Abstract
Both $\ensuremath{\alpha}\text{-Sn}$ and HgTe are expected to have similar topological properties because of their inverted band structure and zero-gap character. We investigate how the different crystal symmetries and the bonding to barrier materials act to the quantum phase transition versus the thickness of the corresponding quantum well (QW) structures. They are simulated by ${(\text{SnSn})}_{N}{(\text{CdTe})}_{M}$ and ${(\text{HgTe})}_{N}{(\text{CdTe})}_{M}(110)$ superlattices. Their electronic structures and eigenstates are studied by means of first-principles calculations using the modified Becke-Johnson exchange-correlation functional and spin-orbit interaction. Significant differences are observed for the two QW materials. A topological transition between trivial insulator and quantum spin Hall phase together with the formation of topologically protected edge states are observed in the case of HgTe QWs, while these features are considerably modified for $\ensuremath{\alpha}\text{-Sn}$. The different behaviors are discussed in the light of the different symmetry, spin-orbit interaction, and interface bonding. For a better understanding of the influence of the interface electrostatics also results for ${(\text{HgTe})}_{N}{(\text{InSb})}_{M}(110)$ systems are discussed.
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