Z2 topological order and the quantum spin Hall effect -: art. no. 146802

The quantum spin Hall (QSH) phase is a time reversal invariant electronic state with a bulk electronic band gap that supports the transport of charge and spin in gapless edge states. We show that this phase is associated with a novel Z(2) topological invariant, which distinguishes it from an ordinary insulator. The Z(2) classification, which is defined for time reversal invariant Hamiltonians, is analogous to the Chern number classification of the quantum Hall effect. We establish the Z(2) order of the QSH phase in the two band model of graphene and propose a generalization of the formalism applicable to multiband and interacting systems.