Eur. Phys. J. Plus (2019) 134: 202
https://doi.org/10.1140/epjp/i2019-12610-6

Regular Article

Graphene properties from curved space Dirac equation

¹ Politecnico di Torino, Dipartimento DISAT, corso Duca degli Abruzzi 24, 10129, Torino, Italy
² Istituto Nazionale di Fisica Nucleare (INFN) - Sezione di Torino, Torino, Italy

^* e-mail: antonio.gallerati@polito.it

Received: 23 October 2018
Accepted: 4 March 2019
Published online: 14 May 2019

Abstract

A mathematical formulation for particle states and electronic properties of a curved graphene sheet is provided, exploiting a massless Dirac spectrum description for charge carriers living in a curved bidimensional background. In particular, we study how the new description affects the characteristics of the sample, writing an appropriate conductivity Kubo formula for the modified background. Finally, we provide a theoretical analysis for the particular case of a cylindrical graphene sample.