Topological Insulator Superlattices

HgTe/CdTe and InAs/GaSb/AlSb superlattices both exhibit a topological insulator transition. In each case, there is an inversion of the s- and p-band ordering for layer thicknesses above a critical value. The resulting topological phase is a 2D bulk insulator at zero temperature, with edges that conduct massless carriers whose direction of motion is locked to their direction of spin. These 1D edge states exhibit essentially dissipationless transport over coherence lengths greater than one micron, with a quantized conductance of e(2)/h per edge. When a current passes, opposite spins are separated to the two sample edges, giving rise to the so-called quantum spin Hall effect. Effects such as these may be exploited in future low temperature spintronic devices. The edge states in HgTe/CdTe differ from those in InAs/GaSb/AlSb in several ways, due to the type II band alignment and weaker electron-hole hybridization of the III-V superlattice. The former exhibit a simple exponential decay over thousands of Angstroms, while the latter are more strongly confined to the edge, with an oscillating wave function whose period increases with the edge state momentum. In any calculation, the edge state dispersion and the nature of the wave-function depend strongly on the boundary conditions used. A k center dot p model is presented using standard boundary conditions for the wave function and its derivative, which yields spin polarized edge states with a finite amplitude at the sample edge. The interaction between states at opposite sample edges is also considered.