Phase Slips in Topological Superconductor Wire Devices

We make a detailed study of phase slips in topological superconducting wires and devices based on topological wires. We begin by investigating a device composed of a topological superconducting wire connected to a non-topological wire (T-S). In the T-segment only slips of the phase by multiples of 4$\pi $ are allowed, while in the S-segment slips by 2$\pi $ are also allowed. We show that near the interface, 2$\pi $ phase slips are also allowed and we comment on the consequences of such phase slips for the Aharonov-Casher effect. We also consider an implementation of a q-bit consisting of a T-S-T device, where the quantum information is stored in the parity of the two topological segments via the four Majorana modes. We show that the central S-segment of this type of device can support 2$\pi $ phase-slips which result in the decoherence of the q-bit.