Zero modes of two-dimensional chiral p-wave superconductors

TL;DR

This paper analyzes fermionic zero modes in two-dimensional chiral p-wave superconductors, showing that the number of Majorana modes depends on the vorticity's parity, with implications for non-Abelian statistics and quantum computing.

Contribution

It provides a general proof that zero modes depend solely on vorticity parity and explicitly finds zero modes for odd-vorticity vortices, advancing understanding of topological superconductors.

Findings

Zero modes depend only on vorticity parity.

Explicit zero mode found for odd-vorticity vortices.

Zero modes are absent for even-vorticity vortices.

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.