Topological Invariants in Fermi Systems with Time-Reversal Invariance
Abstract
We discuss topological invariants for Fermi systems that have time-reversal invariance. The TK${\mathrm{N}}^{2}$ integers (first Chern numbers) are replaced by second Chern numbers, and Berry's phase becomes a unit quaternion, or equivalently an element of SU(2). The canonical example playing much the same role as spin \textonehalf{} in a magnetic field is spin \textonehalf{} in a quadrupole electric field. In particular, the associated bundles are nontrivial and have \ifmmode\pm\else\textpm\fi{} 1 second Chern number. The connection that governs the adiabatic evolution coincides with the symmetric SU(2) Yang-Mills instanton.
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The topological insulator in 3D can be related to the topological invariants in 4 dimensions that underlie the four-dimensional quantum Hall effect.
“Looking ahead, the topological insulator in 3D can be similarly related to the topological invariants in 4 dimensions (53) that underlie the 'four-dimensional quantum Hall effect' (54).”
From Three-Dimensional Topological Insulators (2011) · cites this paper as [53]
The second Chern number invariant of a 4D band structure underlies the four-dimensional quantum Hall effect.
“The second Chern number invariant of a 4D band structure (53) underlies the four-dimensional quantum Hall effect (54).”
From Three-Dimensional Topological Insulators (2011) · cites this paper as [53]
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Topological invariants of time-reversal-invariant band structures
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Murakami, S. (2007) · New Journal of Physics · doi:10.1088/1367-2630/9/9/356 · Cited by 1,176 · see citing works
Murakami, S., Nagaosa, N., & Zhang, S.-C. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.156804 · Cited by 346 · see citing works
Orbital magnetoelectric coupling in band insulators
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Self-citationMeasurement of Chern numbers through center-of-mass responses
Price, H. M., Zilberberg, O., Ozawa, T., Carusotto, I., & Goldman, N. (2016) · Physical Review B · doi:10.1103/physrevb.93.245113 · Cited by 86 · see citing works
- Authors
- Avron, J. E., Sadun, L., Segert, J., & Simon, B.
- Affiliations
- California Institute of Technology (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1988-09-19
- Volume
- 61
- Issue
- 12
- Pages
- 1329-1332
- ISSN
- 0031-9007 (ISSN-L)
- OpenAlex
- W1965292581
- Cited by
- 113
- References
- 13
- Citations by year
- 2026: 1 · 2025: 2 · 2024: 8 · 2023: 6 · 2022: 6 · 2021: 4 · 2020: 8 · 2019: 6 · 2018: 3 · 2017: 4 · 2016: 5 · 2015: 3 · 2014: 2 · 2013: 2 · 2012: 6
- FWCI
- 1.35
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- CaltechAUTHORS (California Institute of Technology) (submittedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Advanced Condensed Matter Physics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and electron transport phenomena
- Keywords
- topological invariants, Fermi systems, time-reversal invariance, second Chern number, Berry phase, associated bundles, Yang-Mills instantons, adiabatic evolution, topological phases
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