Band structure and end states in InAs/GaSb core-shell-shell nanowires

Quantum wells in InAs/GaSb heterostructures can be tuned to a topological regime associated with the quantum spin Hall (QSH) effect, which arises due to an inverted bandgap and hybridized electron and hole states. We investigate electron-hole hybridization and the fate of the QSH effect in a quasi-1D geometry, realized in a core-shell-shell (CSS) nanowire with an insulator core and InAs,GaSb shells. We calculate the band structure using kp theory within the Kane model and the envelope function approximation, then map the result onto a BHZ model which is used to investigate finite-length wires. QSH edge states cannot appear in the CSS nanowires, but we find that the finite-length wires host localized states at the wire ends. These end states are not topologically protected, they are four-fold degenerate and split into two Kramers pairs in the presence of potential disorder along the axial direction. However, there is some remnant of the topological protection of the QSH edge states in the sense that the end states are fully robust to angular disorder, as long as the bulk bandgap is not closed.