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Topological Phases with Parafermions: Theory and Blueprints

Alicea, Jason and Fendley, Paul (2016) Topological Phases with Parafermions: Theory and Blueprints. Annual Review of Condensed Matter Physics, 7 . pp. 119-139. ISSN 1947-5454. http://resolver.caltech.edu/CaltechAUTHORS:20160328-101600140

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Abstract

We concisely review the recent evolution in the study of parafermions—exotic emergent excitations that generalize Majorana fermions and similarly underpin a host of novel phenomena. First we generalize the intimate connection between the Z_2-symmetric Ising quantum spin chain and Majorana fermions to Z_3-symmetric chains and parafermions. In particular, we highlight how parafermion chains host a topological phase featuring protected edge zero modes. We then tour several blueprints for the laboratory realization of parafermion zero modes—focusing on quantum Hall/superconductor hybrids, quantum Hall bilayers, and two-dimensional topological insulators—and describe striking experimental fingerprints that they provide. Finally, we discuss how coupled parafermion arrays in quantum Hall architectures yield topological phases that potentially furnish hardware for a universal, intrinsically decoherence-free quantum computer.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1146/annurev-conmatphys-031115-011336DOIArticle
http://www.annualreviews.org/doi/10.1146/annurev-conmatphys-031115-011336PublisherArticle
Additional Information:© 2016 Annual Reviews. We are indebted to D. Aasen, E. Berg, D. Clarke, A. Essin, M.P.A. Fisher, A. Jermyn, N. Lindner, R. Mong, D. Mross, C. Nayak, Y. Oreg, K. Shtengel, A. Stern, and M. Stoudenmire for collaborations related to this review, as well as to D. Clarke, M. Barkeshli, and S. Parameswaran for helpful comments on the manuscript. We also gratefully acknowledge support from the National Science Foundation through grant DMR-1341822 (J.A.); the Alfred P. Sloan Foundation (J.A.); the Caltech Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation through Grant GBMF1250; and the Walter Burke Institute for Theoretical Physics at Caltech. The authors are not aware of any affiliations, memberships, funding, or financial holdings that might be perceived as affecting the objectivity of this review
Group:IQIM, Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
NSFDMR-1341822
Alfred P. Sloan FoundationUNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Gordon and Betty Moore FoundationGBMF1250
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Record Number:CaltechAUTHORS:20160328-101600140
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20160328-101600140
Official Citation:Topological Phases with Parafermions: Theory and Blueprints Jason Alicea and Paul Fendley Annual Review of Condensed Matter Physics, Vol. 7: 119 -139 (Volume publication date March 2016)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:65696
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:30 Mar 2016 21:17
Last Modified:30 Mar 2016 21:17

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