$Z_2$ Topological Order and the Quantum Spin Hall Effect

Details $Z_2$ Topological Order and the Quantum Spin Hall Effect $Z_2$ Topological Order and the Quantum Spin Hall Effect

2005-06-22

arxiv.org/abs/cond-mat/0506581v2

Phys. Rev. Lett. 95, 146802 (2005)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages RevTeX. Added reference, minor corrections

Scientific paper

10.1103/PhysRevLett.95.146802

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 multi band and interacting systems.

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