Topologically protected Landau levels in bilayer graphene in finite electric fields

TL;DR

This paper demonstrates that in bilayer graphene, the zero-energy Landau level remains sharply defined and robust against disorder even under finite electric fields, due to preserved chiral symmetry.

Contribution

It reveals the persistence of topologically protected Landau levels in bilayer graphene under finite electric fields, highlighting the role of chiral symmetry in their robustness.

Findings

Zero-energy Landau level remains sharp despite disorder.

Valley-split n=0 Landau levels stay anomalously sharp under electric fields.

n=1 Landau levels behave normally with disorder.

Abstract

The zero-energy Landau level of bilayer graphene is shown to be anomalously sharp (delta-function like) against bond disorder as long as the disorder is correlated over a few lattice constants.The robustness of the zero-mode anomaly can be attributed to the preserved chiral symmetry. Unexpectedly, even when we apply a finite potential difference (i.e., an electric field) between the top and the bottom layers, the valley-split $n=0$ Landau levels remain anomalously sharp although they are now shifted away from the zero energy, while the $n=1$ Landau levels exhibit the usual behavior.