The local density of states in the presence of impurity scattering in graphene at high magnetic field

TL;DR

This paper analyzes how impurity scattering affects the local density of states in graphene under high magnetic fields, revealing features related to Landau levels, wavefunction form, and disorder type.

Contribution

It provides a detailed Fourier analysis of LDOS in graphene with impurities at high magnetic fields, linking features to wavefunction chirality and disorder nature.

Findings

Pronounced features at Landau level energies in Fourier-transformed LDOS.

Regions of high intensity around the center and corners of the Brillouin zone.

The ratio of features depends on disorder type, indicating potential or hopping disorder.

Abstract

We study the Fourier transform of the local density of states (LDOS) in graphene in the presence of a single impurity at high magnetic field. We find that the most pronounced features occur for energies of the STM tip matching the Landau level energies. The Fourier transform of the LDOS shows regions of high intensity centered around the center and the corners of the Brillouin zone (BZ). The radial intensity dependence of these features is determined by the form of the wavefunctions of the electrons in the quantum Hall regime. Moreover, some of these regions break rotational symmetry, and their angular dependence is determined by the chirality of the graphene electrons. For the zeroth Landau level, the ratio between the features at the corners and center of the BZ depends on the nature of the disorder: it goes to zero for potential disorder, and is finite for hopping disorder. We believe that a comparison between our analysis and experiments will help understand the form of the quasiparticle wavefunction, as well as the nature of disorder in graphene.