From many valleys to many topological phases - quantum anomalous Hall effect in IV-VI semiconductor quantum wells

TL;DR

This study predicts multiple topological phases with high Chern numbers in IV-VI semiconductor quantum wells, demonstrating their potential for realizing quantum anomalous Hall effects through detailed band structure and Chern number calculations.

Contribution

It introduces a basis transformation for multiband k·p Hamiltonians allowing analysis of wells in arbitrary orientations, predicting various quantum anomalous Hall phases with high Chern numbers.

Findings

Chern numbers range from 1 to 4 depending on parameters

Quantum wells grown along different crystallographic directions show distinct topological phases

Strain compensation is essential for quantized Hall conductance

Abstract

Consistent with prior qualitative expectations for group IV-VI topological crystalline insulators, this work demonstrates, based on band structure and Chern number calculations, that Pb$_{1-x}$Sn$_x$Se/(PbSe)$_{1-y}$(EuS)$_y$ quantum wells constitute a promising and viable platform for realizing a variety of quantum anomalous Hall phases. The proposed basis transformation procedure for the multiband $\mathit{k} \cdot \mathit{p}$ Hamiltonian enables the treatment of wells grown along arbitrary crystallographic directions while explicitly accounting for the anisotropy of the material's isoenergetic surfaces. Numerical studies of $\langle 111\rangle$-, $\langle 110\rangle$- and $\langle 001\rangle$-oriented quantum wells predict attainable Chern numbers with magnitudes ranging from $1$ to $4$, depending on the quantum well width, Sn content, and relative orientation of the four projected $\mathrm{L}$ valleys with respect to the growth direction. The results further indicate that appropriate strain compensation is required to achieve high-quality quantization of the Hall conductance.