Nonlocal correlations of the local density of states in disordered quantum Hall systems

TL;DR

This paper theoretically investigates nonlocal correlations of the local density of states in disordered quantum Hall systems, revealing complex spatial and energy-dependent behaviors relevant to recent STM experiments.

Contribution

It introduces a theoretical framework for understanding nonlocal LDoS correlations in disordered quantum Hall systems, connecting quantum cyclotron rings with STM observations.

Findings

Peaks in LDoS-LDoS correlations occur when intertip distance matches sum of quantum Larmor radii.

Sharp positive correlations near Landau level energies.

Weak anticorrelations at other energies.

Abstract

Motivated by recent high-resolution scanning tunneling microscopy (STM) experiments in the quantum Hall regime both on massive two-dimensional electron gas and on graphene, we consider theoretically the disorder averaged nonlocal correlations of the local density of states (LDoS) for electrons moving in a smooth disordered potential in the presence of a high magnetic field. The intersection of two quantum cyclotron rings around the two different positions of the STM tip, correlated by the local disorder, provides peaks in the spatial dispersion of the LDoS-LDoS correlations when the intertip distance matches the sum of the two quantum Larmor radii. The energy dependence displays also complex behavior: for the local LDoS-LDoS average (i.e., at coinciding tip positions), sharp positive correlations are obtained for tip voltages near Landau level, and weak anticorrelations otherwise.