Theory of broken symmetry quantum Hall states in the $N=1$ Landau level of Graphene

TL;DR

This paper investigates the many-body ground states in the $N=1$ Landau level of graphene, revealing new phases and differences from the $N=0$ level due to lattice-scale corrections to Coulomb interactions.

Contribution

It introduces a model including derivatives of delta interactions for the $N=1$ Landau level, uncovering novel phases and degeneracy lifting effects not seen in the $N=0$ level.

Findings

Degeneracy lifting of quantum Hall ferromagnets at quarter filling.

Discovery of a new phase combining Kekulé and antiferromagnetic characteristics.

Graphene at half-filling of $N=1$ level is in a competition between AF and CDW states.

Abstract

We study many-body ground states for the partial integer fillings of the $N=1$ Landau level in graphene, by constructing a model that accounts for the lattice scale corrections to the Coulomb interactions. Interestingly, in contrast to the $N=0$ Landau level, this model contains not only pure delta function interactions but also some of its derivatives. Due to this we find several important differences with respect to the $N=0$ Landau level. For example at quarter filling when only a single component is filled, there is a degeneracy lifting of the quantum hall ferromagnets and ground states with entangled spin and valley degrees of freedom can become favourable. Moreover at half-filling of the $N=1$ Landau level, we have found a new phase that is absent in the $N=0$ Landau level, that combines characteristics of the Kekul\'{e} state and an antiferromagnet. We also find that according to the parameters extracted in a recent experiment, at half-filling of the $N=1$ Landau level graphene is expected to be in a delicate competition between an AF and a CDW state, but we also discuss why the models for these recent experiments might be missing some important terms.