Spurious and realistic solutions for the quantum spin Hall edge states in InAs/GaSb/AlSb quantum wells

Abstract

A solution of the 4 × 4 k · p Hamiltonian for the quantum spin Hall (QSH) edge states in ideal semiconductor topological insulator (TI) quantum wells (QWs) was recently demonstrated by the author using standard boundary conditions for the wave function and its derivative, in order to address unphysical behavior associated with open boundary conditions (Klipstein 2015 Phys. Rev. B 91 035310). For HgTe/CdTe QWs which have strong s-p hybridization, there are two non-degenerate solutions in each spin direction with a finite amplitude at the edge, one of which was shown to be spurious. For the case of weakly hybridized InAs/GaSb/AlSb QWs, the solutions near the zone center are degenerate, and the question is now settled of which solution is spurious. The physical solutions for the ideal QW are then used as the basis for a perturbation treatment of the edge state dispersions in realistic QWs, where interface, bulk and structural asymmetries are also present. Interactions are included with more remote states than considered previously, as required for a consistent treatment of the TI bulk states, where a large difference exists in the spin splittings of the conduction and valence band edges. The asymmetry perturbations induce only minor changes to the edge state dispersions, which no longer merge smoothly with the bulk band extrema.