"Charging effect" in superconducting and normal-state thin films

It has been observed experimentally that changing the number of electrons on previously neutral thin films produces measurable shifts in the superconducting transition temperature T_c and normal-state conductivity σ_n with a number of interesting features. We offer a theoretical explanation of this "charging effect" by a modification of a Friedel-type sum rule to include situations in which the sample does not exhibit charge neutrality.