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Phys. Rev. Lett. 100, 186807 (2008) [4 pages]

Many-Body Generalization of the Z2 Topological Invariant for the Quantum Spin Hall Effect

Sung-Sik Lee1,2 and Shinsei Ryu1
1Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
2Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada

Received 26 October 2007; published 7 May 2008

We propose a many-body generalization of the Z2 topological invariant for the quantum spin Hall insulator, which does not rely on single-particle band structures. The invariant is derived as a topological obstruction that distinguishes topologically distinct many-body ground states on a torus. It is also expressed as a Wilson loop of the SU(2) Berry gauge field, which is quantized due to time-reversal symmetry.

©2008 The American Physical Society

URL: http://link.aps.org/doi/10.1103/PhysRevLett.100.186807
DOI: 10.1103/PhysRevLett.100.186807
PACS: 73.43.-f; 72.25.Hg; 85.75.-d
  • 73.43.-f
    Quantum Hall effects
  • 72.25.Hg
    Electrical injection of spin polarized carriers
  • 85.75.-d
    Magnetoelectronics; spintronics
  • YEAR: 2008

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