B(H) constitutive relations near H-c1 in disordered superconductors

We provide a self-contained account of the B vs. H constitutive relation ne ar H-c1 in Type II superconductors with various types of quenched random di sorder. The traditional Abrikosov result, B similar to [ln(H - H-c1)](-2), valid in the absence of disorder and thermal fluctuations, changes signific antly in the presence of disorder. Moreover, the constitutive relations wil l depend strongly on the type of disorder. In the presence of point disorde r, B similar to (H - H-c1)(3/2) in three-dimensional (thick) superconductor s as shown by Nattermann and Lipowsky. In two-dimensional (thin film) super conductors with point disorder, B similar to (H - H-c1). In the presence of parallel columnar disorder, we find that B similar to exp[-C-3/(H - H-c1)] in three dimensions, while B similar to exp[-C-2/(H - H-c1)(1/2)] in two d imensions. In the presence of nearly isotropically splayed disorder, we fin d that B similar to (H - H-c1)(3/2) in both two and three dimensions. (C) 2 000 Elsevier Science B.V. All rights reserved.