Energy gaps at neutrality point in bilayer graphene in a magnetic field

TL;DR

This paper analyzes the energy gaps at the neutrality point in bilayer graphene under a magnetic field, identifying two phases with nonzero energy gaps and describing their phase diagram and scaling behavior.

Contribution

It introduces a theoretical analysis of the $ u=0$ quantum Hall state in bilayer graphene using the Baym-Kadanoff formalism and RPA polarization function, revealing two distinct gapped phases.

Findings

Two phases with nonzero energy gaps: ferromagnetic and layer asymmetric.

Energy gap scales linearly with magnetic field, approximately 14 K/T.

Phase diagram depends on 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 gap scales linearly, $\Delta E\sim 14 B[T]K, with magnetic field.