Related papers: Dirac-Weyl equation on a hyperbolic graphene surfa…
Viscous phenomena are the hallmark of the hydrodynamic flow exhibited by Dirac fermions in clean graphene at high enough temperatures. We report a quantitative calculation of the electronic shear and Hall viscosities in graphene based on…
The Maxwell equations for the electromagnetic potential, supplemented by the Lorenz gauge condition, are decoupled and solved exactly in de Sitter space-time studied in static spherical coordinates. There is no source besides the…
A monolayer of graphene irradiated with circularly polarized light suggests a unique platform for surface electromagnetic wave (plasmon-polariton) manipulation. In fact, the time periodicity of the Hamiltonian leads to a geometric…
This is a short review of two-dimensional Dirac fermions in graphene and similar systems such as boron nitride, quasi-2D organic salts $\alpha$-(BEDT-TTF)$_2$I$_3$, artificial graphene with cold atoms in optical lattices, etc. The emphasis…
We investigate the quantum motion of a neutral Dirac particle bouncing on a mirror in curved spacetime. We consider different geometries: Rindler, Kasner-Taub and Schwarzschild, and show how to solve the Dirac equation by using geometrical…
The low energy excitations of graphene can be described by a massless Dirac equation in two spacial dimensions. Curved graphene is proposed to be described by coupling the Dirac equation to the corresponding curved space. This covariant…
The virial theorem for a system of interacting electrons in a crystal, which is described within the framework of the tight-binding model, is derived. We show that, in particular case of interacting massless electrons in graphene and other…
We study the effects of strain on the electronic properties and persistent current characteristics of a graphene ring using the Dirac representation. For a slightly deformed graphene ring flake, one obtains sizable pseudomagnetic (gauge)…
The computation of the optical conductivity of strained and deformed graphene is discussed within the framework of quantum field theory in curved spaces. The analytical solutions of the Dirac equation in an arbitrary static background…
The effects of a propagating sinusoidal out-of-plane flexural deformation in the electronic properties of a tense membrane of graphene are considered within a non-perturbative approach, leading to an electron-ripple coupling. The…
We consider the three-dimensional Dirac equation in spherical coordinates with coupling to static electromagnetic potential. The space components of the potential have angular (non-central) dependence such that the Dirac equation is…
Interest on 2 + 1 dimensional electron systems has increased considerably after the realization of novel properties of graphene sheets, in which the behaviour of electrons is effectively described by relativistic equations. Having this fact…
We transform the two-dimensional Dirac-Weyl equation, which governs the charge carriers in graphene, into a non-linear first-order differential equation for scattering phase shift, using the so-called variable phase method. This allows us…
The popularity of graphene--a pseudospin-1/2 two-dimensional Dirac-Weyl material--has prompted the search for related materials and the characterization of their properties. In this work, the magneto-optical conductivity is calculated for…
Many of graphene's unique electronic properties emerge from its Dirac-like electronic energy spectrum. Similarly, it is expected that a nanophotonic system featuring Dirac dispersion will open a path to a number of important research…
Graphene as a two-dimensional (2D) topological Dirac semimetal has attracted much attention for its outstanding properties and potential applications. However, three-dimensional (3D) topological semimetals for carbon materials are still…
We obtain exact solutions to the two-dimensional (2D) Dirac equation for the one-dimensional P\"oschl-Teller potential which contains an asymmetry term. The eigenfunctions are expressed in terms of Heun confluent functions, while the…
We show that the physics of deformation in $\alpha$-, $\beta$-, and $6,6,12$-graphyne is, despite their significantly more complex lattice structures, remarkably close to that of graphene, with inhomogeneously strained graphyne described at…
We obtain a class of adiabatic solutions of Dirac equation for the charged massless relativistic quasi-particles that arise from the low-energy excitations \cite{foot-1} in a 2D graphene sheet, interacting with an electromagnetic field. The…
The emergence of a flat band in Dirac-Weyl materials offers new possibilities for electronic transitions, leading to stronger interaction with light. As a result, the optical conductivity can be significantly enhanced in these flat-band…