Perspective: 3D quantum Hall effect

Abstract

The discovery of the quantum Hall effect in 2D systems opens the door to topological phases of matter. A quantum Hall effect in 3D is a long-sought phase of matter and has inspired many efforts and claims. In the perspective, we review our proposal that guarantees a 3D quantum Hall effect. The proposal employs the topologically-protected Fermi arcs and the "wormhole" tunneling via the Weyl nodes in a 3D topological semimetal. The 1D edge states in this 3D quantum Hall effect show an example of (d-2)-dimensional boundary states. Possible signatures of the 3D quantum Hall effect have been observed in the topological Dirac semimetals, but with many questions, which will attract more works to verify the mechanism and realize the 3D quantum Hall in the future.

An extended version based on a Perspective published on National Science Review

References in corpus (17)

• Berry Phase Effects on Electronic Properties
• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Weyl Semimetal in a Topological Insulator Multilayer
• Chern semi-metal and Quantized Anomalous Hall Effect in HgCr2Se4
• Quantum Hall effects in a Weyl Semi-Metal: possible application in pyrochlore Iridates
• Quantum Oscillations from Surface Fermi-Arcs in Weyl and Dirac Semi-Metals
• Three-dimensional quantum Hall effect and metal-insulator transition in ZrTe5
• 3D quantum Hall effect of Fermi arcs in topological semimetals
• Observation of the quantum Hall effect in confined films of the three-dimensional Dirac semimetal Cd3As2
• Quantum Hall states observed in thin films of Dirac semimetal Cd3As2
• Evolution of Weyl orbit and quantum Hall effect in Dirac semimetal Cd3As2
• Unexpected edge conduction in HgTe quantum wells under broken time reversal symmetry
• Atomic Scale Visualization of Quantum Interference on a Weyl Semimetal Surface by Scanning Tunneling Microscopy/Spectroscopy
• Hofstadter butterfly and integer quantum Hall effect in three dimensions
• Theory of the Three Dimensional Quantum Hall Effect in Graphite
• Quantum oscillations from generic surface Fermi arcs and bulk chiral modes in Weyl semimetals
• Three-Dimensional Quantum Anomalous Hall Effect in Ferromagnetic Insulators

Cited by in corpus (11)

• Colloquium: Quantum anomalous Hall effect
• Topological charge-entropy scaling in kagome Chern magnet TbMn${}_6$Sn${}_6$
• Theory for the Charge-Density-Wave Mechanism of 3D Quantum Hall Effect
• Field-Tunable One-Sided Higher-Order Topological Hinge States in Dirac Semimetals
• Quantum Transport in Topological Semimetals under Magnetic Fields (II)
• Three-dimensional quantum Hall effect and magnetothermoelectric properties in Weyl semimetals
• Quantum Hall effect originated from helical edge states in Cd${}_3$As${}_2$
• Two Types of 3D Quantum Hall Effects in Multilayer WTe${}_2$
• Fractional Quantum Hall Effect Based on Weyl Orbits
• Theoretical study for 3D quantum Hall effect in a periodic electron system
• Transitions from Composite Fermi Liquid to Moore-Read States in Weyl Semimetals