Flux-periodic persistent current in mesoscopic superconducting rings close toTc

We study the function-induced persistent current close to ${\mathit{T}}_{\mathit{c}}$ in effectively one-dimensional superconducting rings threaded by a magnetic flux \ensuremath{\varphi}. Using a transfer-operator approach to the Ginzburg-Landau theory we calculate the dependences of the persistent current on temperature, flux, and ${\mathit{T}}_{\mathit{c}}$. In agreement with a simple physical argument we find that the temperature dependence of the current amplitude is similar to that of the order-parameter fluctuations 〈\ensuremath{\Vert}\ensuremath{\Delta}${\mathrm{\ensuremath{\Vert}}}^{2}$〉. We discuss the observability of a flux-periodic response below ${\mathit{T}}_{\mathit{c}}$ in view of the existence of metastable states and phase slips. Our predictions apply to experiments on superconductors whose ${\mathit{T}}_{\mathit{c}}$ is larger than the correlation energy ${\mathit{E}}_{\mathit{c}}$.