Theory of the Little-Parks effect in spin-triplet superconductors

The celebrated Little-Parks effect in thin mesoscopic superconducting rings has recently gained great attention due to its potential to probe half-quantum vortices in spin-triplet superconductors. However, there remain puzzles like how to stabilize these half-quantum vortices and what time scale of intrinsic resistive fluctuations between stable states is observable in a spin-triplet superconducting ring. Here, we theoretically investigate the magnetoresistance of mesoscopic spin-triplet superconducting rings resulting from thermal vortex tunneling below the critical temperature based on the Ginzburg- Landau theory. Assuming a spin triplet superconductor with predominantly (↑↑) and (↓↓) Cooper pairs, we show that a coupling term that imposes a penalty to the charge supercurrents is necessary to stabilize the half quantum vortex fluxoid states. We solve the differential Ginzburg-Landau equations of such a spin-triplet superconducting ring to obtain the saddle point configuration of the order parameters, from which we calculate the decay rate for persistent current in a ring due to thermal vortex tunneling. We identify a characteristic two peak Little parks oscillation in resistance. We analyze the differentiablity criterion for the two peak structure which is maximized for large inter-spin coupling, applied magnetic field, and a very large thin-wall superconducting ring close to the critical temperature.