Theory of off-diagonal disorder in multilayer topological insulator

TL;DR

This paper investigates how off-diagonal disorder affects the electronic states, phase stability, and edge modes in multilayer topological insulators, revealing robustness in some phases and vulnerability in others.

Contribution

It introduces a detailed analysis of off-diagonal disorder effects in multilayer topological insulators, highlighting the disorder's impact on bulk states, phase transitions, and edge mode localization.

Findings

Weyl phase remains robust under strong disorder.

Anomalous quantum Hall phase survives only with weak fluctuations.

Disorder can delocalize edge states and affect conductance.

Abstract

We study multilayer topological insulators with random interlayer tunneling, known as off-diagonal disorder. Within the Burkov-Balents model a single Hermitian defect creates a bound state whose energy crosses the middle of the gap in the trivial phase but never in the topological phase; a non-Hermitian defect splits this level yet preserves the same crossing rule, so the effect serves as a local marker of topology. However, the key distinction persists: the bound state crosses zero in the trivial phase but not in the topological phase. Two complementary diagrammatic approaches give matching densities of states for the normal, topological, Weyl and anomalous quantum Hall regimes. Off diagonal disorder inserts bulk states into the gap and can close it: the Weyl phase remains robust under strong disorder, whereas the anomalous quantum Hall phase survives only for weak fluctuations, and the added bulk states shrink the Hall plateau, clarifying experimental deviations. Finally, we analyze edge modes. Uniform disorder shortens their localization length slightly, while Gaussian and Lorentzian disorder enlarge it and in the Gaussian case can even delocalize the edges. Although chirality is maintained, the enhanced overlap permits tunneling between opposite edges and pulls the longitudinal conductance away from its quantized value.