Essin, Andrew M. and Gurarie, Victor (2015) Delocalization of boundary states in disordered topological insulators. Journal of Physics A: Mathematical and Theoretical, 48 (11). Art. No. 11FT01. ISSN 1751-8113. doi:10.1088/1751-8113/48/11/11FT01. https://resolver.caltech.edu/CaltechAUTHORS:20141027-092105733
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Abstract
We use the method of bulk-boundary correspondence of topological invariants to show that disordered topological insulators have at least one delocalized state at their boundary at zero energy. Those insulators which do not have chiral (sublattice) symmetry have in addition the whole band of delocalized states at their boundary, with the zero energy state lying in the middle of the band. This result was previously conjectured based on the anticipated properties of the supersymmetric (or replicated) sigma models with WZW-type terms, as well as verified in some cases using numerical simulations and a variety of other arguments. Here we derive this result generally, in arbitrary number of dimensions, and without relying on the description in the language of sigma models.
| Item Type: | Article | ||||||||||||
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| Additional Information: | © 2015 IOP Publishing Ltd. Received 17 October 2014, revised 28 January 2015, Accepted for publication 3 February 2015, Published 23 February 2015. The authors are grateful to P Ostrovsky for sharing insights concerning the boundaries of three-dimensional disordered topological insulators. This work was supported by the NSF grants DMR-1205303 and PHY-1211914 (VG), and by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation through Grant GBMF1250 (AE). | ||||||||||||
| Group: | Institute for Quantum Information and Matter | ||||||||||||
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| Subject Keywords: | topological insulators, quenched disorder, Anderson localization | ||||||||||||
| Issue or Number: | 11 | ||||||||||||
| Classification Code: | PACS: 11.30.Pb. MSC: 81Q60 | ||||||||||||
| DOI: | 10.1088/1751-8113/48/11/11FT01 | ||||||||||||
| Record Number: | CaltechAUTHORS:20141027-092105733 | ||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20141027-092105733 | ||||||||||||
| Official Citation: | Delocalization of boundary states in disordered topological insulators Andrew M Essin and Victor Gurarie 2015 J. Phys. A: Math. Theor. 48 11FT01 | ||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
| ID Code: | 50831 | ||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||
| Deposited By: | Tony Diaz | ||||||||||||
| Deposited On: | 27 Oct 2014 16:30 | ||||||||||||
| Last Modified: | 12 Jul 2022 19:45 |
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