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 (11)

• Fault-tolerant quantum computation by anyons
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Non-abelian statistics of half-quantum vortices in p-wave superconductors
• Resonantly-paired fermionic superfluids
• Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State
• Proposed experiments to probe the non-abelian ν=5/2 quantum Hall state
• Proposal to stabilize and detect half-quantum vortices in strontium ruthenate thin films: Non-Abelian braiding statistics of vortex matter in a $p_x+i{p}_y$ superconductor
• Quasiholes and fermionic zero modes of paired fractional quantum Hall states: the mechanism for nonabelian statistics
• Quantum phase transitions across p-wave Feshbach resonance
• Detecting non-Abelian Statistics with Electronic Mach-Zehnder Interferometer

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