Abelian Chern-Simons Theory for the Fractional Quantum Hall Effect in Graphene

TL;DR

This paper develops a multicomponent abelian Chern-Simons theory for the fractional quantum Hall effect in graphene, providing real-time correlation functions and calculating Hall conductivities at finite temperature.

Contribution

It introduces a novel fermionic functional integral approach using Keldysh formalism for FQH in graphene, deriving an exact effective action and response tensors.

Findings

Derived Hall conductivities for various FQH states.

Obtained an exact effective action for Chern-Simons gauge fields.

Calculated real-time correlation functions at finite temperature.

Abstract

We develop a theory for the pseudorelativistic fractional quantum Hall effect in graphene, which is based on a multicomponent abelian Chern-Simons theory in the fermionic functional integral approach. Calculations are performed in the Keldysh formalism, directly giving access to real-time correlation functions at finite temperature. We obtain an exact effective action for the Chern-Simons gauge fields, which is expanded to second order in the gauge field fluctations around the mean-field solution. The one-loop fermionic polarization tensor as well as the electromagnetic response tensor in random phase approximation are derived, from which we obtain the Hall conductivities for various FQH states, lying symmetrically around charge neutrality.