The upper critical field in the extended van-Hove scenario

We present a study of the superconducting pairing susceptibility K-T(r) for a two-dimensional isotropic system with a strong power-law divergence in t he density of states N(epsilon) similar to epsilon (-1+(1/b)), b > 1. We sh ow that the pair propagator has the scaling form, K-T(r) = r(b- 3)F(T(1/b)r ). A, anomalous short-range behavior is found, straightforwardly leading to positive curvature in the upper critical field! for b less than or similar to2 and to a zero temperature divergence, H-c2 similar to T-2+(4/b), for b > 2. (C) 2001 Elsevier Science B.V. All rights reserved.