Possible quantization and half-quantization in the anomalous Hall effect caused by in-plane magnetic field

Abstract

In this paper we propose that quantized and nearly half-quantized intrinsic anomalous Hall effect can be induced by in-plane external magnetic field through the Zeeman coupling in nonmagnetic two-dimensional (2D) systems with sizable spin-orbital coupling but without twofold rotational symmetry. An analytical result is derived for the 2D electron gas model with ${C}_{3v}$ symmetry. Further, based on the $\mathbit{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{p}$ Hamiltonian derived from first principle calculations, we find that the quantized and nearly half-quantized Hall conductance can be observed in ${\mathrm{Sb}}_{2}{\mathrm{Te}}_{3}$ thin film in the clean limit with strong in-plane magnetic field $B>20\phantom{\rule{4pt}{0ex}}\mathrm{T}$ and low temperature $T<100\phantom{\rule{4pt}{0ex}}\mathrm{mK}$.