Quantized Hall conductance as a topological invariant
Abstract
Whenever the Fermi level lies in a gap (or mobility gap) the bulk Hall conductance can be expressed in a topologically invariant form showing the quantization explicitly. The new formulation generalizes the earlier result by Thouless, Kohmoto, Nightingale, and den Nijs to the situation where many-body interaction and substrate disorder are also present. When applying to the fractional quantized Hall effect, we draw the conclusion that there must be a symmetry breaking in the many-body ground state. The possibility of writing the fractionally quantized Hall conductance as a topological invariant is also discussed.
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An elegant way to generalize the topological invariant definition physically while keeping the same mathematical structure was developed by Niu, Thouless, and Wu.
“An elegant way to generalize the definition physically, while keeping the same mathematical structure, was developed by Niu, Thouless, and Wu (55).”
From Three-Dimensional Topological Insulators (2011) · cites this paper as [55]
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- Authors
- Niu, Q., Thouless, D. J., & Wu, Y.-S.
- Affiliations
- University of Washington (US)
- ORCID
- Niu, Qian
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 1985-03-15
- Volume
- 31
- Issue
- 6
- Pages
- 3372-3377
- ISSN
- 0163-1829 (ISSN-L)
- OpenAlex
- W2093699506
- Cited by
- 1,136
- References
- 27
- Citations by year
- 2026: 47 · 2025: 68 · 2024: 68 · 2023: 63 · 2022: 63 · 2021: 80 · 2020: 73 · 2019: 65 · 2018: 52 · 2017: 55 · 2016: 51 · 2015: 50 · 2014: 43 · 2013: 42 · 2012: 25
- FWCI
- 8.81
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical review. B, Condensed matter (publishedVersion)
- PubMed (publishedVersion)
- Funders
- National Science Foundation
- U.S. Department of Energy
- Royal Society
- Division of Materials Research
- 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
- Hall conductance quantization, topological invariants, fractional quantum Hall effect, mobility gap, many-body interactions, symmetry breaking, many-body ground state
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