In-gap impurity states as the hallmark of the Quantum Spin Hall phase

We study the different response to an impurity of the two topologically different phases shown by a two dimensional insulator with time reversal symmetry, namely, the Quantum Spin Hall and the normal phase. We consider the case of graphene as a toy model that features the two phases driven, respectively, by intrinsic spin-orbit coupling and inversion symmetry breaking. We find that strictly normalizable in-gap impurity states only occur in the Quantum Spin Hall phase and carry dissipationless current whose quirality is determined by the spin and pseudospin of the residing electron. Our results imply that topological order can be unveiled by local probes of defect states.