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$Z_2$ Topological Order and the Quantum Spin Hall Effect

C. L. Kane·E. J. Mele
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Abstract

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 multi band and interacting systems.

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C. L. Kane, E. J. Mele. 2005-06-27. $Z_2$ Topological Order and the Quantum Spin Hall Effect. https://doi.org/10.1103/physrevlett.95.146802

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