Anderson localization and ‘‘universal’’ degradation ofTcin high-temperature superconductors

Anderson, Muttalib, and Ramakrishnan (AMR) showed that strong disorder leads to a frequency (ω) dependent increase of the Coulomb repulsion in a three-dimensional superconductor. Their one-free-parameter theory agrees nicely with the experimentally observed decrease in ${\mathit{T}}_{\mathit{c}}$ but only for a fitted critical resistivity (${\mathrm{\rho }}_{\mathit{c}}$) that is very much smaller than the free-electron-gas estimate (${\mathrm{\rho }}_{\mathit{c}}^{\mathit{f}}$). We reexamine the effect of AMR’s disorder-enhanced Coulomb repulsion using the Eliashberg equations for ${\mathit{T}}_{\mathit{c}}$ rather than the simple two-square-well aproximation to them which is suspect when there are more than two characteristic frequencies involved. The most important modification of the original calculation is the inclusion of the Coulomb contribution to the renormalization function Z(ω).