Coulomb interaction and magnetic catalysis in the quantum Hall effect in graphene

TL;DR

This paper investigates how Coulomb interactions influence symmetry breaking and magnetic catalysis in the quantum Hall effect in graphene, explaining experimental observations through a low-energy Dirac quasiparticle model.

Contribution

It introduces a detailed analysis of Landau level mixing and Coulomb effects on gap parameters and Fermi velocity, providing a theoretical framework matching experimental quantum Hall data.

Findings

Coulomb interaction causes gap parameters to decrease with higher Landau levels.

The model reproduces the observed quantum Hall plateaus in graphene.

Fermi velocity renormalization varies with Landau level index.

Abstract

The dynamics of symmetry breaking responsible for lifting the degeneracy of the Landau levels in the integer quantum Hall effect in graphene is studied in a low-energy model with the Coulomb interaction. The gap equation for Dirac quasiparticles is analyzed for both the lowest and higher Landau levels, taking into account the Landau levels mixing. It is shown that the characteristic feature of the long-range Coulomb interaction is the decrease of the gap parameters with increasing the Landau level index $n$ ("running" gaps). The renormalization (running) of the Fermi velocity as a function of $n$ is also studied. The solutions of the gap equation reproduce correctly the experimentally observed integer quantum Hall plateaus in graphene in strong magnetic fields.