Topology, Delocalization via Average Symmetry and the Symplectic Anderson Transition
Open accessAbstract
A field theory of the Anderson transition in two-dimensional disordered systems with spin-orbit interactions and time-reversal symmetry is developed, in which the proliferation of vortexlike topological defects is essential for localization. The sign of vortex fugacity determines the Z(2) topological class of the localized phase. There are two distinct fixed points with the same critical exponents, corresponding to transitions from a metal to an insulator and a topological insulator, respectively. The critical conductivity and correlation length exponent of these transitions are computed in an N=1-[symbol: see text] expansion in the number of replicas, where for small [symbol: see text] the critical points are perturbatively connected to the Kosterlitz-Thouless critical point. Delocalized states, which arise at the surface of weak topological insulators and topological crystalline insulators, occur because vortex proliferation is forbidden due to the presence of symmetries that are violated by disorder, but are restored by disorder averaging.
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Weak disorders that preserve the crystalline symmetry on average should preserve the Dirac points and their topological surface states.
“Weak disorders that preserve the crystalline symmetry on average should preserve the DPs and their topological surface states.29,47”
From Type-II Dirac photons (2017) · cites this paper as [47]
The discussion of WTI and TCI surfaces (page not indexed) says that average translation or mirror symmetry prevents localization even under strong disorder, supporting the claim about robust surface states. It does not establish that disorder preserves the Dirac points themselves; its result concerns delocalization of surface states. (LLM, conf=0.85)
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Cited by
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Symmetry-protected topological photonic crystal in three dimensions
Lu, L., Fang, C., Fu, L., Johnson, S. G., Joannopoulos, J. D., & Soljačić, M. (2016) · Nature Physics · doi:10.1038/nphys3611 · Cited by 329 · see citing works
Self-citationTopological Mirror Superconductivity
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- Authors
- Fu, L., & Kane, C. L.
- Affiliations
- Massachusetts Institute of Technology (US)
- ORCID
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2012-12-14
- Volume
- 109
- Issue
- 24
- Pages
- 246605-246605
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2020542184
- Cited by
- 178
- References
- 3
- Citations by year
- 2026: 7 · 2025: 12 · 2024: 12 · 2023: 13 · 2022: 7 · 2021: 14 · 2020: 10 · 2019: 9 · 2018: 11 · 2017: 8 · 2016: 17 · 2015: 22 · 2014: 22 · 2013: 14
- FWCI
- 9.60
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- ScholarlyCommons (University of Pennsylvania) (submittedVersion)
- Scholarly Commons (University of Pennsylvania) (submittedVersion)
- DSpace@MIT (Massachusetts Institute of Technology) (submittedVersion, cc-by-nc)
- arXiv (Cornell University)
- Bulletin of the American Physical Society
- 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 › Atomic and Molecular Physics, and Optics › Quantum and electron transport phenomena
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Keywords
- Anderson transition, two-dimensional disordered systems, spin-orbit coupling, time-reversal symmetry, vortex proliferation, topological defects, metal-insulator transition, critical conductivity, correlation length exponent, Kosterlitz-Thouless transition, weak topological insulator, topological crystalline insulators, delocalization, disorder averaging
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