On the mystery of the missing pie in graphene

TL;DR

This paper explores the electromagnetic current density in graphene using a pseudo-relativistic massless Dirac model, demonstrating how this theory explains the observed current density and quantum conductivity in the presence of a constant electric field.

Contribution

It provides a detailed analysis linking the Dirac field theory in 2+1 dimensions to measurable electrical properties of graphene under uniform electric fields.

Findings

The Dirac model reproduces the measured current density in graphene.

The model explains the minimum quantum conductivity observed.

The theory accounts for the effects of a constant homogeneous electric field.

Abstract

We investigate in some detail the structure of the electromagnetic current density for the pseudo-relativistic massless spinor effective model for graphene. It is shown that the pseudo-relativistic massless Dirac field theory in {\em 2+1} space-time dimensions and in the presence of a constant homogeneous electric field actually leads to the measured current density and to the minimum quantum conductivity.