Related papers: Numerical quasi-conformal transformations for elec…
In this work we compare two fundamentally different approaches to the electronic transport in deformed graphene: a) the condensed matter approach in which current flow paths are obtained by applying the non-equilibrium Green's function…
In nearly compensated graphene, disorder-assisted electron-phonon scattering or "supercollisions" are responsible for both quasiparticle recombination and energy relaxation. Within the hydrodynamic approach, these processes contribute weak…
We present a diagrammatic approach to construct self-energy approximations within many-body perturbation theory with positive spectral properties. The method cures the problem of negative spectral functions which arises from a…
The electronic spectrum of sheets of graphite (plane honeycomb lattice) folded into regular polihedra is studied. A continuum limit valid for sufficiently large molecules and based on a tight binding approximation is derived. It is found…
We show how to approximate Dirac dynamics for electronic initial states by semi- and non-relativistic dynamics. To leading order, these are generated by the semi- and non-relativistic Pauli hamiltonian where the kinetic energy is related to…
Electron properties of graphene are described in terms of Dirac fermions. Here we thoroughly outline the elastic scattering theory for the two-dimensional massive Dirac fermions in the presence of an axially symmetric potential. While the…
Embedding materials in optical cavities has emerged as a strategy for tuning material properties. Accurate simulations of electrons in materials interacting with quantum photon fluctuations of a cavity are crucial for understanding and…
Application of secondary quantized self-consistent Dirac -- Hartree -- Fock approach to consider electronic properties of monolayer graphene with accounting of spin-polarized states allows to coherently explain experimental results on…
Diagrammatic perturbation theory is a powerful tool for the investigation of interacting many-body systems, the self-energy operator $\Sigma$ encoding all the variety of scattering processes. In the simplest scenario of correlated electrons…
An eikonal expansion is used to provide systematic corrections to the eikonal approximation through order $1/k^2$, where $k$ is the wave number. Electron wave functions are obtained for the Dirac equation with a Coulomb potential. They are…
A formalism is proposed to study the electronic and transport properties of graphene sheets with corrugations as the one recently synthesized. The formalism is based on coupling the Dirac equation that models the low energy electronic…
We discuss the two-center, time-dependent Dirac equation describing the dynamics of an electron during a peripheral, relativistic heavy-ion collision at extreme energies. We derive a factored form, which is exact in the high-energy limit,…
The wave equation describing the interaction of two electrons in graphene at arbitrary value of the Fermi energy $E_F$ is derived. For the solutions of this equation, we have found the explicit forms of the density and the current which…
We develop a tight-binding model description of semi-Dirac electronic spectra, with highly anisotropic dispersion around point Fermi surfaces, recently discovered in electronic structure calculations of VO$_2$/TiO$_2$ nano-heterostructures.…
Graphene quantum dots provide a platform for manipulating electron behaviors in two-dimensional (2D) Dirac materials. Most previous works were of the "forward" type in that the objective was to solve various confinement, transport and…
Electron fractionalization is intimately related to topology. In one-dimensional systems, fractionally charged states exist at domain walls between degenerate vacua. In two-dimensional systems, fractionalization exists in quantum Hall…
Despite extensive existing studies, a complete understanding of the role of disorder in affecting the physical properties of two-dimensional Dirac fermionic systems remains a standing challenge, largely due to obstacles encountered in…
The gap equation for Dirac quasiparticles in monolayer graphene in constant magnetic and pseudomagnetic fields, where the latter is due to strain, is studied in a low-energy effective model with contact interactions. Analyzing solutions of…
We explore the gapped graphene structure in the two-dimensional plane in the presence of the Rosen-Morse potential and an external uniform magnetic field. In order to describe the corresponding structure, we consider the propagation of…
Motivated by recent experimental observations of size quantization of electron energy levels in graphene quantum dots \cite{ponomarenko} we investigate the level statistics in the simplest tight-binding model for different dot shapes by…