Quantum Hall effect and Landau levels without spatial long-range correlations

TL;DR

This paper demonstrates that Landau levels and quantum Hall effects can exist in two-dimensional non-crystalline lattices without long-range spatial order, broadening the understanding of topological quantum phenomena beyond crystalline materials.

Contribution

It introduces a generalization of Landau levels and quantum Hall effects to disordered 2D systems lacking spatial long-range correlations.

Findings

Landau-like bands appear in non-crystalline 2D systems with short-range correlations.

Quantum Hall effects can occur without crystalline order.

Well-resolved Landau bands support topological quantum phenomena in disordered systems.

Abstract

The spectrum of charged particles in translation-invariant systems in a magnetic field is characterized by the Landau levels, which play a fundamental role in the thermodynamic and transport properties of solids. The topological nature and the approximate degeneracy of the Landau levels are known to also survive on crystalline lattices with discrete translation symmetry when the magnetic flux through a primitive cell is small compared to the flux quantum. Here we show that the notion of Landau levels and the quantum Hall effect can be generalized to 2d non-crystalline lattices without spatial long-range order. Remarkably, even when the spatial correlations decay over microscopic distances, 2d systems can exhibit a number of well-resolved Landau-like bands. The existence of these bands imply that non-crystalline systems in magnetic fields can support the hallmark quantum effects which have been typically associated with crystalline solids.