Quantum-Hall physics and three dimensions

TL;DR

This paper reviews recent experimental advances in understanding the quantum Hall effect in three-dimensional materials, highlighting how 3D systems exhibit some quantum Hall phenomena previously thought unique to 2D systems.

Contribution

It provides a comprehensive summary of recent experimental findings that clarify the role of quantum Hall physics in three-dimensional materials.

Findings

Observation of plateau-like Hall conductivities in 3D materials

Finite longitudinal resistivity in 3D quantum Hall systems

Emergence of quantum Hall physics in 3D from recent experiments

Abstract

The discovery of the quantum Hall effect (QHE) in 1980 marked a turning point in condensed matter physics: given appropriate experimental conditions, the Hall conductivity {\sigma}_xy of a two-dimensional (2D) electron system is exactly quantized. But what happens to the QHE in three dimensions (3D)? Experiments over the past 40 years showed that some of the remarkable physics of the QHE, in particular plateau-like Hall conductivities {\sigma}_xy accompanied by minima in the longitudinal resistivity \r{ho}_xx, can also be found in 3D materials. However, since typically \r{ho}_xx remains finite and a quantitative relation between {\sigma}_xy and the conductance quantum e^2/h could not be established, the role of quantum Hall physics in 3D remains unsettled. Following a recent series of exciting experiments, the QHE in 3D has now returned to the centre stage. Here, we summarize the leap in understanding of 3D matter in magnetic fields emerging from these experiments.