Z2Topological Order and the Quantum Spin Hall Effect

2005/06/27 by C. L. Kane, E. J. Mele, E. J. Melé · 21 citations
Materials Science · Mathematics · Physics and Astronomy · #Chern class #Combinatorics #Condensed matter physics #Gapless playback #Graphene research and applications #Invariant (physics) #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum #Quantum and electron transport phenomena #Quantum mechanics #Topological Materials and Phenomena #Topological insulator #Topological order #Topology (electrical circuits) #cond-mat.mes-hall

paper · pdf · doi:10.1103/physrevlett.95.146802

published as Phys. Rev. Lett. 95, 146802 (2005) · 4 pages RevTeX. Added reference, minor corrections

arxiv created 2005/06/27 · openalex publication_date 2005/09/28 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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 Z2 topological invariant, which distinguishes it from an ordinary insulator. The Z2 classification, which is defined for time reversal invariant Hamiltonians, is analogous to the Chern number classification of the quantum Hall effect. We establish the Z2 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.

Citations

• Homotopy and Quantization in Condensed Matter Physics
• SU(2)non-Abelian holonomy and dissipationless spin current in semiconductors
• Quantized Hall Conductance in a Two-Dimensional Periodic Potential
• Spin-Hall Insulator
• Dissipationless Quantum Spin Current at Room Temperature
• The Index of Elliptic Operators: V

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