2D massless QED Hall half-integer conductivity and graphene

TL;DR

This paper derives the half-integer quantum Hall effect in 2D massless QED, showing how graphene's Hall conductivity plateaus emerge from fundamental quantum field theory calculations in a magnetized medium.

Contribution

It provides a theoretical derivation of the half-integer quantum Hall effect in 2D massless QED using photon self-energy tensor analysis and compactification, connecting quantum field theory with graphene phenomena.

Findings

Half-integer quantum Hall conductivity derived in 2D massless QED.

Reproduction of graphene Hall conductivity plateaus.

Main features of QHE obtained in the static, zero-temperature limit.

Abstract

Starting from the photon self-energy tensor in a magnetized medium, the 3D complete antisymmetric form of the conductivity tensor is found in the static limit of a fermion system $C$ non-invariant under fermion-antifermion exchange. The massless relativistic 2D fermion limit in QED is derived by using the compactification along the dimension parallel to the magnetic field. In the static limit and at zero temperature the main features of quantum Hall effect (QHE) are obtained: the half-integer QHE and the minimum value proportional to $e^2/h$ for the Hall conductivity . For typical values of graphene the plateaus of the Hall conductivity are also reproduced.