Competing Laughlin state and Wigner crystal in bilayer graphene

TL;DR

This paper explores the competition between Laughlin states and Wigner crystals in bilayer graphene's fractional quantum Hall regime, showing that electric bias and magnetic field tuning can induce phase transitions.

Contribution

It demonstrates that electric bias and magnetic field tuning can switch the ground state between Laughlin and Wigner crystal phases in bilayer graphene.

Findings

Laughlin state is stable at ν=1/3 without bias.

Electric bias can induce a transition to a Wigner crystal at ν=1/3.

The ν=2/3 state remains stable and incompressible.

Abstract

We study the fractional quantum Hall effect in the central Landau level of bilayer graphene. By tuning the external applied magnetic field and the electric bias between the two layers one can access a regime where there is a degeneracy between Landau levels with orbital characters corresponding to N=0 and N=1 Galilean Landau levels. While the Laughlin state is generically the ground state for filling $\nu=1/3$ we find that it can be destroyed and replaced by a Wigner crystal at the same filling factor by tuning the bias and applied field. This competition does not take place at $\nu=2/3$ where the incompressible ground state remains stable. The possibility of electrically inducing the Wigner crystal state opens a new range of studies of this state of matter.