Topological Surface States in Three-Dimensional Magnetic Insulators
Open accessAbstract
An electron moving in a magnetically ordered background feels an effective magnetic field that can be both stronger and more rapidly varying than typical externally applied fields. One consequence is that insulating magnetic materials in three dimensions can have topologically nontrivial properties of the effective band structure. For the simplest case of two bands, these "Hopf insulators" are characterized by a topological invariant as in quantum Hall states and Z2 topological insulators, but instead of a Chern number or parity, the underlying invariant is the Hopf invariant that classifies maps from the three-sphere to the two-sphere. This Letter gives an efficient algorithm to compute whether a given magnetic band structure has nontrivial Hopf invariant, a double-exchange-like tight-binding model that realizes the nontrivial case, and a numerical study of the surface states of this model.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
A residual Z2 topological invariant remains in the QSH even when spin is not conserved, and the QSH can be considered adiabatically connected to the two-QH-layer model with n preserved mod 2.
“However, a residual Z 2 topological invariant remains, 9,29 and we can consider the QSH as being adiabatically connected to the two-QH-layer model, but with the topological invariant n only preserved mod2.”
From Antiferromagnetic topological insulators (2010) · cites this paper as [29]
In the rhombus geometry, the spin-orbit coupling from X to Y vanishes because the cross products d1×d2 from the two paths cancel.
“In this geometry this coupling vanishes as the cross products d 1 × d 2 from the two paths cancel.”
From Antiferromagnetic topological insulators (2010) · cites this paper as [29]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Quantum Spin Hall Insulator State in HgTe Quantum Wells
König, M., Wiedmann, S., Brüne, C., Roth, A., Buhmann, H., Molenkamp, L. W., Qi, X.-L., & Zhang, S.-C. (2007) · Science · doi:10.1126/science.1148047 · Cited by 6,151 · see citing works
Topological Insulators in Three Dimensions
Fu, L., Kane, C. L., & Mele, E. J. (2007) · Physical Review Letters · doi:10.1103/physrevlett.98.106803 · Cited by 4,651 · see citing works
A topological Dirac insulator in a quantum spin Hall phase
Hsieh, D., Qian, D., Wray, L., Xia, Y., Hor, Y. S., Cava, R. J., & Hasan, M. Z. (2008) · Nature · doi:10.1038/nature06843 · Cited by 3,523 · see citing works
Flagged first, then by citations
Research works printed but not linked: 1
- [17]S. Deser, R. Jackiw, and S. Templeton, Annals of Physics 140 , 372 (1982).
Cited by
Sorted by citations
Observation of a large-gap topological-insulator class with a single Dirac cone on the surface
Xia, Y., Qian, D., Hsieh, D., Wray, L., Pal, A., Lin, H., Bansil, A., Grauer, D., Hor, Y. S., Cava, R. J., et al. (2009) · Nature Physics · doi:10.1038/nphys1274 · Cited by 3,765 · see citing works
“The strong-topological-insulator phase contains surface states (SSs) with novel electromagnetic properties [7, 8, 9, 10, 11, 12, 13, 14, 15].”
BackgroundObservation of unidirectional backscattering-immune topological electromagnetic states
Wang, Z., Chong, Y., Joannopoulos, J. D., & Soljačić, M. (2009) · Nature · doi:10.1038/nature08293 · Cited by 3,123 · see citing works
Topological bands for ultracold atoms
Cooper, N. R., Dalibard, J., & Spielman, I. B. (2019) · Reviews of Modern Physics · doi:10.1103/revmodphys.91.015005 · Cited by 940 · see citing works
Antiferromagnetic topological insulators
Mong, R. S. K., Essin, A. M., & Moore, J. E. (2010) · Physical Review B · doi:10.1103/physrevb.81.245209 · Cited by 663 · see citing works
Self-citationExploring topological phases with quantum walks
Kitagawa, T., Rudner, M. S., Berg, E., & Demler, E. (2010) · Physical Review A · doi:10.1103/physreva.82.033429 · Cited by 534 · see citing works
- Authors
- Moore, J. E., Ran, Y., & Wen, X.-G.
- Affiliations
- Lawrence Berkeley National Laboratory (US)
- University of California, Berkeley (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2008-10-31
- Volume
- 101
- Issue
- 18
- Pages
- 186805-186805
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2086129240
- Cited by
- 186
- References
- 3
- Citations by year
- 2026: 7 · 2025: 13 · 2024: 21 · 2023: 17 · 2022: 16 · 2021: 15 · 2020: 11 · 2019: 10 · 2018: 13 · 2017: 13 · 2016: 7 · 2015: 8 · 2014: 5 · 2013: 3 · 2012: 7
- FWCI
- 3.87
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University)
- 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 › Magnetic properties of thin films
- Keywords
- topological surface states, magnetic insulators, Hopf invariant, effective magnetic field, double exchange model, tight-binding model, topological band structure, three-dimensional topological insulators, surface states
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 ›
Are you an author, or do you see a problem with this page? Request a review
