Fractional Quantum Hall phases of graphene beyond ultra-short range intervalley-anisotropic interaction

TL;DR

This paper investigates how extending the range of valley-anisotropy interactions in monolayer graphene affects fractional quantum Hall phases, revealing new phases and phase transitions using a Yukawa interaction model.

Contribution

It introduces a Yukawa interaction model to study non-ultra-short range effects on quantum Hall phases in graphene, uncovering new phases and phase transition behaviors.

Findings

Dropping the USR condition shifts phase transition borders.

A new bond-ordered phase appears beyond USR.

The ferromagnetic phase splits into two competing states.

Abstract

Recent experimental and theoretical development in the Quantum Hall effect in monolayer graphene showed that the previous model of the valley-anisotropy interaction is incomplete, as it was assumed to be ultra-short range (USR). In this work, we use exact diagonalization to go beyond the ultra-short range to find the different phases for $\nu=2/3$. We model the interaction as Yukawa so that we can control the range as a proof of concept. Even in this simple setting, we discovered how dropping the USR condition shifts the transition borders in favour of certain phases, leads to a new bond-ordered phase appearing, and breaks the ferromagnetic phase in two competing states as a result of lifting the USR-driven degeneracy.