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Colloquium : Topological band theory
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First-principles band theory, properly augmented by topological considerations, has provided a remarkably successful framework for predicting new classes of topological materials. This Colloquium discusses the underpinnings of the topological band theory and its materials applications.
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“As mentioned above, a QAHI system is in principle similar to the integer quantum Hall system, but the former occurs without an external magnetic field and LLs (76,79) and thus carries great promise for possible applications in spintronics.”
From Transport of Topological Semimetals (2019) · cites this paper as [79]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
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“topological band theory (Hasan and Kane, 2010;Qi and Zhang, 2011;Bansil, Lin, and Das, 2016) directly applies to the Bloch bands associated with the effective Hamiltonian Ĥeff , i.e., the socalled “Floquet spectrum.””
From Topological photonics (2019) · cites this paper as Bansil, Lin, and Das, 2016
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“In this regard, ab initio calculations have proven extremely powerful in identifying real materials that exhibit not just these, but many topological phases (Bansil et al. , 2016).”
From Weyl and Dirac semimetals in three-dimensional solids (2018) · cites this paper as Bansil et al., 2016
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“Apparently, the magnetic field necessary to produce an integer quantum Hall system is no longer needed for a QSHI system (76,79), as the magnetic field is cancelled out when the time-reversal copies of integer quantum Hall systems are brought together.”
From Transport of Topological Semimetals (2019) · cites this paper as [79]
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Weyl and Dirac semimetals in three-dimensional solids
Armitage, N. P., Mele, E. J., & Vishwanath, A. (2018) · Reviews of Modern Physics · doi:10.1103/revmodphys.90.015001 · Cited by 4,528
“…the extensive contributions of ab initio techniques to the discovery of topological materials (including Weyl and Dirac states) were reviewed in Bansil et al., 2016; Weng et al., 2016a. Kharzeev, 2014 reviews connections of Weyl fermions in solid-state physics to the chiral anomaly in quantum…”
BackgroundOzawa, T., Price, H. M., Amo, A., Goldman, N., Hafezi, M., Lu, L., Rechtsman, M. C., Schuster, D., Simon, J., Zilberberg, O., et al. (2019) · Reviews of Modern Physics · doi:10.1103/revmodphys.91.015006 · Cited by 3,722
Baltz, V., Manchon, A., Tsoi, M., Moriyama, T., Ono, T., & Tserkovnyak, Y. (2018) · Reviews of Modern Physics · doi:10.1103/revmodphys.90.015005 · Cited by 2,792
Edge States and Topological Invariants of Non-Hermitian Systems
Yao, S., & Wang, Z. (2018) · Physical Review Letters · doi:10.1103/physrevlett.121.086803 · Cited by 2,250
Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
Kunst, F. K., Edvardsson, E., Budich, J. C., & Bergholtz, E. J. (2018) · Physical Review Letters · doi:10.1103/physrevlett.121.026808 · Cited by 1,376
Metadata
- Authors
- Bansil, A., Lin, H., & Das, T.
- Affiliations
- Northeastern University (US)
- Venue
- Reviews of Modern Physics
- Publisher
- American Physical Society (APS)
- Published
- 2016-06-29
- Volume
- 88
- Issue
- 2
- ISSN
- 0034-6861 (ISSN-L)
- 1539-0756
- OpenAlex
- W2293673104
- Cited by
- 1,587
- References
- 645
- Citations by year
- 2026: 111 · 2025: 152 · 2024: 190 · 2023: 161 · 2022: 164 · 2021: 194 · 2020: 222 · 2019: 145 · 2018: 140 · 2017: 89 · 2016: 17
- FWCI
- 61.63
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Reviews of Modern Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- arXiv (Cornell University) (public-domain)
- Funders
- U.S. Department of Energy (DE-FG02-07ER46352, DE-AC02-05CH11231, DE-SC0012575)
- National Research Foundation Singapore (NRF-NRFF2013-03)
- Topics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Topological Materials and Phenomena
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Advanced Condensed Matter Physics
- Physical Sciences › Materials Science › Materials Chemistry › 2D Materials and Applications
- Keywords
- topological band theory, topological materials, topological phases, band topology, topological insulators, topological semimetals
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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