Renormalization of the upper critical field by superconducting fluctuations

We study the effect of superconducting fluctuations on the upper critical field of a disordered superconducting film at low temperatures. The first-order fluctuation correction is found explicitly. In the framework of the perturbative analysis, superconducting fluctuations are shown to shift the upper-critical-field line toward lower fields and do not lead to an upward curvature. Higher-order corrections to the quadratic-term coefficient in the Ginzburg-Landau free energy functional are studied. We extract a family of the mostly divergent diagrams and formulate a general rule of calculating a diagram of an arbitrary order. We find that the singularity gets more severe with increasing perturbation-theory order. We conclude that the renormalization of the Ginzburg-Landau coefficients by superconducting fluctuations is an essentially nonperturbative effect. As a result, the genuine transition line may be strongly shifted from the classical mean-field curve in a two-dimensional superconductor.