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$Z_2$ Topological Order and the Quantum Spin Hall Effect
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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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Cited by 1 Pith paper
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A 1d lattice model for the boundary of the quantum spin-Hall insulator
A finite-dimensional 1d lattice model with a non-onsite symmetry action realizes the anomalous boundary of the 2d quantum spin-Hall insulator, including fractional domain-wall charge and Kramers parity switching under...
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