Suppression of 2\pi\ phase-slip due to hidden zero modes in one dimensional topological superconductors

Abstract

We study phase slips in one-dimensional topological superconducting wires. These wires have been proposed as building blocks for topologically protected qubits in which the quantum information is distributed over the length of the device and thus is immune to local sources of decoherence. However, phase-slips are non-local events that can result in decoherence. Phase slips in topological superconductors are peculiar for the reason that they occur in multiples of 4\pi\ (instead of 2\pi\ in conventional superconductors). We re-establish this fact via a beautiful analogy to the particle physics concept of dynamic symmetry breaking by explicitly finding a "hidden" zero mode in the fermion spectrum computed in the background of a 2\pi\ phase-slip. Armed with the understanding of phase-slips in topological superconductors, we propose a simple experimental setup with which the predictions can be tested by monitoring tunneling rate of a superconducting flux quantum through a topological superconducting wire.