Graphene, Dirac equation and analogue gravity

Abstract

We provide an updated study of some electronic properties of graphene nanoscrolls, exploiting a related curved space Dirac equation for the charge carriers. To this end, we consider an explicit parametrization in cylindrical coordinates, together with analytical solutions for the pseudoparticle modes living on the two–dimensional background. These results are then used to obtain a compact expression for the sample optical conductivity, deriving from a Kubo formula adapted to the 1+2 dimensional curved space. The latter formulation is then adopted to perform some simulations for a cylindrical nanoscroll geometry.

Massless Rarita-Schwinger equations: Half and three halves spin solution

“…The result ( 16), applied to three-dimensional Chern-Simons supergravity produces a spin-1 2 model of Dirac fermions coupled to the U(1) gauge field and the gravity background [23,28,29] that turns out to be suitable for the description of electrons in graphene-like materials [30][31][32][33][34][35][36][37][38][39][40][41][42][43].…”

Theoretical studies on optical properties of Beltrami-shaped curved graphene

“…Let us now focus on the longitudinal optical conductivity σ ii using the formalism provided in [40,43], where the real part of σ ii , being associated with absorption, is expressed as…”

“…As a framework for studying observable phenomena in the context of quantum field in curved spacetime, this approach has been the subject of intense studies concerning mostly the measurable effects related to the electronic structure of graphene [29,30,[38][39][40]. This underlines the importance of 2D Dirac materials and investigating their properties in condensed matter in connection with theoretical high energy physics [40][41][42][43].…”

so(2, 1) algebra, local Fermi velocity, and position-dependent mass Dirac equation

“…Study of Dirac equation has been of perennial interest in problems of relativistic and nonrelativistic quantum mechanics [1]. It has found numerous applications in many areas of physics including the ones that give physical understanding of the properties of charge carriers of graphene's electronic structure (see, for example, [2][3][4][5][6][7]).…”