Spin quantum Hall effect and plateau transitions in multilayer network models

TL;DR

This paper investigates the spin quantum Hall effect and plateau transitions in multilayer network models, revealing that multiple layers exhibit independent transitions with properties similar to single-layer systems, even with weak coupling.

Contribution

It demonstrates that multilayer network models in class C have multiple independent plateau transitions, challenging previous assumptions for the unitary class.

Findings

Two separate plateau transitions in a two-layer model.

Transitions have the same critical properties as single-layer models.

Plateau transitions occur even with very weak interlayer coupling.

Abstract

We study the spin quantum Hall effect and transitions between Hall plateaus in quasi two-dimensional network models consisting of several coupled layers. Systems exhibiting the spin quantum Hall effect belong to class C in the symmetry classification for Anderson localisation, and for network models in this class there is an established mapping between the quantum problem and a classical one involving random walks. This mapping permits numerical studies of plateau transitions in much larger samples than for other symmetry classes, and we use it to examine localisation in systems consisting of $n$ weakly coupled layers. Standard scaling ideas lead one to expect $n$ distinct plateau transitions, but in the case of the unitary symmetry class this conclusion has been questioned. Focussing on a two-layer model, we demonstrate that there are two separate plateau transitions, with the same critical properties as in a single-layer model, even for very weak interlayer coupling.