Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published October 11, 2012 | Published + Submitted
Journal Article Open

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

Abstract

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.

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.

Attached Files

Published - PhysRevX.2.041002.pdf

Submitted - 1204.5733v1.pdf

Files

1204.5733v1.pdf
Files (1.7 MB)
Name Size Download all
md5:32b252777e335736f56611a15d0e62b3
1.0 MB Preview Download
md5:7388bf3deaadb9f42c9a529ce66b7887
687.3 kB Preview Download

Additional details

Created:
August 22, 2023
Modified:
October 17, 2023