivities is presented. The semiclassical Volovik effect is presented in a quantum mechanical way. The quasiparticle scattering from the random magnetic field which was completely missed in all the previous semiclassical approaches is the dominant scattering mechanism at sufficient high magnetic field. The implications for experiments are discussed.     

On the Chirality Quantum Phase Transition of the Dirac Oscillator

Dirac oscillator subjects to an external magnetic field is re-examined. We show that this model can be mapped onto different quantum optics models if one insists to introduce two kinds of phonons which associate with the excitations of Dirac oscillator and magnetic field respectively. The conclusion about chirality quantum phase transition in the paper “Chirality quantum phase transition in the Dirac oscillator” (Bermudez et al. Phys. Rev. A, 77, 063815 2008) is only valid for a specific mapped quantum optics models rather than the Dirac oscillator itself. Thus, the conclusions about chirality quantum phase transitions in this paper are not universal.     

Contact conductance between graphene and quantum wires

The contact conductance between graphene and two quantum wires which serve as the leads to connect graphene and electron reservoirs is theoretically studied. Our investigation indicates that the contact conductance depends sensitively on the graphene-lead coupling configuration. When each quantum wire couples solely to one carbon atom, the contact conductance vanishes at the Dirac point if the two carbon atoms coupling to the two leads belong to the same sublattice of graphene. We find that such a feature arises from the chirality of the Dirac electron in graphene. Such a chirality associated with conductance zero disappears when a quantum wire couples to multiple carbon atoms. The general result irrelevant to the coupling configuration is that the contact conductance decays rapidly with the increase of the distance between the two leads. In addition, in the weak graphene-lead coupling limit, when the distance between the two leads is much larger than the size of the graphene-lead contact areas and the incident electron energy is close to the Dirac point, the contact conductance is proportional to the square of the product of the two graphene-lead contact areas, and inversely proportional to the square of the distance between the two leads.     

Spinor analysis of Yang-Mills theory in the Minkowski space

Self-duality equations for Yang-Mills fields and the Dirac equation with an external (anti-) selfdual gauge field are studied in the Minkowski space by spinorial methods. For the Dirac equations, all (four) possible combinations of the fermion chirality and duality of the external fields are considered.     

Magnetic and quasiparticle excitation spectra of an itinerant J1-J2 model for iron-pnictide superconductors

We calculate the magnetic and quasiparticle excitation spectra of an itinerant J(1)-J(2) model for iron-pnictide superconductors. In addition to an acoustic spin-wave branch, the magnetic spectrum has a second, optical branch, resulting from the coupled four-sublattice magnetic structure. The spin-wave velocity has also a planar directional anisotropy, due to the collinear or striped antiferromagnetism. Within the magnetically ordered phase, the quasiparticle spectrum is composed of two Dirac cones, resulting from the folding of the magnetic Brillouin zone. We discuss the relevance of our findings to the understanding of both neutron scattering and photoemission spectroscopy results for SrFe(2)As(2).     

Maximal symmetry and mass generation of Dirac fermions and gravitational gauge field theory in six-dimensional spacetime

The relativistic Dirac equation in four-dimensional spacetime reveals a coherent relation between the dimensions of spacetime and the degrees of freedom of fermionic spinors. A massless Dirac fermion generates new symmetries corresponding to chirality spin and charge spin as well as conformal scaling transformations. With the introduction of intrinsic W-parity, a massless Dirac fermion can be treated as a Majorana-type or Weyl-type spinor in a six-dimensional spacetime that reflects the intrinsic quantum numbers of chirality spin. A generalized Dirac equation is obtained in the six-dimensional spacetime with a maximal symmetry. Based on the framework of gravitational quantum field theory proposed in Ref. [1] with the postulate of gauge invariance and coordinate independence, we arrive at a maximally symmetric gravitational gauge field theory for the massless Dirac fermion in six-dimensional spacetime. Such a theory is governed by the local spin gauge symmetry SP(1,5) and the global Poincar′e symmetry P(1,5)= SO(1,5) P~(1,5) as well as the charge spin gauge symmetry SU(2). The theory leads to the prediction of doubly electrically charged bosons. A scalar field and conformal scaling gauge field are introduced to maintain both global and local conformal scaling symmetries. A generalized gravitational Dirac equation for the massless Dirac fermion is derived in the six-dimensional spacetime. The equations of motion for gauge fields are obtained with conserved currents in the presence of gravitational effects. The dynamics of the gauge-type gravifield as a Goldstone-like boson is shown to be governed by a conserved energy-momentum tensor, and its symmetric part provides a generalized Einstein equation of gravity. An alternative geometrical symmetry breaking mechanism for the mass generation of Dirac fermions is demonstrated.     

The tunneling density-of-states of interacting massless Dirac fermions

We calculate the tunneling density-of-states (DOS) of a disorder-free two-dimensional interacting electron system with a massless-Dirac band Hamiltonian. The DOS exhibits two main features: (i) linear growth at large energies with a slope that is suppressed by quasiparticle velocity enhancement, and (ii) a rich structure of plasmaron peaks which appear at negative bias voltages in an n-doped sample and at positive bias voltages in a p-doped sample. We predict that the DOS at the Dirac point is non-zero even in the absence of disorder because of electron–electron interactions, and that it is then accurately proportional to the Fermi energy. The finite background DOS observed at the Dirac point of graphene sheets and topological insulator surfaces can therefore be an interaction effect rather than a disorder effect.     

