Quantum Spin Hall Effect
Open accessAbstract
The quantum Hall liquid is a novel state of matter with profound emergent properties such as fractional charge and statistics. The existence of the quantum Hall effect requires breaking of the time reversal symmetry caused by an external magnetic field. In this work, we predict a quantized spin Hall effect in the absence of any magnetic field, where the intrinsic spin Hall conductance is quantized in units of 2(e/4pi). The degenerate quantum Landau levels are created by the spin-orbit coupling in conventional semiconductors in the presence of a strain gradient. This new state of matter has many profound correlated properties described by a topological field theory.
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Kane and Mele showed that starting from the 2D time-reversal-invariant crystal, there are two topological classes; instead of an integer-valued topological invariant, there is a Z2 invariant with two values, even and odd.
“Kane and Mele showed that starting from the 2D T -invariant crystal, there are two topological classes; instead of an integer-valued topological invariant, there is a ' Z 2 invariant with two values, 'even' and 'odd'.”
From Three-Dimensional Topological Insulators (2011) · cites this paper as [64]
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Self-citation
- Authors
- Bernevig, B. A., & Zhang, S.-C.
- Affiliations
- Stanford University (US)
- ORCID
- Bernevig, B. Andrei
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2006-03-14
- Volume
- 96
- Issue
- 10
- Pages
- 106802-106802
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2136592254
- Cited by
- 2,164
- References
- 19
- Citations by year
- 2026: 73 · 2025: 126 · 2024: 147 · 2023: 119 · 2022: 133 · 2021: 138 · 2020: 180 · 2019: 124 · 2018: 98 · 2017: 126 · 2016: 111 · 2015: 121 · 2014: 130 · 2013: 124 · 2012: 112
- FWCI
- 26.32
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- University of North Texas Digital Library (University of North Texas) (submittedVersion)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation (0342832)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and electron transport phenomena
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Advanced Condensed Matter Physics
- Keywords
- quantum spin Hall effect, spin Hall conductance, time-reversal symmetry breaking, spin-orbit coupling, strain gradient, topological field theory, quantum Hall liquid, fractional statistics, semiconductors
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