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Second-order topological insulators and superconductors with an order-two crystalline symmetry
Open accessAbstract
While topological insulators have a gapped bulk band structure, they have gapless surface states. Recently, it was shown that the presence of additional crystalline symmetries can lead to topological phases that combine a gapped bulk spectrum with gapless states on edges or corners of the crystal. Such topological phases have been called ``higher-order topological phases''. This article presents a complete classification of second-order topological insulators and superconductors with mirror, twofold-rotation, or inversion symmetry. The authors show that crystals with a mirror symmetry and a nontrivial bulk band structure either have gapless surfaces or gapless edges. On the other hand, there are crystals with twofold rotation or inversion symmetry with a nontrivial bulk topology but without surface or edge states.
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Cites
Topological insulators and superconductors
Qi, X.-L., & Zhang, S.-C. (2011) · Reviews of Modern Physics · doi:10.1103/revmodphys.83.1057 · Cited by 14,394
Quantized electric multipole insulators
Benalcazar, W. A., Bernevig, B. A., & Hughes, T. L. (2017) · Science · doi:10.1126/science.aah6442 · Cited by 2,029
Bradlyn, B., Elcoro, L., Cano, J., Vergniory, M. G., Wang, Z., Felser, C., Aroyo, M. I., & Bernevig, B. A. (2017) · Nature · doi:10.1038/nature23268 · Cited by 1,624
Observation of a phononic quadrupole topological insulator
Serra-Garcia, M., Peri, V., Süsstrunk, R., Bilal, O. R., Larsen, T., Villanueva, L. G., & Huber, S. D. (2018) · Nature · doi:10.1038/nature25156 · Cited by 982
Teo, J. C. Y., Fu, L., & Kane, C. L. (2008) · Physical Review B · doi:10.1103/physrevb.78.045426 · Cited by 761
Quantized response and topology of magnetic insulators with inversion symmetry
Turner, A. M., Zhang, Y., Mong, R. S. K., & Vishwanath, A. (2012) · Physical Review B · doi:10.1103/physrevb.85.165120 · Cited by 278
Cited by
Higher-order topology in bismuth
Schindler, F., Wang, Z., Vergniory, M. G., Cook, A. M., Murani, A., Sengupta, S., Kasumov, A. Y., Deblock, R., Jeon, S., Drozdov, I., et al. (2018) · Nature Physics · doi:10.1038/s41567-018-0224-7 · Cited by 837
Xie, B.-Y., Su, G.-X., Wang, H.-F., Su, H., Shen, X.-P., Zhan, P., Lu, M.-H., Wang, Z.-L., & Chen, Y.-F. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.233903 · Cited by 594
Higher-order topological insulators and superconductors protected by inversion symmetry
Khalaf, E. (2018) · Physical Review B · doi:10.1103/physrevb.97.205136 · Cited by 528
Higher-order topological states in photonic kagome crystals with long-range interactions
Li, M., Zhirihin, D., Gorlach, M., Ni, X., Filonov, D., Slobozhanyuk, A., Alù, A., & Khanikaev, A. B. (2020) · Nature Photonics · doi:10.1038/s41566-019-0561-9 · Cited by 448
Higher-Order Topological Corner States Induced by Gain and Loss
Luo, X.-W., & Zhang, C. (2019) · Physical Review Letters · doi:10.1103/physrevlett.123.073601 · Cited by 283
Metadata
- Authors
- Geier, M., Trifunovic, L., Hoskam, M., & Brouwer, P. W.
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2018-05-25
- Volume
- 97
- Issue
- 20
- ISSN
- 2469-9950 (ISSN-L)
- 2469-9969
- OpenAlex
- W2785766218
- Cited by
- 410
- References
- 6
- FWCI
- 23.84
- Type
- journal article
- Language
- en
- Open access
- bronze
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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