Topological insulators in magnetic fields: Quantum Hall effect and edge channels with non-quantized \theta-term

TL;DR

This paper explores how magnetic fields create edge channels in topological insulators, revealing quantized Hall effects even when bulk properties are non-quantized, and discusses the resulting edge channel dynamics.

Contribution

It demonstrates that the Hall effect remains quantized via the heta-term changes despite broken time-reversal symmetry, and models the interplay of effects leading to quantum Hall transitions.

Findings

Hall effect remains quantized despite non-quantized heta-term

Orbital and Zeeman effects induce quantum Hall transitions

Edge channels form a network enabling new investigations

Abstract

We investigate how a magnetic field induces one-dimensional edge channels when the two-dimensional surface states of three-dimensional topological insulators become gapped. The Hall effect, measured by contacting those channels, remains quantized even in situations where the \theta-term in the bulk and the associated surface Hall conductivities, \sigma_{xy}^S, are not quantized due to the breaking of time-reversal symmetry. The quantization arises as the \theta-term changes by \pm 2 \pi n along a loop around n edge channels. Model calculations show how an interplay of orbital and Zeeman effects leads to quantum Hall transitions, where channels get redistributed along the edges of the crystal. The network of edges opens new possibilities to investigate the coupling of edge channels.