Symmetry breaking by the sea of Dirac-Landau levels in graphene

TL;DR

This paper investigates how short-range interactions in graphene's Dirac-Landau levels lead to symmetry breaking, resulting in a valley-ordered antiferromagnetic phase consistent with recent experiments.

Contribution

It demonstrates that SU(4) symmetry breaking interactions induce a valley-ordered antiferromagnetic phase in graphene at specific filling factors using a mean field approach.

Findings

Valley symmetry broken, antiferromagnetic spin order at ν=±1

Consistency with recent experimental observations

Identification of the dominant interaction leading to symmetry breaking

Abstract

The quantum Hall states of graphene have a filled Dirac sea of Landau levels. The short ranged SU(4) symmetry breaking interactions can induce a staggered polarization of the sea of Dirac-Landau levels. We study this effect in the extended Hubbard model on a honeycomb lattice using mean field variational wavefunctions. We find a valley symmetry broken, anti-ferromagnetic spin ordered phase at $\nu=\pm 1$ when the on-site interaction is dominant. Our mean field solution is consistent with the recently reported experimental results of Z. Jiang et. al.\cite{jiang}