Magnetoelectric coupling, Berry phase, and Landau level dispersion in a biased bilayer graphene

TL;DR

This paper investigates the energy spectrum of biased bilayer graphene under electric and magnetic fields, revealing nonmonotonic Landau level behavior, Berry phase effects, and valley-dependent pseudo-Zeeman shifts, with implications for electronic properties.

Contribution

It introduces a quasiclassical approach that incorporates pseudospin and Berry phase effects to explain Landau level behavior in biased bilayer graphene.

Findings

Landau levels show nonmonotonic dependence on electric field.

Berry phase causes shifts in energy quantization and pseudo-Zeeman effects.

Derived formulas for anomalous Hall conductivity and other pseudospin-related quantities.

Abstract

We study the energy spectrum of a graphene bilayer in the presence of transverse electric and magnetic fields. We find that the resulting Landau levels exhibit a nonmonotonic dependence on the electric field, as well as numerous level crossings. This behavior is explained using quasiclassical quantization rules that properly take into account the pseudospin of the quasiparticles. The pseudospin generates the Berry phase, which leads to a shift in energy quantization and results in a pseudo-Zeeman effect. The latter depends on the electric field, alternates in sign among the two valleys, and also reduces the band gap. Analytic formulas for other pseudospin-related quantities, such as the anomalous Hall conductivity, are derived and compared with prior theoretical work.