Effect of opposite-spin coupling on the edge states of two-dimensional topological insulator

The Bernevig-Hughes-Zhang model for a two-dimensional topological insulator, insulator with conducting edges, is modified. In particular, we introduce a coupling between opposite spins that preserves the model’s time reversal invariance. We derive the wave function and the existence conditions for the edge states. With these conditions and tight-binding calculations, we show that that the edge states are robust when the coupling is weak and lesser than the material parameter characterizing the spin-orbit coupling.