Supercurrent Decay by Vortex Nucleation in the Presence of an Array of Pinning Centres: a Renormalization Group Approach

We study the phenomenon of decay of a supercurrent in a superconducting thin film due to the spontaneous homogeneous nucleation of quantized vortex-antivortex pairs in the absence of an external magnetic field and in the presence of a periodic pinning potential. We describe the vortex nucleation by means of a Schwinger-type path-integral calculation including the effects of quantum dissipation. The overdamped case is treated exactly, whilst the case in which a periodic array of pinning centres is present is dealt with by means of a renormalization group (RG) approach in frequency space. This yields an approximate but very appealing analytic result for the dependence of the vortex nucleation rate on the externally-driven supercurrent. In this formula the rate dependence displays oscillations which are connected to the pinning periodicity and correspond to the vortex nucleation length probing over the pinning sites as the current density is varied. Our RG treatment describes the vortex nucleation process in both the confined and the mobile phases of the dissipation-driven localization transition characterising the motion of dissipating quantum particles in a periodic potential.