Three-dimensional quantum anomalous Hall effect in Weyl semimetals

TL;DR

This paper introduces a three-dimensional quantum anomalous Hall effect in Weyl semimetals, revealing complex boundary states and tunable Hall resistance, expanding the understanding of topological phases and potential device applications.

Contribution

It extends the quantum anomalous Hall effect to three dimensions, demonstrating new boundary states and transport behaviors in Weyl semimetals.

Findings

Hosts two chiral surface states and a pair of chiral hinge states

Hall resistance quantizes to 0, ±h/e^2 depending on Fermi energy

Fermi energy tuning controls boundary state locations

Abstract

The quantum anomalous Hall effect (QAHE) is a quantum phenomenon in which a two-dimensional system exhibits a quantized Hall resistance $h/e^2$ in the absence of magnetic field, where $h$ is the Planck constant and $e$ is the electron charge. In this work, we extend this novel phase to three dimensions and thus propose a three-dimensional QAHE exhibiting richer and more versatile transport behaviors. We first confirm this three-dimensional QAHE through the quantized Chern number, then establish its bulk-boundary correspondence, and finally reaffirm it via the distinctive transport properties. Remarkably, we find that the three-dimensional QAHE hosts two chiral surface states along one spatial direction while a pair of chiral hinge states along another direction, and the location of the hinge states depends sensitively on the Fermi energy. These two types of boundary states are further connected through a perpendicular chiral surface states, whose chirality is also Fermi energy dependent. Consequently, depending on the transport direction, its Hall resistance can quantize to $0$, $h/e^2$, or $\pm h/e^2$ when the Fermi energy is tuned across the charge neutral point. This three-dimensional QAHE not only fill the gap in the Hall effect family but also holds significant potentials in device applications such as in-memory computing.