# Non abelian statistics of fractionalized Majorana fermions

 TYPE Theor./Math. Physics Seminar Speaker: Dr. Netanel Lindner Affiliation: Caltech Organizer: Avron Date: 13.05.2012 Time: 13:00 Location: Lidow Nathan Rosen (300) Remark: Special lunch time seminar
 Abstract: We study the non-abelian statistics characterizing systems wherecounter-propagating gapless modes on the edges of fractional quantumHall states are gapped by proximity-coupling to superconductors andferromagnets.  We find that each interface between a region on theedge coupled to a superconductor and a region coupled to a ferromagnetcorresponds to a non-abelian anyon of quantum dimension $\sqrt{2m}$,where $1/m$ is the filling fraction of the quantum Hall states. Wecalculate the unitary transformations that are associated withbraiding of these anyons, and show that they are able to realize aricher set of non-abelian representations of the braid group than theset realized by non-abelian anyons based on Majorana fermions. Wecarry out this calculation both explicitly and by applying generalconsiderations. Finally, we show that topological manipulations withthese anyons cannot realize universal quantum computation.