Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states

By N. Lindner, Erez Berg, G. Refael, A. Stern. 2012

170 citations recorded by the source corpus.

We study the non-abelian statistics characterizing systems where counter-propagating 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 $\nu= 1/m$, while electrons of the opposite spin occupy a similar state with $\nu = -1/m$. 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 $\sqrt{2m}$. 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.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/89cbe4aafef6717a7a2a73f6e47405e4ec8ee483

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In Atomic and Molecular Physics, and Optics

1. J. Alicea
2. N. Lindner
3. A. Stern
4. C. Nayak
5. P. Fendley
6. Roger S. K. Mong
7. Erez Berg
8. Y. Oreg

In Materials Chemistry

1. P. Fendley
2. A. Stern
3. Erez Berg
4. C. Nayak
5. Y. Oreg
6. J. Alicea
7. N. Lindner
8. C. Beenakker

Citations in the corpus

• Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure (2013, background): “The first term reflects a fractional Josephson coupling between adjacent superconducting segments [59,79–81], mediated by charge-2e=3 tunneling across the intervening tunneling-gapped region.”