Quantum anomalous Hall effect in magnetic topological insulators

TL;DR

This paper provides a comprehensive theoretical overview of the quantum anomalous Hall effect in magnetic topological insulators, detailing mechanisms, phase diagrams, and recent experimental observations in 2D and 3D systems.

Contribution

It offers a detailed theoretical framework and review of the QAH effect in magnetic topological insulators, including phase diagrams and recent experimental findings.

Findings

Magnetic order induces QAH effect in 2D topological insulators.

Chiral edge states predicted on magnetic domain walls in 3D.

Recent experiments confirm the QAH effect in magnetic topological insulators.

Abstract

The search for topologically non-trivial states of matter has become an important goal for condensed matter physics. Here, we give a theoretical introduction to the quantum anomalous Hall (QAH) effect based on magnetic topological insulators in two-dimension (2D) and three-dimension (3D). In 2D topological insulators, magnetic order breaks the symmetry between the counter-propagating helical edge states, and as a result, the quantum spin Hall effect can evolve into the QAH effect. In 3D, magnetic order opens up a gap for the topological surface states, and chiral edge state has been predicted to exist on the magnetic domain walls. We present the phase diagram in thin films of a magnetic topological insulator and review the basic mechanism of ferromagnetic order in magnetically doped topological insulators. We also review the recent experimental observation of the QAH effect. We discuss more recent theoretical work on the coexistence of the helical and chiral edge states, multi-channel chiral edge states, the theory of the plateau transition, and the thickness dependence in the QAH effect.