Non-Abelian statistics of half-quantum vortices in p-wave superconductors.
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TLDR
From the properties of the solutions to Bogoliubov-de Gennes equations in the vortex core, the non-Abelian statistics of vortices are derived identical to that for the Moore-Read (Pfaffian) quantum Hall state.Abstract:
Excitation spectrum of a half-quantum vortex in a $p$-wave superconductor contains a zero-energy Majorana fermion. This results in a degeneracy of the ground state of the system of several vortices. From the properties of the solutions to Bogoliubov--de Gennes equations in the vortex core we derive the non-Abelian statistics of vortices identical to that for the Moore-Read (Pfaffian) quantum Hall state.read more
Citations
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References
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Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect
N. Read,Dmitry Green +1 more
TL;DR: In this article, the authors considered the pairing of fermions in two dimensions for fully gapped cases with broken parity (P) and time reversal (T), especially cases in which the gap function is an orbital angular momentum (l) eigenstate.
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Nonabelions in the fractional quantum Hall effect
Gregory W. Moore,N. Read +1 more
TL;DR: In this article, the relation between the order parameter in the fractional quantum Hall effect and the chiral algebra in rational conformal field theory is stressed, and new order parameters for several states are given.
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Bound Fermion states on a vortex line in a type II superconductor
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Knots and physics
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2n-quasihole states realize 2n−1-dimensional spinor braiding statistics in paired quantum Hall states
Chetan Nayak,Frank Wilczek +1 more
TL;DR: In this paper, it was shown that simple multi-quasihole wave functions for the v = 1 2 Pfaffian paired Hall state exhibit an exponential degeneracy at fixed positions, and for 2n quasiholes the states realize a spinor representation of an expanded (continuous) non-Abelian statistics group SO(2n).
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