Zero modes of two-dimensional chiral p-wave superconductors

Details Zero modes of two-dimensional chiral p-wave superconductors Zero modes of two-dimensional chiral p-wave superconductors

2006-10-04

arxiv.org/abs/cond-mat/0610094v1

Phys. Rev. B 75, 212509 (2007)

Physics

Condensed Matter

Superconductivity

Scientific paper

10.1103/PhysRevB.75.212509

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.

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