Effects of orientation and strain on the topological characteristics of CdTe/ α -Sn quantum wells

It is known that compressive or tensile planar strain determines the band structure topology of the diamond cubic allotrope of tin ($\ensuremath{\alpha}$-Sn) to be either a Dirac semimetal (DSM) or topological insulator (TI), respectively. Using analytical techniques, we show that quantum confinement in negatively strained CdTe/$\ensuremath{\alpha}$-Sn quantum wells induces a phase transition from the DSM state to a quasi-three-dimensional TI as $\ensuremath{\alpha}$-Sn thickness is decreased. The critical thickness of the transition is found to depend strongly on the orientation of the CdTe, and magnitude of the epitaxial strain, which can be experimentally tuned. This result provides a new rationale for why $\ensuremath{\alpha}$-Sn has been observed in a three-dimensional (3D) TI state when pseudomorphically grown on zincblende substrates possessing smaller lattice constants. Additional impacts of strain and orientation on the electronic properties and spin texture of $\ensuremath{\alpha}$-Sn are explored. In particular, we examine the impact of orientation on the critical length of the Bernevig-Hughes-Zhang transition from a 2D TI to trivial insulator, as well as on the Rashba spin orbit coupling effects of an external electric field.