Superconductivity in disordered thin films

Superconductivity disappears in (mesoscale) disordered thin films at a sheet resistance R_□ or order 10 kΩ per square. This and other observed features of systems with both atomic and meso-scale disorder are briefly reviewed, as also theoretical models mainly based on the Josephson junction lattice. These are known to be inadequate. A new approach is described, with the sole assumption that the pair amplitude |Δ| does not vary spatially. The energy cost of wavevector (q) and frequency (ω) dependent phase fluctuations θ_qω is expressed exactly in terms of disordered normal state properties. It is shown that because of perfect screening, the ω² dependent term has an extra factor |q| in two dimensions relative to the Josephson junction lattice form. The q² or phase gradient term is calculated as a function of R_□. A rapid and large drop in stiffness occurs for R_□ ∼  10 kΩ when the electron localization length and pair coherence length become comparable. At this level of disorder, the pair amplitude fluctuates spatially, so that the above approach becomes inadequate. Several indications are that a charged Bose system in a random potential would be a realistic model for disordered thin film superconductors at low temperature.