Nonlocal effect on the fluctuation conductivity of granular superconductors

The theory of fluctuation conductivity for small impurity concentration is developed. We consider all fluctuation corrections of the first order in the case of dilute impurity concentration including nonlocal electron scattering in the clean superconductor. By using Green’s function technique we first calculate the Cooperon (impurity vertex) C(q→,ω1,ω2) and fluctuation propagator K(Ωk, q) in the presence of impurities. We show that in the clean limit the density-of-states quantum corrections are canceled by the Maki–Thompson (MT) term and it results in the reduction of the total fluctuation correction in clean case to the Aslamazov–Larkin (AL) term only.