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Annual Review of Condensed Matter Physics

Volume 7, 2016

Topological Phases with Parafermions: Theory and Blueprints

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 -symmetric Ising quantum spin chain and Majorana fermions to -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.

Keyword(s): non-Abelian anyons, quantum Hall effect, superconductivity, topological quantum computation
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/content/journals/10.1146/annurev-conmatphys-031115-011336
2016-03-10
2025-04-28
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/content/journals/10.1146/annurev-conmatphys-031115-011336
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Topological Phases with Parafermions: Theory and Blueprints
Annual Review of Condensed Matter Physics 7, 119 (2016); https://doi.org/10.1146/annurev-conmatphys-031115-011336
/content/journals/10.1146/annurev-conmatphys-031115-011336
/content/journals/10.1146/annurev-conmatphys-031115-011336
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