Ordered states in AB bilayer graphene in SU(4)-symmetric model

TL;DR

This paper uses an SU(4)-symmetric model to classify and analyze various ordered states in AB bilayer graphene, revealing extensive degeneracies and the influence of external factors on the ground state.

Contribution

It introduces a mean field approach to classify ordered states in AB bilayer graphene within an SU(4) symmetric framework, highlighting degeneracies and non-universality of ground states.

Findings

Identifies multiple possible ordered states including quantum Hall and density wave phases.

Shows extensive degeneracies in the SU(4)-symmetric model.

External perturbations can lift degeneracies and influence the ground state.

Abstract

We apply SU(4)-symmetric model to examine possible ordered states in AB stacked bilayer graphene (AB-BLG). The Hamiltonian of the system possesses this symmetry under certain assumptions. In such a model the multicomponent order parameter can be presented as a $4\times4$ matrix $\hat{Q}$. Using a mean field approximation, we derive a self-consistency equation for $\hat{Q}$. Among possible solutions of the obtained equation there are anomalous quantum Hall states, spin, charge, spin-valley density waves, inter-layer excitonic phases and their combinations. We argue that the proposed approach is a useful tool for classification of the ordered states in AB-BLG. The ordered states of the SU(4)-symmetric model demonstrate extensive degeneracies. The degeneracies can be removed by taking into account the neglected non-SU(4)-symmetric terms, disorder, substrate, as well as other perturbations. The ordered states have varying sensitivity to these factors. This suggests that, for AB-BLG, a ground state ordering type is a non-universal property, susceptible to particulars of extrinsic conditions.