相关论文: Lorentz Covariance of Dirac Electrons in Solids: D…
A Dirac electron system in solids mimics a relativistic quantum physics that is compatible with Maxwell's equations, by which we anticipate unified electromagnetic responses. We find a large orbital diamagnetism only along the interplane…
Electrons in solids are characterized by the energy bands, which indicate that electrons are considered to be "elementary particles" with specific effective masses and g-factors reflecting features of each solid. There are cases where these…
Classical electromagnetism is linear. However, fields can polarize the vacuum Dirac sea, causing quantum nonlinear electromagnetic phenomena, e.g., scattering and splitting of photons, that occur only in very strong fields found in neutron…
We review the problem of electron-electron interactions in graphene. Starting from the screening of long range interactions in these systems, we discuss the existence of an emerging Dirac liquid of Lorentz invariant quasi-particles in the…
The Dirac equation for an electron in two spatial dimensions in the Coulomb and homogeneous magnetic fields is discussed. For weak magnetic fields, the approximate energy values are obtained by semiclassical method. In the case with strong…
Features of electronic currents in solids are truly diverse depending on circumstances, e.g. non-equilibrium transport currents leading to dissipation and persistent currents flowing in equilibrium. Differences between these currents may be…
A covariant relativistic formalism for the electron-photon and nuclear dynamics is summarised making more accurate predictions in agreement with experiments for Compton scattering in shells with large electron binding energy. An exact…
The Dirac equation with the Coulomb potential is studied. It is shown that there exists a new invariant in addition to the known Dirac and Johnson-Lippman ones. The solution of the Dirac equation, using the generalized invariant, and…
The Dirac equation is extended for a relativistic electron in an orthorhombically-anisotropic conduction band. Its covariance is established with general proper and improper Lorentz transformations. In the non-relativistic limit, the…
A Lorentz-covariant system of wave equations is formulated for a quantum-mechanical three-body system in one space dimension, comprised of one photon and two identical massive spin one-half Dirac particles, which can be thought of as two…
We analyze the equations of quantum electrodynamics and establish that the electron must be described by two bispinors that satisfy two mutually connected Dirac equations. The equations of the electronic and electromagnetic fields are…
In this article we present a detailed description of an electron in a uniform magnetic field evolving under the Schr\"odinger equation using ladder operators. Based on this analysis, we describe the same physical system using the Dirac…
The Dirac equation offers a precise analytical description of relativistic two-particle bound states, when one of the constituent is very heavy and radiative corrections are neglected. Looking at the high-Z hydrogen-like atom in the…
The relativistic Dirac equation covers the fundamentals of electronic phenomena in solids and as such it effectively describes the electronic states of the topological insulators like Bi$_2$Se$_3$ and Bi$_2$Te$_3$. Topological insulators…
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…
In this paper we discuss some aspects concerning the electromagnetic sector of the abelian Lee-Wick (LW) quantum electrodynamics (QED). Using the Dirac's theory of constrained systems, the higher-order canonical quantization of the LW…
In two-dimensional (2D) electron systems in a magnetic field, the Coulomb interaction among charge carriers, under Landau quantization, essentially governs a variety of many-body phenomena while there are also phenomena, such as the…
We study the Quantum Electrodynamics of 2D and 3D Dirac semimetals by means of a self-consistent resolution of the Schwinger-Dyson equations, aiming to obtain the respective phase diagrams in terms of the relative strength of the Coulomb…
We perform mean-field study of possible magnetic instabilities in Dirac semimetals. We find that Dirac electrons naturally host antiferromagnetic or spin density wave ground states, though their specific configurations may vary depending on…
The aim of this habilitation thesis is to present recent results, obtained during the period 2012-2017, related to interaction effects in condensed matter physics systems such as planar Dirac liquids, e.g., graphene and graphene-like…