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

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.