Anisotropic Superconductivity in Highly Disordered Systems

The gap equation for anisotropic Superconductivity is solved in the presence of elastic scatterings by nonmagnetic and magnetic impurities, which are treated by the self-consistent Born approximation, and inelastic scatterings, which are phenomenologically treated. When elastic scatterings are strong, even at T = 0 K, coherence peaks almost disappear and the gap is a pseudogap, i.e., the density of states rho(E) is nonzero at the chemical potential, which means that the T-linear specific heat coefficient is nonzero in the superconducting state. At T = 0 K in such a case, the low-energy part of rho(epsilon) or the gap spectrum has a concave-cap V shape, which is in contrast to a convex-cup V shape in the absence of scattering. When elastic or inelastic scatterings are strong, the ratio epsilon(G)(0)/k(B)T(c) is much larger than its mean-field value of about 4, where epsilon(G)(0) is the gap at T = 0 K and T-c is the superconducting critical temperature. The large epsilon(G)(0)/k(B)T(c) similar or equal to 8 and the linear decrease in Tc in residual resistivity, both of which are observed in cuprate superconductors and the latter of which is inconsistent with the Abrikosov and Gor'kov theory, can be explained by the temperature-dependent pair breaking estimated from the T-linear coefficient of resistivity, which is about 1 mu Omega cm/K.