Model Characterization of Gapless Edge Modes of Topological Insulators Using Intermediate Brillouin-Zone Functions
Open accessAbstract
We characterize gapless edge modes in translation invariant topological insulators. We show that the edge mode spectrum is a continuous deformation of the spectrum of a certain gluing function defining the occupied state bundle over the Brillouin zone. Topologically nontrivial gluing functions, corresponding to nontrivial bundles, then yield edge modes exhibiting spectral flow. We illustrate our results for the case of chiral edge states in two-dimensional Chern insulators, as well as helical edges in quantum spin Hall states.
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Unlike fermionic quantum systems with occupied Fermi seas, there is no Pauli principle for classical excitations in a circuit, and the band projector does not have a direct physical interpretation.
“But unlike fermionic quantum systems with occupied Fermi seas, there is no Pauli principle for classical excitations in a circuit (but see Ref. 29 for a demonstration of wavepacket pumping in optical systems), and the band projector does not have a direct physical interpretation.”
From Topolectrical-circuit realization of topological corner modes (2018) · cites this paper as [29]
The eigenvalues ν±(ky) of the Wilson-loop operator Wx(ky) are in one-to-one correspondence to the spectrum of an edge perpendicular to the x-coordinate (or perpendicular to y when x and y are interchanged).
“The eigenvalues ν ± ( k y ) of W x ( k y ) are in one-to-one correspondence to the spectrum of an edge perpendicular to the x -coordinate 27 (or perpendicular to y when x and y are interchanged).”
From Observation of a phononic quadrupole topological insulator (2018) · cites this paper as [27]
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Cited by
Sorted by citations
Benalcazar, W. A., Bernevig, B. A., & Hughes, T. L. (2017) · Physical Review B · doi:10.1103/physrevb.96.245115 · Cited by 1,389 · see citing works
Topolectrical-circuit realization of topological corner modes
Imhof, S., Berger, C., Bayer, F., Brehm, J., Molenkamp, L. W., Kiessling, T., Schindler, F., Lee, C. H., Greiter, M., Neupert, T., et al. (2018) · Nature Physics · doi:10.1038/s41567-018-0246-1 · Cited by 1,034 · see citing works
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 · see citing works
- Authors
- Fidkowski, L., Jackson, T. S., & Klich, I.
- Affiliations
- Microsoft (United States) (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2011-07-11
- Volume
- 107
- Issue
- 3
- Pages
- 036601-036601
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W1800177308
- Cited by
- 123
- References
- 24
- Citations by year
- 2026: 6 · 2025: 6 · 2024: 6 · 2023: 8 · 2022: 7 · 2021: 22 · 2020: 29 · 2019: 8 · 2018: 10 · 2017: 3 · 2016: 4 · 2015: 2 · 2014: 3 · 2013: 4 · 2012: 3
- FWCI
- 2.08
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation
- 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 insulators, gapless edge modes, spectral flow, chiral edge states, Chern insulator, helical edge states, quantum spin Hall effect, translationally invariant systems
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