Transport of Dirac quasiparticles in graphene: Hall and optical conductivities

TL;DR

This paper derives analytical expressions for graphene's ac and dc conductivities under magnetic fields, revealing unusual behaviors linked to Dirac quasiparticles and explaining phenomena like the odd integer quantum Hall effect.

Contribution

It provides the first analytical formulas for graphene's Hall and optical conductivities considering Dirac quasiparticles in magnetic fields.

Findings

Unusual frequency and field dependence of conductivities

Explanation of the odd integer quantum Hall effect

Behavior of Hall angle and Nernst signal with excitonic gap

Abstract

The analytical expressions for both diagonal and off-diagonal ac and dc conductivities of graphene placed in an external magnetic field are derived. These conductivities exhibit rather unusual behavior as functions of frequency, chemical potential and applied field which is caused by the fact that the quasiparticle excitations in graphene are Dirac-like. One of the most striking effects observed in graphene is the odd integer quantum Hall effect. We argue that it is caused by the anomalous properties of the Dirac quasiparticles from the lowest Landau level. Other quantities such as Hall angle and Nernst signal also exhibit rather unusual behavior, in particular when there is an excitonic gap in the spectrum of the Dirac quasiparticle excitations.