Theory of integer quantum Hall effect in insulating bilayer graphene

TL;DR

This paper proposes a variational ground state model for insulating bilayer graphene under magnetic fields, explaining the behavior of quantum Hall states and their experimental observations with realistic interactions.

Contribution

It introduces a comprehensive variational approach to describe the quantum Hall effect in bilayer graphene, accounting for Zeeman coupling, exchange interactions, and remote hopping effects.

Findings

Activation gap shows quadratic to linear crossover with magnetic field.

Excellent agreement with recent experimental data.

Predicts additional Hall states at specific filling factors.

Abstract

A variational ground state for insulating bilayer graphene (BLG), subject to quantizing magnetic fields, is proposed. Due to the Zeeman coupling, the layer anti-ferromagnet (LAF) order parameter in fully gapped BLG gets projected onto the spin easy plane, and simultaneously a ferromagnet order, which can further be enhanced by exchange interaction, develops in the direction of the magnetic field. The activation gap for the $\nu=0$ Hall state then displays a crossover from quadratic to linear scaling with the magnetic field, as it gets stronger, and I obtain excellent agreement with a number of recent experiments with realistic strengths for the ferromagnetic interaction. A component of the LAF order, parallel to the external magnetic field, gives birth to additional incompressible Hall states at filling $\nu=\pm 2$, whereas the remote hopping in BLG yields $\nu=\pm 1$ Hall states. Evolution of the LAF order in tilted magnetic fields, scaling of the gap at $\nu=2$, the effect of external electric fields on various Hall plateaus, and different possible hierarchies of fractional quantum Hall states are highlighted.