Dynamics and phase diagram of the $\nu=0$ quantum Hall state in bilayer graphene

TL;DR

This paper analyzes the dynamics and phase diagram of the $ u=0$ quantum Hall state in bilayer graphene using the Baym-Kadanoff formalism, identifying two phases with nonzero energy gaps and their dependence on magnetic field and gate voltage imbalance.

Contribution

It introduces a detailed theoretical analysis of the $ u=0$ quantum Hall state in bilayer graphene, including phase diagram mapping and energy gap scaling, with comparison to experimental data.

Findings

Identifies ferromagnetic and layer asymmetric phases with nonzero energy gaps.

Shows energy gaps scale linearly with magnetic field, approximately 10 B[T]K.

Provides a phase diagram in the plane of gate voltage imbalance and magnetic field.

Abstract

Utilizing the Baym-Kadanoff formalism with the polarization function calculated in the random phase approximation, the dynamics of the $\nu=0$ quantum Hall state in bilayer graphene is analyzed. Two phases with nonzero energy gap, the ferromagnetic and layer asymmetric ones, are found. The phase diagram in the plane $(\tilde{\Delta}_0,B)$, where $\tilde{\Delta}_0$ is a top-bottom gates voltage imbalance, is described. It is shown that the energy gaps in these phases scale linearly, $\Delta E\sim 10 B[T]K, with magnetic field. The comparison of these results with recent experiments in bilayer graphene is presented.