Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Superconducting analogue of the parafermion fractional quantum Hall
  states   Read and Rezayi $Z_k$ parafermion wavefunctions describe
$\nu=2+\frac{k}{kM+2}$ fractional quantum Hall (FQH) states. These states
support non-Abelian excitations from which protected quantum gates can be
designed. However, there is no experimental evidence for these non-Abelian
anyons to date. In this paper, we study the $\nu=2/k$ FQH-superconductor
heterostructure and find the superconducting analogue of the $Z_k$ parafermion
FQH state. Our main tool is the mapping of the FQH into coupled one-dimensional
(1D) chains each with a pair of counter-propagating modes. We show that by
inducing intra-chain pairing and charge preserving backscattering with
identical couplings, the 1D chains flow into gapless $Z_{k}$ parafermions when
$k< 4$. By studying the effect of inter-chain coupling, we show that every
parafermion mode becomes massive except for the two outermost ones. Thus, we
achieve a fractional topological superconductor whose chiral edge state is
described by a $Z_k$ parafermion conformal field theory. For instance, we find
that a $\nu=2/3$ FQH in proximity to a superconductor produces a $Z_3$
parafermion superconducting state. This state is topologically
indistinguishable from the non-Abelian part of the $\nu=12/5$ Read-Rezay state.
Both of these systems can host Fibonacci anyons capable of performing universal
quantum computation through braiding operations.

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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: cs
28
The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: eess