Valley symmetry breaking in bilayer graphene: a test to the minimal model

TL;DR

This paper investigates valley symmetry breaking in biased bilayer graphene under magnetic fields, predicting anomalous quantum Hall steps and non-semiclassical de Haas-van Alphen effects that challenge minimal models.

Contribution

It introduces a self-consistent 4-band continuum model with Hartree correction to explain valley asymmetry effects in bilayer graphene.

Findings

Prediction of anomalous steps in Hall conductivity

Observation of non-semiclassical de Haas-van Alphen oscillations

Valley degeneracy lifting due to Landau level splitting

Abstract

Physical properties reflecting valley asymmetry of Landau levels in a biased bilayer graphene under magnetic field are discussed. Within the $4-$band continuum model with Hartree-corrected self-consistent gap and finite damping factor we predict the appearance of anomalous steps in quantized Hall conductivity due to the degeneracy lifting of Landau levels. Moreover, the valley symmetry breaking effect appears as a non-semiclassical de Haas-van Alphen effect where the reduction of the oscillation period to half cannot be accounted for through quasi-classical quantization of the orbits in reciprocal space, still valley degenerate.