Electronic structure and wave functions of interface states in HgTe-CdTe quantum wells and superlattices

We report on extensive tight-binding calculations of electronic states in HgTe-CdTe heterojunctions, quantum wells, and superlattices. The method of solution is based on the Green's function and a powerful renormalization technique. While the band structures that we obtain are basically consistent with previous calculations by other authors with several different methods and parametrizations, we have made substantial progress in the detailed study of the corresponding wave functions and their atomic-orbital content. That allows a conclusive identification and analysis of the peculiar interface states that occur in these microstructures, and shows the crucial role played by the s-p mixing that derives from coupling of ${\mathrm{\Gamma }}_8$- and ${\mathrm{\Gamma }}_6$-like bands of the composing materials. In particular, the critical concentration ${\mathrm{x}}_{\mathrm{a}}$ at which the semimetal-semiconductor transition occurs in the ${\mathrm{Hg}}_{1\mathrm{-}\mathrm{x}}$${\mathrm{Cd}}_{\mathrm{x}}$Te simple alloy is shown to be related to a critical concentration ${\mathrm{x}}_{\mathrm{c}}$ occurring in (HgTe${)}_{\mathrm{m}}$(${\mathrm{Hg}}_{1\mathrm{-}\mathrm{x}}$${\mathrm{Cd}}_{\mathrm{x}}$Te${)}_{\mathrm{n}}$ superlattice alloys, at which interfacial states (anti)cross, with maximum s-p mixing. We also apply a modified (two- or n-step) Lanczos method to determine real and imaginary parts of all the components of the wave-function amplitude, to confirm or further investigate the complete nodal structure. Finally, we present some results regarding the question of large versus small valence-band offset for this type of interface.