Stability of zero-mode Landau levels in bilayer graphene against disorder in the presence of the trigonal warping

TL;DR

This paper investigates how zero-energy Landau levels in bilayer graphene remain stable or become broadened under disorder, considering the effects of trigonal warping and topological protection.

Contribution

It demonstrates that certain Landau levels retain their sharpness due to topological chirality protection despite trigonal warping and disorder.

Findings

Two Landau levels remain sharp under disorder.

The other two Landau levels are broadened and split.

Topological chirality protects some Landau levels from disorder.

Abstract

The stability of the zero-energy Landau levels in bilayer graphene against the chiral symmetric disorder is examined in the presence of the trigonal warping. Based on the tight-binding lattice model with a bond disorder correlated over several lattice constants, it is shown that among the four Landau levels per spin and per valley, two Landau levels exhibit the anomalous sharpness as in the absence of the trigonal warping, while the other two are broadened, yielding split peaks in the density of states. This can be attributed to the fact that the total chirality in each valley is +2 or -2, which is protected topologically even in the presence of an intra-valley scattering due to disorder.