Journal
ANNUAL REVIEW OF CONDENSED MATTER PHYSICS, VOL 7
Volume 7, Issue -, Pages 119-139Publisher
ANNUAL REVIEWS
DOI: 10.1146/annurev-conmatphys-031115-011336
Keywords
non-Abelian anyons; topological quantum computation; quantum Hall effect; superconductivity
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Funding
- EPSRC [EP/N01930X/1] Funding Source: UKRI
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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.
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