Landau levels and oscillator strength in a biased bilayer of graphene

TL;DR

This paper derives analytical expressions for Landau levels and oscillator strengths in biased graphene bilayers under magnetic fields, revealing how bias affects electronic transitions and their magnetic field dependence.

Contribution

It provides the first explicit analytical formulas for eigenstates and Landau levels in biased bilayer graphene, extending previous approximate models.

Findings

Landau level spectrum depends on interlayer coupling, bias, and magnetic field

Oscillator strengths and transition rules are explicitly calculated

Bias causes significant shifts in transition energies and magnetic field dependence

Abstract

We obtain analytical expressions for the eigenstates and the Landau level spectrum of biased graphene bilayers in a magnetic field. The calculations are performed in the context of a four-band continuum model and generalize previous approximate results. Solutions are presented for the spectrum as a function of interlayer coupling, the potential difference between the layers and the magnetic field. The explicit expressions allow us to calculate the oscillator strength and the selection rules for electric dipole transitions between the Landau states. Some transitions are significantly shifted in energy relative to those in an unbiased bialyer and exhibit a very different magnetic field dependence.