Lorentz violation and black-hole thermodynamics: Compton scattering process

A Lorentz-noninvariant modification of quantum electrodynamics (QED) is considered, which has photons described by the nonbirefringent sector of modified Maxwell theory and electrons described by the standard Dirac theory. These photons and electrons are taken to propagate and interact in a Schwarzschild spacetime background. For appropriate Lorentz-violating parameters, the photons have an effective horizon lying outside the Schwarzschild horizon. A particular type of Compton scattering event, taking place between these two horizons (in the photonic ergoregion) and ultimately decreasing the mass of the black hole, is found to have a nonzero probability. These events perhaps allow for a violation of the generalized second law of thermodynamics in the Lorentz-noninvariant theory considered.     

Dynamical mean field study of the Dirac liquid

Renormalization is one of the basic notions of condensed matter physics. Based on the concept of renormalization, the Landau’s Fermi liquid theory has been able to explain, why despite the presence of Coulomb interactions, the free electron theory works so well for simple metals with extended Fermi surface (FS). The recent synthesis of graphene has provided the condensed matter physicists with a low energy laboratory of Dirac fermions where instead of a FS, one has two Fermi points. Many exciting phenomena in graphene can be successfully interpreted in terms of free Dirac electrons. In this paper, employing dynamical mean field theory (DMFT), we show that an interacting Dirac sea is essentially an effective free Dirac theory. This observation suggests the notion of Dirac liquid as a fixed point of interacting 2 + 1 dimensional Dirac fermions. We find one more fixed point at strong interactions describing a Mott insulating state, and address the nature of semi-metal to insulator (SMIT) transition in this system.     

The complete proof of the virial theorem in the refined TFD theory for all electrons of an atom in a solid

The complete proof of the virial theorem in refined Thomas－Fermi－Dirac theory for all electrons of an atom in a solid is given.     

Physical interpretation of a modified Lorentz dielectric function for metals based on the Lorentz–Dirac force

It is proposed that a recently used ad hoc modified Lorentz dielectric function for metals can be physically interpreted via the Lorentz–Dirac force. The Lorentz–Dirac force considers the radiation reaction of electrons, an effect that is ignored in classical dispersion relationships. A suitable reduced order form of the Lorentz–Dirac force that does not suffer from pre-acceleration and runaway artifacts is employed in the derivation of the modified dispersion model. The frequency characteristics and the causality of the Lorentz–Dirac dielectric model are studied in detail. Furthermore, the superiority of the Lorentz–Dirac dielectric function as a means of improved fitting of experimental data is demonstrated for gold, silver, and silicon in the infrared and optical region.     

Quantum transport through 3D Dirac materials

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.     

Polarization correlations in electron-nucleus bremsstrahlung: the short-wavelength limit

The short-wavelength limit of the electron-nucleus bremsstrahlung is re-investigated with special emphasis on the polarization correlations between incoming electron and emitted photons. A theoretical analysis of these correlations is performed within both the rigorous relativistic Dirac theory and the Dirac-Sommerfeld-Maue (DSM) approach which approximates the initial electronic state by a Sommerfeld-Maue wavefunction. Based on detailed calculations carried out for bremsstrahlung of electrons scattered from medium- and high-Z bare ions, we argue that the DSM approach is complementary to the exact partial-wave theory at sufficiently high collision energies. For such high-relativistic domains predictions are made for the polarization correlations relating to linearly polarized radiation.     

Stability and instability of relativistic electrons in classical electromagnetic fields

The stability of matter composed of electrons and static nuclei is investigated for a relativistic dynamics for the electrons given by a suitably projected Dirac operator and with Coulomb interactions. In addition there is an arbitrary classical magnetic field of finite energy. Despite the previously known facts that ordinary nonrelativistic matter with magnetic fields, or relativistic matter without magnetic fields, is already unstable when a, the fine structure constant, is too large, it is noteworthy that the combination of the two is still stableprovided the projection onto the positive energy states of the Dirac operator, whichdefines the electron, is chosen properly. A good choice is to include the magnetic field in the definition. A bad choice, which always leads to instability, is the usual one in which the positive energy states are defined by the free Dirac operator. Both assertions are proved here. This paper is dedicated to Bernard Jancovici on the occasion of his 65th birthday.     

