Anderson localization and superconducting transition temperature in two-dimensional systems

Effects of the Anderson localization on superconducting transition temperature T_c are examined by calculating a two-electron propagator K rigorously up to 0(?_Fτ₀)^?1ln(Tτ₀)], where τ₀ is the electron life time due to impurity scattering and ?_F the Fermi energy. The results show that in K the pair-breaking terms cancel out among themselves exactly and the remaining terms which contribute to the correction to the density of states and to the renormalization of electron-electron interaction by impurity scattering lead to the changes in T_c of 0{ln(Tτ₀)}²] and of 0{ln(Tτ₀)}³], respectively.