A Hartree-Fock study of the $\nu=0$ quantum Hall state of monolayer graphene with short range interactions

TL;DR

This paper models the $ u=0$ quantum Hall state in monolayer graphene using a Hartree-Fock approach, incorporating short-range interactions to explain experimentally observed phase transitions.

Contribution

It introduces a simple model with short-range interactions and a self-consistent Hartree-Fock analysis to support the observed phase transition in the $ u=0$ quantum Hall state.

Findings

Phase diagrams align with experimental data

Short-range interactions significantly affect the phase transition

Retaining negative energy Landau levels is crucial for accurate modeling

Abstract

Recent experiments involving tilted graphene samples have shown evidence of a continuous phase transition in the $\nu=0$ quantum Hall bulk state. We present here a simple model that supports such a transition. In addition to a long range SU(4) symmetric Coulomb interaction, we include Hubbard on-site and nearest neighbor interactions with tunable coupling strengths, and perform a self-consistent Hartree-Fock analysis. A large sea of negative energy Landau levels is retained, and is shown to have important qualitative and quantitative effects. Phase diagrams are constructed within the space of physically relevant parameters, yielding results consistent with experimental observation.