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Topological defects and gapless modes in insulators and superconductors
Open accessAbstract
We develop a unified framework to classify topological defects in insulators and superconductors described by spatially modulated Bloch and Bogoliubov de Gennes Hamiltonians. We consider Hamiltonians $\mathcal{H}(\mathbf{k},\mathbf{r})$ that vary slowly with adiabatic parameters $\mathbf{r}$ surrounding the defect and belong to any of the ten symmetry classes defined by time-reversal symmetry and particle-hole symmetry. The topological classes for such defects are identified and explicit formulas for the topological invariants are presented. We introduce a generalization of the bulk-boundary correspondence that relates the topological classes to defect Hamiltonians to the presence of protected gapless modes at the defect. Many examples of line and point defects in three-dimensional systems will be discussed. These can host one dimensional chiral Dirac fermions, helical Dirac fermions, chiral Majorana fermions, and helical Majorana fermions, as well as zero-dimensional chiral and Majorana zero modes. This approach can also be used to classify temporal pumping cycles, such as the Thouless charge pump, as well as a fermion parity pump, which is related to the Ising non-Abelian statistics of defects that support Majorana zero modes.
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Cites
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Cited by
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
Weyl and Dirac semimetals in three-dimensional solids
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“Then, following (Teo and Kane, 2010), who considered space dependent band structures H(k, r) to account for topological defects, the space coordinates can be treated as ‘negative’ dimensions.”
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
Lu, L., Joannopoulos, J. D., & Soljačić, M. (2014) · Nature Photonics · doi:10.1038/nphoton.2014.248 · Cited by 3,655
Classification of topological quantum matter with symmetries
Chiu, C.-K., Teo, J. C. Y., Schnyder, A. P., & Ryu, S. (2016) · Reviews of Modern Physics · doi:10.1103/revmodphys.88.035005 · Cited by 2,736
Self-citation
Metadata
- Authors
- Teo, J. C. Y., & Kane, C. L.
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2010-09-22
- Volume
- 82
- Issue
- 11
- ISSN
- 1098-0121 (ISSN-L)
- 1550-235X
- OpenAlex
- W1992940474
- Cited by
- 798
- References
- 27
- FWCI
- 16.55
- Type
- journal article
- Language
- en
- Open access
- green
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