The Relativistic Dynamics of the Combined Particle–Field System in Renormalized Classical Electrodynamics

This paper develops a general theory for the nonlinear, renormalized interaction between charged particles and electromagnetic fields. For the combined “particle + field” system, a fundamental relativistically invariant dynamical equation is derived from first principles. This theory was first obtained in an alternative way by one of us (J.K.) in an earlier paper. Here, we prove that the initial-value problem for the “particle + field” system is well-posed. The existence and uniqueness result is based on a careful analysis of the singularites of the electromagnetic field along the trajectory of the moving charged particle. Furthermore, the Banach fixed-point principle is used. The theory improves the classical Dirac theory for the motion of electrons. In particular, it is shown how to deal with the Dirac paradox of runaway solutions. Received: 10 December 1997 / Accepted: 21 April 1998     

BCS Superconductivity of Dirac electrons in graphene layers

Possible superconductivity of electrons with the Dirac spectrum is analyzed using the BCS model. We calculate the critical temperature, the superconducting energy gap, and the supercurrent as functions of the doping level and of the pairing interaction strength. Zero doping is characterized by the existence of a quantum critical point such that the critical temperature vanishes below some finite value of the interaction strength. However, the critical temperature remains finite for any nonzero electron or hole doping level when the Fermi energy is shifted away from the Dirac point. As distinct from usual superconductors, the supercurrent density is not proportional to the number of electrons but is strongly decreased due to the presence of the Dirac point.     

Realization of Graphene Physics Through a Fully Optical System

The two-dimensional form of carbon known as graphene awaken the scientific community interest due to its exotic electronic properties, emerging from the behavior of electrons near the Fermi level as massless Dirac fermions in a (1+2)-dimensional “relativistic” space-time, which renders a bridge between condensed matter and relativistic quantum field theory. Optical systems are also prodigal in providing analogues of complex quantum mechanical systems. Here, it is proposed an optical realization capable of capturing the essential physics of the Dirac equation in (1+2)-D dimensions, simulating the properties of graphene through the use of lightwave technology.     

Manipulation of resonant tunneling by substrate-induced inhomogeneous energy band gaps in graphene with square superlattice potentials

We investigate the resonant transmission of Dirac electrons through inhomogeneous band gap graphene with square superlattice potentials by transfer matrix method. The effects of the incident angle of the electrons, Fermi energy and substrate-induced Dirac gaps on the transmission are considered. It is found that the Dirac gap of graphene adds another degree of freedom with respect to the incident angle, the Fermi energy and the parameters of periodic superlattice potentials (i.e., the number, width and height of the barriers) for the transmission. In particular, the inhomogeneous Dirac gap induced by staggered substrates can be used to manipulate the transmission. The properties of the conductance and Fano factor at the resonant peaks are found to be affected by the gaps significantly. The results may be helpful for the practical application of graphene-based electronic devices.     

Dynamic conductivity modified by impurity resonant states in doping three-dimensional Dirac semimetals

The impurity effect is studied in three-dimensional Dirac semimetals in the framework of a T-matrix method to consider the multiple scattering events of Dirac electrons off impurities. It has been found that a strong impurity potential can significantly restructure the energy dispersion and the density of states of Dirac electrons. An impurity-induced resonant state emerges and significantly modifies the pristine optical response. It is shown that the impurity state disturbs the common longitudinal optical conductivity by creating either an optical conductivity peak or double absorption jumps, depending on the relative position of the impurity band and the Fermi level. More importantly, these conductivity features appear in the forbidden region between the Drude and interband transition, completely or partially filling the Pauli block region of optical response. The underlying physics is that the appearance of resonance states as well as the broadening of the bands leads to a more complicated selection rule for the optical transitions, making it possible to excite new electron-hole pairs in the forbidden region. These features in optical conductivity provide valuable information to understand the impurity behaviors in 3D Dirac materials.     

Magnetic-like field inducing negative Dirac mass in graphene on hexagonal boron nitride

The tight-binding electrons in graphene grown on top of hexagonal boron nitride (h-BN) substrate are studied. The two types of surfaces on the h-BN substrate give rise to Dirac fermions having positive and negative masses. The positive and negative masses of the Dirac fermions lead to the gapped graphene to behave as a “pseudo” ferromagnet. A very large (pseudo) tunneling magnetoresistance is predicted when the Fermi level approaches the gap region. The energy gap due to the breaking of sublattice symmetry in graphene on h-BN substrate is analogous to magnetic-induced energy gap on surface of topological insulators. We point out that positive and negative masses may correspond to signs of magnetic-like field perpendicular to graphene sheet acting on pseudo magnetic dipole moment of electrons, leading to pseudo-Larmor precession and Stern–Gerlach magnetic force.     

