3D quantum Hall effect

Hai-Zhou Lu

doi:10.1093/nsr/nwy082

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.

Highlights

The discovery of the quantum Hall effect in 2D systems opens the door to topological phases of matter
Klaus von Klitzing discovered that in strong magnetic fields the Hall resistance of a 2D electron gas can be quantized into a series of plateaus in terms of (h/e2)/n [1], where e is the elementary charge, h is Plancks constant, n is an integer known as Chern number
When the Fermi energy is placed between two Landau levels, each edge state contributes a Hall conductance of e2/h and vanishing longitudinal conductance in the Hallbar measurement

Summary

Introduction

The discovery of the quantum Hall effect in 2D systems opens the door to topological phases of matter. In a strong magnetic field, the energy spectrum of a 2D electron gas is quantized into Landau levels. The Landau levels deform at the sample edges and cross the Fermi energy, forming 1D edge states.

Results

Conclusion