Graphene, Dirac equation and analogue gravity

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