Disorder-dependent slopes of the upper critical field in nodal and nodeless superconductors

We study the slopes of the upper critical field ∂_TH_c2|_T_c≡∂ H__c2/∂ T at T_c in anisotropic superconductors with transport (non-magnetic) scattering employing the Ginzburg-Landau theory, developed for this situation by S. Pokrovsky and V. Pokrovsky, Phys. Rev. B 54, 13275 (1996). We found unexpected behavior of the slopes for a d-wave superconductor and in a more general case of materials with line nodes in the order parameter. Specifically, the presence of line nodes causes ∂_TH_c2|_T_c to decrease with increasing non-magnetic scattering parameter P, unlike the nodeless case where the slope increases. In a pure d-wave case, the slope ∂ H_c2|_T_c changes from decreasing to increasing when scattering parameter approaches P≈0.91 P_ crit, where P_ crit≈0.2807 at which T_c→0 that implies the the existence of a gapless state in d-wave superconductors with transport scattering in the interval, 0.91 P_crit更多