Levitation of quantum Hall critical states in a lattice model with spatially correlated disorder

TL;DR

This paper investigates how quantum Hall critical states move and float in a lattice model with spatially correlated disorder, revealing both weak and strong levitation behaviors across Landau gaps and clarifying previous conflicting results.

Contribution

It demonstrates the levitation of quantum Hall critical states in a lattice model with correlated disorder and resolves discrepancies in prior studies by analyzing different disorder types and band mixing effects.

Findings

Weak levitation of critical states at low disorder

Strong levitation across Landau gaps at higher disorder

Behavior consistent across various disorder correlations

Abstract

The fate of the current carrying states of a quantum Hall system is considered in the situation when the disorder strength is increased and the transition from the quantum Hall liquid to the Hall insulator takes place. We investigate a two-dimensional lattice model with spatially correlated disorder potentials and calculate the density of states and the localization length either by using a recursive Green function method or by direct diagonalization in connection with the procedure of level statistics. From the knowledge of the energy and disorder dependence of the localization length and the density of states (DOS) of the corresponding Landau bands, the movement of the current carrying states in the disorder--energy and disorder--filling-factor plane can be traced by tuning the disorder strength. We show results for all sub-bands, particularly the traces of the Chern and anti-Chern states as well as the peak positions of the DOS. For small disorder strength $W$ we recover the well known weak levitation of the critical states, but we also reveal, for larger $W$, the strong levitation of these states across the Landau gaps without merging. We find the behavior to be similar for exponentially, Gaussian, and Lorentzian correlated disorder potentials. Our study resolves the discrepancies of previously published work in demonstrating the conflicting results to be only special cases of a general lattice model with spatially correlated disorder potentials. To test whether the mixing between consecutive Landau bands is the origin of the observed floating, we truncate the Hilbert space of our model Hamiltonian and calculate the behavior of the current carrying states under these restricted conditions.