Quantum spin Hall effect in α-Sn/CdTe(001) quantum-well structures.

The electronic and topological properties of heterovalent and heterocrystalline a-Sn/CdTe(001) quantum wells (QWs) are studied in dependence on the thickness of α-Sn by means of ab initio calculations. We calculate the topological Z2 invariants of the respective bulk crystals, which identify α-Sn as strong three-dimensional (3D) topological insulators (TIs), whereas CdTe is a trivial insulator. We predict the existence of two-dimensional (2D) topological interface states between both materials and show that a topological phase transition from a trivial insulating phase into the quantum spin Hall (QSH) phase in the QW structures occurs at much higher thicknesses than in the HgTe case. The QSH effect is characterized by the localization, dispersion, and spin polarization of the topological interface states. We address the distinction of the 3D and 2D TI characters of the studied QW structures, which is inevitable for an understanding of the underlying quantum state of matter. The 3D TI nature is characterized by two-dimensional topological interface states, while the 2D phase exhibits one-dimensional edge states. The two different state characteristics are often intermixed in the discussion of the topology of 2D QW structures, especially, the comparison of ab initio calculations and experimental transport studies. [ABSTRACT FROM AUTHOR]