Abstract
A self-consistent analytical solution of the problem of the superconductivity of ultrathin metal films is found within the tight-binding model for normal-metal electrons with a simple example of a film of three atomic layers. Superconductivity is not destroyed in atomically thin films if the energies of the electron subsystem lie near the Fermi surface at least for some values of the quasimomentum component along the film. A substantial increase in the critical temperature of an ultrathin metal film as compared to its bulk value is possible if the electron excitation spectrum contains low-energy modes with an anomalously weak dispersion.
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