Zero modes of two-dimensional chiral p-wave superconductors

Abstract

We discuss fermionic zero modes in the two-dimensional chiral p-wave superconductors. We show quite generally, that without fine-tuning, in a macroscopic sample there is only one or zero of such Majorana-fermion modes depending only on whether the total vorticity of the order parameter is odd or even, respectively. As a special case of this, we find explicitly the one zero mode localized on a single odd-vorticity vortex, and show that, in contrast, zero modes are absent for an even-vorticity vortex. One zero mode per odd vortex persists, within an exponential accuracy, for a collection of well-separated vortices, shifting to finite E or -E energies as two odd vortices approach. These results should be useful for the demonstration of the non-Abelian statistics that such zero-mode vortices are expected to exhibit, and for their possible application in quantum computation.

References in corpus (2)

• Resonantly-paired fermionic superfluids
• Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State

Cited by in corpus (8)

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• Testable signatures of quantum non-locality in a two-dimensional chiral p-wave superconductor
• Near zero modes in condensate phases of the Dirac theory on the honeycomb lattice
• Vortices, zero modes and fractionalization in bilayer-graphene exciton condensate
• Non-Abelian statistics as a Berry phase in exactly solvable models
• Graphene with geometrically induced vorticity
• Midgap spectrum of the fermion-vortex system
• Unconventional superfluidity in Bose-Fermi Mixtures