Effects of Van Hove singularities on the upper critical field
We present a study of the superconducting pairing susceptibility KT(r) for a two-dimensional isotropic system with a strong power-law divergence in the density of states N()~-1 + 1/b, b>1. We show that the pair propagator has the scaling form KT(r) = rb-3F(T1/br). An anomalous short-range behaviour is found, leading straightforwardly to positive curvature in the upper critical field, for b2, and to a zero-temperature divergence, Hc2~T-2 + 4/b, for b>2.