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Mirror Majorana zero modes in spinful superconductors/superfluids -Non-Abelian braiding of integer quantum vortices-

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 Added by Masatoshi Sato
 Publication date 2013
  fields Physics
and research's language is English




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It has been widely believed that half quantum vortices are indispensable to realize topological stable Majorana zero modes and non-Abelian anyons in spinful superconductors/superfluids. Contrary to this wisdom, we here demonstrate that integer quantum vortices in spinful superconductors can host topologically stable Majorana zero modes because of the mirror symmetry. The symmetry protected Majorana fermions may exhibit non-Abelian anyon braiding.



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The possible stable singular vortex (SV) and half-quantum vortex (HQV) of the superfluid $^3$He-A phase confined in restricted geometries are investigated. The associated low-energy excitations are calculated in connection with the possible existence of Majorana zero modes obeying non-Abelian statistics. The energetics between those vortices is carefully examined using the standard Ginzburg-Landau (GL) functional with a strong-coupling correction. The Fermi liquid effect, which is not included in the GL functional, is considered approximately within the London approach. This allows us to determine the stability regions in pressure, temperature, and applied field for SV and HQV. The existence of the Majorana zero mode and its statistics, either Abelian or non-Abelian under braiding of SVs, is studied by solving the Bogoliubov-de Gennes equation for spinful chiral p-wave superfluids at sufficiently low temperatures. We determined several conditions controllable external parameters for realizing the non-Abelian statistics of Majorana zero modes e.g., pressure, field direction, and strength.
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