Quantum-Hall physics and three dimensions

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 σ_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 σ_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 σ_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.

References in corpus (11)

• Nonlocal edge state transport in the quantum spin Hall state
• Quantum Hall effect in a bulk antiferromagnet EuMnBi${}_2$ with magnetically confined two-dimensional Dirac fermions
• Signatures of Electron Fractionalization in Ultraquantum Bismuth
• Fermi pockets and quantum oscillations of the Hall coefficient in high temperature superconductors
• Dimensional reduction, quantum Hall effect and layer parity in graphite films
• Bulk quantum Hall effect of spin-valley-coupled Dirac fermions in a polar antiferromagnet BaMnSb${}_2$
• Quantum anomalous Hall edge channels survive up to the Curie temperature
• Nuclear Magnetic Resonance in High Magnetic Field: Application to Condensed Matter Physics
• Thermodynamically Induced Transport Anomaly in Dilute Metals ZrTe${}_5$ and HfTe${}_5$
• Signatures of a magnetic-field-induced Lifshitz transition in the ultra-quantum limit of the topological semimetal ZrTe${}_5$
• Effect of uniaxial stress on the electronic band structure of NbP

Cited by in corpus (5)

• Theory of anomalous Hall effect in transition-metal pentatelluride ${\mathrm{ZrTe}}_5$ and ${\mathrm{HfTe}}_5$
• Quantum Hall effect and Landau levels without spatial long-range correlations
• Importance of the semimetallic state for the quantum Hall effect in HfTe${}_5$
• Spin-Triplet Excitonic Insulator in the Ultra-Quantum Limit of HfTe5
• Three-dimensional quantum Hall states as a chiral electromagnetic filter