Topological Phases with Parafermions: Theory and Blueprints
- Creators
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Alicea, Jason
- Fendley, Paul
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.
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 reviewAdditional details
- Eprint ID
- 65696
- DOI
- 10.1146/annurev-conmatphys-031115-011336
- Resolver ID
- CaltechAUTHORS:20160328-101600140
- DMR-1341822
- NSF
- Alfred P. Sloan Foundation
- Institute for Quantum Information and Matter (IQIM)
- GBMF1250
- Gordon and Betty Moore Foundation
- Walter Burke Institute for Theoretical Physics, Caltech
- Created
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2016-03-30Created from EPrint's datestamp field
- Updated
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2021-11-10Created from EPrint's last_modified field
- Caltech groups
- Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics