Correlated random hopping disorder in graphene at high magnetic fields: Landau level broadening and localization properties

TL;DR

This paper investigates how correlated long-range hopping disorder affects the density of states and localization in graphene's lowest Landau levels at high magnetic fields, revealing exponential narrowing of Landau level broadening with increased disorder correlation length.

Contribution

It provides new insights into the impact of correlated ripples-induced disorder on Landau level broadening and valley degeneracy breaking in graphene under high magnetic fields.

Findings

Landau level broadening shrinks exponentially with disorder correlation length.

Broadening increases linearly with magnetic field and disorder amplitude.

Robust splitting of the lowest Landau level peak due to valley degeneracy breaking.

Abstract

We study the density of states and localization properties of the lowest Landau levels of graphene at high magnetic fields. We focus on the effects caused by correlated long-range hopping disorder, which, in exfoliated graphene, is induced by static ripples. We find that the broadening of the lowest Landau level shrinks exponentially with increasing disorder correlation length. At the same time, the broadening grows linearly with magnetic field and with disorder amplitudes. The lowest Landau level peak shows a robust splitting, whose origin we identify as the breaking of the sublattice (valley) degeneracy.