Pauli’s Exclusion Principle in Spinor Coordinate Space

The Pauli exclusion principle is interpreted using a geometrical theory of electrons. Spin and spatial motion are described together in an eight dimensional spinor coordinate space. The field equation derives from the assumption of conformal waves. The Dirac wave function is a gradient of the scalar wave in spinor space. Electromagnetic and gravitational interactions are mediated by conformal transformations. An electron may be followed through a sequence of creation and annihilation processes. Two electrons are branches of a single particle. Each satisfies a Dirac equation, but together they are a solution of the curvature condition. As two so identified electrons approach each other, the exclusion principle develops from the boundary conditions in spinor space. The gradient motion does not allow the particles to overlap. Since the spinor-gradient of the scalar wave function is odd in the coordinates, the sign of the wave function must change at the electron-electron boundary. The exclusion principle becomes geometry intrinsic and all electrons are combined into one field. Further applications are proposed including the possibility of improved numerical calculations in atomic and molecular systems. There also may be extensions to nuclear or particle physics. Implications are expected for the properties of rotating objects in a gravitational field.     

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

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.     

Magnetic confinement of massless Dirac fermions in graphene

Because of Klein tunneling, electrostatic potentials are unable to confine Dirac electrons. We show that it is possible to confine massless Dirac fermions in a monolayer graphene sheet by inhomogeneous magnetic fields. This allows one to design mesoscopic structures in graphene by magnetic barriers, e.g., quantum dots or quantum point contacts.     

Bound states of Dirac fermions in monolayer gapped graphene in the presence of local perturbations

In graphene,conductance electrons behave as massless relativistic particles and obey an analogue of the Dirac equation in two dimensions with a chiral nature.For this reason,the bounding of electrons in graphene in the form of geometries of quantum dots is impossible.In gapless graphene,due to its unique electronic band structure,there is a minimal conductivity at Dirac points,that is,in the limit of zero doping.This creates a problem for using such a highly motivated new material in electronic devices.One of the ways to overcome this problem is the creation of a band gap in the graphene band structure,which is made by inversion symmetry breaking(symmetry of sublattices).We investigate the confined states of the massless Dirac fermions in an impured graphene by the short-range perturbations for "local chemical potential" and "local gap".The calculated energy spectrum exhibits quite different features with and without the perturbations.A characteristic equation for bound states(BSs) has been obtained.It is surprisingly found that the relation between the radial functions of sublattices wave functions,i.e.,f_m~+(r),g_m~+(r),and f_m~-(r),g_m~-(r),can be established by SO(2) group.     

An Orbital‐Free Quantum Hypernetted Chain Model Based Perturbation Theory for Equation of State of Hydrogen and Helium in Warm Dense Regime

We present in this work, a thermodynamic perturbation theory for equation of state of hydrogen and helium in the warm dense regime. The system is modeled as a mixture of classical point ions and quantum electrons. A perturbation series for Helmholtz free energy and correlation functions of the ions and electrons as a function of density and temperature is proposed. Combining the classical thermodynamic perturbation theory and the orbitial‐free quantum hyper‐netted chain theory, a systematic procedure to obtain the terms of the perturbation series is developed. The ion‐ion correlations are treated within the hyper‐netted chain approximation and the ion‐electron correlations are treated within the Thomas‐Fermi‐Dirac‐Weizsäcker approximation. The method has been applied to obtain isotherms of hydrogen and helium in the warm dense regime. The isotherms are compared with available ab‐initio data and the results are analyzed. A good agreement with ab‐initio data has been observed for pressures greater than one Mbar. Advantages and limitations of the present method are discussed along with possible future improvements. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Relativistic multiple scattering theory of electrons by ferromagnets

In view of investigating for 3d- and 4f-ferromagnetic crystals the elastic scattering and the emission of polarized low-energy electrons as well as the bulk electronic structure, a relativistic multiple scattering theory has been developed, in which the exchange interaction with the magnetic ground state electrons is treated in a local density functional approximation. In a layer-KKR-type approach, the Dirac equation, which contains an effective magnetic field term, is first solved for a single crystal atom and subsequently for a monoatomic layer and for a semi-infinite crystal. Spin-orbit coupling and magnetic exchange interaction are thus simultaneously taken into account.