Upper critical field in disordered two-dimensional superconductors

We present calculations of the upper critical field Hc2(T) in superconducting films as a function of increasing disorder (as measured by the normal state resistance per square R_). In contradiction to previous work, we find that there is no anomalous low temperature positive curvature in Hc2 vs T as disorder is increased. We show that the previous prediction of this effect is due to an unjustified analytical approximation of sums occurring in the perturbative calculation. Our treatment includes both a careful analysis of first-order perturbation theory, and a nonperturbative resummation technique. No anomalous curvature is found in either case. We present our results in graphical form.