Surface quantized anomalous Hall current and magneto-electric effect in magnetically disordered topological insulators

TL;DR

This paper demonstrates that in magnetically disordered topological insulators, surface states become localized but exhibit a quantized transverse conductivity, enabling the realization of the topological magnetoelectric effect.

Contribution

It provides a theoretical analysis showing the persistence of quantized Hall conductance despite surface state localization due to magnetic disorder.

Findings

Surface states are localized by magnetic disorder.

Transverse conductivity remains quantized at ± e^2/2h.

Facilitates experimental realization of topological magnetoelectric effect.

Abstract

We study theoretically the role of quenched magnetic disorder at the surface of a topological insulator by numerical simulation and scaling analysis. It is found that all the surface states are localized while the transverse conductivity is quantized to be $\pm {{e^2} \over {2 h}}$ as long as the Fermi energy is within the bulk gap. This greatly facilitates the realization of the topological magnetoelectric effect proposed by Qi {\it et al.} (Phys. Rev. B\textbf{78}, 195424 (2008)) with the surface magnetization direction being controlled by the simultaneous application of magnetic and electric fields .