Fractional quantum Hall effect in strained graphene: stability of Laughlin states in disordered (pseudo)magnetic fields

TL;DR

This paper investigates the stability of fractional quantum Hall states in strained graphene with pseudomagnetic disorder, showing that small fluctuations preserve the effect, while large fluxes can induce a phase transition destroying it.

Contribution

It provides an explicit Laughlin-like wave function for strained graphene and analyzes the stability of quantum Hall states under different pseudomagnetic disorder conditions.

Findings

Small pseudomagnetic flux fluctuations preserve quantum Hall states.

Large fluxes can cause a glass transition and destroy fractional quantum Hall effect.

The stability depends on the amplitude and nature of the pseudomagnetic disorder.

Abstract

We address the question of the stability of the (fractional) quantum Hall effect (QHE) in presence of pseudomagnetic disorder generated by mechanical deformations of a graphene sheet. Neglecting the potential disorder and taking into account only strain-induced random pseudomagnetic fields, it is possible to write down a Laughlin-like trial ground-state wave function explicitly. Exploiting the Laughlin plasma analogy, we demonstrate that in the case of fluctuating pseudomagnetic fluxes of relatively small amplitude both the integer and fractional quantum Hall effects are always stable upon the deformations. By contrast, in the case of bubble-induced pseudomagnetic fields in graphene on a substrate (a small number of large fluxes) the disorder can be strong enough to cause a glass transition in the corresponding classical Coulomb plasma, resulting in the destruction of fractional quantum Hall regime and in a quantum phase transition to a non-ergodic state of the lowest Landau level.