Mass, energy, and the electron

The two-component solutions of the Dirac equation currently in use are not separately a particle equation or an antiparticle equation. We present a unitary transformation that uncouples the four-component, force-free Dirac equation to yield a two-component spinor equation for the force-free motion of a relativistic particle and a corresponding two-component, time-reversed equation for an antiparticle. The particle-antiparticle nature of the two equations is established by applying to the solutions of these two-component equations criteria analogous to those applied for establishing the four-component particle and antiparticle solutions of the four-component Dirac equation. Wave function solutions of our two-component particle equation describe both a right and a left circularly polarized particle. Interesting characteristics of our solutions include spatial distributions that are confined in extent along directions perpendicular to the motion, without the artifice of wave packets, and an intrinsic chirality (handedness) that replaces the usual definition of chirality for particles without mass. Our solutions demonstrate that both the rest mass and the relativistic increase in mass with velocity of the force-free electron are due to an increase in the rate of Zitterbewegung with velocity. We extend this result to a bound electron, in which case the loss of energy due to binding is shown to decrease the rate of Zitterbewegung.     

Visualizing electronic chirality and Berry phases in graphene systems using photoemission with circularly polarized light

Electronic chirality near the Dirac point is a key property of graphene systems, which is revealed by the spectral intensity patterns as measured by angle-resolved photoemission spectroscopy under various polarization conditions. Specifically, the strongly modulated circular patterns for monolayer (bilayer) graphene rotate by ±90° (±45°) in changing from linearly to circularly polarized light; these angles are directly related to the phases of the wave functions and thus visually confirm the Berry's phase of π (2π) around the Dirac point. The details are verified by calculations.     

Level spacing statistics for two-dimensional massless Dirac billiards

Classical-quantum correspondence has been an intriguing issue ever since quantum theory was proposed. The searching for signatures of classically nonintegrable dynamics in quantum systems comprises the interesting field of quantum chaos. In this short review, we shall go over recent efforts of extending the understanding of quantum chaos to relativistic cases. We shall focus on the level spacing statistics for two-dimensional massless Dirac billiards, i.e., particles confined in a closed region. We shall discuss the works for both the particle described by the massless Dirac equation(or Weyl equation)and the quasiparticle from graphene. Although the equations are the same, the boundary conditions are typically different,rendering distinct level spacing statistics.     

Transition probabilities in 134Pr: a test for chirality in nuclear systems

Exited states in 134Pr were populated in the fusion-evaporation reaction 119Sn(19F,4n)134Pr. Recoil distance Doppler-shift and Doppler-shift attenuation measurements using the Euroball spectrometer, in conjunction with the inner Bismuth Germanate ball and the Cologne plunger, were performed at beam energies of 87 MeV and 83 MeV, respectively. Reduced transition probabilities in 134Pr are compared to the predictions of the two quasiparticle + triaxial rotor and interacting boson fermion-fermion models. The experimental results do not support the presence of static chirality in 134Pr underlying the importance of shape fluctuations. Only within a dynamical context the presence of intrinsic chirality in 134Pr can be supported.     

Zero mode solutions of quark Dirac equations in QCD as the sources of chirality violating condensates

It is demonstrated, that chirality violating condensates in massless QCD arise from zero mode solutions of Dirac equations in arbitrary gluon fields. Basing of this idea, the model is suggested, which allows one to calculate quark condensate magnetic susceptibilities in the external constant electromagnetic field.     

Optical self-energy in graphene due to correlations

In highly correlated systems one can define an optical self-energy in analogy to its quasiparticle (QP) self-energy counterpart. This quantity provides useful information on the nature of the excitations involved in inelastic scattering processes. Here we calculate the self-energy of the intraband optical transitions in graphene originating in the electron-electron interaction (EEI) as well as electron-phonon interaction (EPI). Although optics involves an average over all momenta (k) of the charge carriers, the structure in the optical self-energy is nevertheless found to mirror mainly that of the corresponding quasiparticles for k equal to or near the Fermi momentum k(F). Consequently, plasmaronic structures which are associated with momenta near the Dirac point at k = 0 are not important in the intraband optical response. While the structure of the electron-phonon interaction (EPI) reflects the sharp peaks of the phonon density of states, the excitation spectrum associated with the electron-electron interaction is in comparison structureless and flat and extends over an energy range which scales linearly with the value of the chemical potential. We introduce a method whereby detailed quantitative information on such excitation spectra can be extracted from optical data. Modulations seen on the edge of the interband optical conductivity as it rises towards its universal background value are traced to structure in the quasiparticle self-energies around k(F) of the lower Dirac cone associated with the occupied states.     

Irrational versus rational charge and statistics in two-dimensional quantum systems

We show that quasiparticle excitations with irrational charge and irrational exchange statistics exist in tight-binding systems described, in the continuum approximation, by the Dirac equation in (2+1)-dimensional space and time. These excitations can be deconfined at zero temperature, but when they are, the charge rerationalizes to the value 1/2 and the exchange statistics to that of "quartons" (half-semions).     

Robust transport properties in graphene

Two-dimensional Dirac fermions are used to discuss quasiparticles in graphene in the presence of impurity scattering. Transport properties are completely dominated by diffusion. This may explain why recent experiments did not find weak localization in graphene. The diffusion coefficient of the quasiparticles decreases strongly with increasing strength of disorder. Using the Kubo formalism, however, we find a robust minimal conductivity that is independent of disorder. This is a consequence of the fact that the change of the diffusion coefficient is fully compensated by a change of the number of delocalized quasiparticle states.