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Anomalous edge states and the bulk-edge correspondence for periodically-driven two dimensional systems

Rudner, Mark S. and Lindner, Netanel H. and Berg, Erez and Levin, Michael (2013) Anomalous edge states and the bulk-edge correspondence for periodically-driven two dimensional systems. Physical Review X, 3 (3). Art. No. 031005. ISSN 2160-3308. http://resolver.caltech.edu/CaltechAUTHORS:20130607-134048462

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Abstract

Recently, several authors have investigated topological phenomena in periodically driven systems of noninteracting particles. These phenomena are identified through analogies between the Floquet spectra of driven systems and the band structures of static Hamiltonians. Intriguingly, these works have revealed phenomena that cannot be characterized by analogy to the topological classification framework for static systems. In particular, in driven systems in two dimensions (2D), robust chiral edge states can appear even though the Chern numbers of all the bulk Floquet bands are zero. Here, we elucidate the crucial distinctions between static and driven 2D systems, and construct a new topological invariant that yields the correct edge-state structure in the driven case. We provide formulations in both the time and frequency domains, which afford additional insight into the origins of the “anomalous” spectra that arise in driven systems. Possibilities for realizing these phenomena in solid-state and cold-atomic systems are discussed.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1212.3324arXivDiscussion Paper
http://dx.doi.org/10.1103/PhysRevX.3.031005 DOIArticle
http://journals.aps.org/prx/abstract/10.1103/PhysRevX.3.031005PublisherArticle
Additional Information:Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Received 14 January 2013; published 23 July 2013. We thank Gil Refael, Daniel Podolsky, and P. Zoller for helpful discussions. This work was supported by NSF Grants No. DMR-090647 and No. PHY-0646094 (M. R.), as well as Grants No. DMR-1103860 and No. DMR- 0705472 (E. B.). E. B. also acknowledges support from the ISF under Grant No. 7113640101. M. L. acknowledges support from the Alfred P. Sloan Foundation. N. L. acknowledges support by DARPA under Grant No. N66001-12-1-4034. N. L. and M. R. acknowledge support provided by the Institute for Quantum Information and Matter (IQIM), an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation.
Group:IQIM, Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
NSFDMR-0906475
NSFPHY-0646094
NSFDMR-1103860
NSFDMR-0705472
Israel Science Foundation (ISF)7113640101
Alfred P. Sloan FoundationUNSPECIFIED
Defense Advanced Research Projects Agency (DARPA)N66001-12-1-4034
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSF Physics Frontiers CenterUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Record Number:CaltechAUTHORS:20130607-134048462
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20130607-134048462
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38856
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:11 Jun 2013 18:19
Last Modified:09 Jan 2016 01:14

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