Quantum fluctuations in continuous superconducting films

Abstract

Motivated by recent experiments on ultrathin continuous superconducting films, we study the dependence ofT c and Δ (for zero temperatures) on the film thicknessd. Using field-theoretical methods, we express the Coulomb interaction in terms of a fluctuating potential, and the fluctuation correction to the free energy (in one-loop approximation) is determined. Based on the standard dirty-limit expressions for the response functions, we findT c and Δ by a numerical investigation of the gap equation. Generally, we find that the decrease ofT c and Δ vs.d −1 is quite similar, but depends sensitively on both the large-wave-vector cut-off and the strength of the interaction. In particular, however, for a strong interaction (Coulomb interaction), the order parameter is more strongly suppressed than the critical temperature, which is due to long-wavelength fluctuations of the phase and the potential.