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Fractionalizing Majorana fermions: non-Abelian Statistics on the Edges of Abelian Quantum Hall States

Lindner, Netanel H. and Berg, Erez and Refael, Gil and Stern, Ady (2012) Fractionalizing Majorana fermions: non-Abelian Statistics on the Edges of Abelian Quantum Hall States. Physical Review X, 2 (4). Art. No. 041002. ISSN 2160-3308. doi:10.1103/PhysRevX.2.041002.

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We study the non-abelian statistics characterizing systems where counterpropagating gapless modes on the edges of fractional quantum Hall states are gapped by proximity coupling to superconductors and ferromagnets. The most transparent example is that of a fractional quantum spin Hall state, in which electrons of one spin direction occupy a fractional quantum Hall state of v = 1/m, while electrons of the opposite spin occupy a similar state with v = -1/m. However, we also propose other examples of such systems, which are easier to realize experimentally. We find that each interface between a region on the edge coupled to a superconductor and a region coupled to a ferromagnet corresponds to a non-Abelian anyon of quantum dimension √(2m). We calculate the unitary transformations that are associated with braiding of these anyons, and show that they are able to realize a richer set of non-Abelian representations of the braid group than the set realized by non-abelian anyons based on Majorana fermions. We carry out this calculation both explicitly and by applying general considerations. Finally, we show that topological manipulations with these anyons cannot realize universal quantum computation.

Item Type:Article
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Lindner, Netanel H.0000-0003-1879-3902
Stern, Ady0000-0002-9493-268X
Additional Information:Published 2012 by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Received 1 May 2012; published 11 October 2012. N. H. L. and E. B. have contributed equally to this work. We thank Maissam Barkeshli, Lukasz Fidkowsky, Bert Halperin, Alexei Kitaev, Chetan Nayak, and John Preskill for useful discussions. E. B. was supported by the National Science Foundation under Grant Nos. DMR-0757145 and DMR-0705472. A. S. thanks the US-Israel Binational Science Foundation, the Minerva Foundation, and Microsoft Station Q for financial support. N. H. L. and G. R. acknowledge funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation, and DARPA. N. H. L. was also supported by the David and Lucile Packard Foundation. This work was supported in part by the National Science Foundation Grant No. 1066293 and the hospitality of the Aspen Center for Physics. Note added.—We recently became aware that a similar idea is being pursued by David Clarke, Jason Alicea, and Kirill Shtengel [65]. In addition, two papers on related subjects [66,67] have appeared.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
US-Israel Binational Science Foundation (BSF)UNSPECIFIED
Minerva foundationUNSPECIFIED
Microsoft Station QUNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Defense Advanced Research Projects Agency (DARPA)UNSPECIFIED
David and Lucile Packard FoundationUNSPECIFIED
Aspen Center for PhysicsUNSPECIFIED
Subject Keywords:Condensed Matter Physics; Superconductivity; Topological Insulators
Issue or Number:4
Classification Code:PACS: 74.78.Na; 73.43.-f; 03.65.Vf; 03.67.Lx
Record Number:CaltechAUTHORS:20120430-073146103
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Official Citation:Lindner, N. H., E. Berg, et al. (2012). "Fractionalizing Majorana Fermions: Non-Abelian Statistics on the Edges of Abelian Quantum Hall States." Physical Review X 2(4): 041002.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:30386
Deposited By: Tony Diaz
Deposited On:27 Jun 2012 18:44
Last Modified:09 Nov 2021 19:47

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