Coulomb interactions, Dirac sea polarization and $SU(4)$ symmetry breaking of the integer quantum Hall states of graphene

TL;DR

This paper explores how the filled Dirac sea influences $SU(4)$ symmetry breaking in graphene's quantum Hall states, revealing new phases and computing phase diagrams and excitation gaps, aligning with experimental data.

Contribution

It introduces a model including Coulomb, Hubbard, and nearest neighbor interactions to analyze Dirac sea effects on symmetry breaking and phase structure in graphene.

Findings

Dirac sea polarization induces new symmetry-broken phases.

Phase diagram mapped in $U$-$V$ interaction space.

Calculated excitation gaps match experimental observations.

Abstract

We investigate effects of the filled Dirac sea on the $SU(4)$ symmetry breaking in the integer quantum Hall states of graphene with long-ranged Coulomb interactions. Our model also includes Hubbard and nearest neighbour repulsive interactions with strengths $U$ and $V$ respectively. We find that the symmetry breaking of the $n=0$ Landau levels induces an $SU(4)$ polarization of the Dirac sea. This results in several phases which are absent when the effects of the Dirac sea are neglected. We compute the phase diagram in the $U$-$V$ space. We also calculate the excitation gaps in tilted magnetic fields for all the phases. We compare our model results with experiments and find a range of $U$ and $V$ that are consistent with them.