Optical conductivity and transparency in an effective model for graphene

Horacio Falomir,Alfredo Raya,Enrique Muñoz,Marcelo Loewe

doi:10.1103/physrevb.98.195430

Abstract

Motivated by experiments confirming that the optical transparency of graphene is defined through the fine structure constant and that it could be fully explained within the relativistic Dirac fermions in 2D picture, in this article we investigate how this property is affected by next-to-nearest neighbor coupling in the low-energy continuum description of graphene. A detailed calculation within the linear response regime allows us to conclude that, somewhat surprisingly, the zero-frequency limit of the optical conductivity that determines the transparency remains robust up to this correction.

Highlights

Graphene is a two-dimensional allotrope of carbon, arranged as a honeycomb lattice with a C3v ⊗ Z2 symmetry [1] that determines its remarkable physical properties [2, 3, 4, 5]
We choose the contour time path (CTP) formalism to explicitly calculate the polarization tensor as a retarded correlator of the current operators, which provides the correct definition of the optical conductivity within linear response theory
We conclude that the optical conductivity, and the transparency in graphene are not affected by next-to-nearest neighbor contributions to the tight-binding microscopic model, that translate into a quadratic correction to the kinetic energy, as considered in this work

Summary

Introduction

Graphene is a two-dimensional allotrope of carbon, arranged as a honeycomb lattice with a C3v ⊗ Z2 symmetry [1] that determines its remarkable physical properties [2, 3, 4, 5]. These retarded correlators differ from the usual time-ordered ones that, by construction, are obtained via functional differentiation of the standard generating functional constructed form a path-integral formulation in quantum field theory. We choose the CTP formalism to explicitly calculate the polarization tensor as a retarded correlator of the current operators, which provides the correct definition of the optical conductivity within linear response theory. With these ideas in mind, we have organized the remaining of this article as follows: In Sect. We seek to calculate the polarization tensor, defined as a retarded current-current correlator that, in linear response, determines the optical conductivity.

The polarization tensor

Conclusions