Non-Abelian statistics of half-quantum vortices in p-wave superconductors.

By D. Ivanov. Physical Review Letters, 2000

1,265 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/4868fa76655fb6c339f7c7f71cd16dba0efe8921

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

Citations in the corpus

Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states (2012, background): “The search for non-Abelian systems originated from the Moore-Read theory [5] for the 1⁄4 5=2 fractional quantum Hall (FQH) state and went on to consider other quantumHall states [8,9], spin systems [10], p-wave superconductors [11–13], topological insulators coupled in proximity to superconductors [”
Measurement as a Shortcut to Long-Range Entangled Quantum Matter (2022, background): “The band structure of c Majorana fermions is described by a px±ipy superconductor (±1 sign depends on the direction of the applied magnetic field), which supports gapped fermionic excitations, and crucially, binds an unpaired Majorana mode to each vortex [50, 51].”
Chiral superconductivity from repulsive interactions in doped graphene (2011, background): “) and the fractional quantum Hall state at 5/2 fillin”
Topological insulators and superconductors (2010, methodology): “…vortex of a topological superconductor with odd topological quantum numberN carries an odd number of Majorana zero modes (Volovik, 1999), giving rise to non-Abelian statistics (Ivanov, 2001; Read and Green, 2000) which could provide a platform for topological quantum computing (Nayaket al., 2008).”
Non-Abelian braiding on photonic chips (2021, methodology): “striking properties and intriguing applications in the topological quantum computing [4,5], the investigation of non-Abelian anyons and their braiding remains largely restricted to fermionic systems [10-16] and their realization still faces challenges such as stringent requirements of pristine mater”
Non-Abelian Anyons and Topological Quantum Computation (2007, methodology): “2000 showed that the same topological properties mentioned above are realized by a p+ ip-wave superconductor, thereby cementing the identiﬁcation between such a paired state and the Moore-Read state. Ivanov, 2001 computed the braiding matrices by this approach (see also Stern et al., 2004; Stone and”