Topological phases with parafermions: theory and blueprints

Journal article

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.

Authors: Alicea, J; Fendley, P

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Annual Reviews
• Journal: Annual Review of Condensed Matter Physics
• Volume: 7
• Issue: 1
• Pages: 119-139
• Publication date: 2016-03-01
• DOI: 10.1146/annurev-conmatphys-031115-011336
• EISSN: 1947-5462
• ISSN: 1947-5454
• Language: English
• Keywords: quantum Hall effect; superconductivity; non-Abelian anyons; topological quantum computation