A toy model for quantum spin Hall effect

In this Communication, we investigate a toy model of three-dimensional topological insulator surface, coupled homogeneously to a fictitious pseudo spin-$\frac{1}{2}$ particle. We show that this toy model captures the interesting features of topological insulator surface states, which include topological quantum phase transition and quantum spin hall effect. We further incorporate an out-of-plane magnetic field and obtain the Landau levels.