Superfluid3He-B in a realistic thin film. Gap and critical current

We examine³He-B confined to a thin film on a rough substrate with a freestanding upper surface by using quasiclassical techniques. First, the dependence of the gap on surface roughness, film width, and boundary condition formulation is examined in detail for the current-free state. The evaluation is conducted using both the Randomly Rippled Wall and the Thin Dirty Layer surface models in order to compare them. Second, the current bearing state for a submicron film resting on a rough substrate is calculated using the Thin Dirty Layer surface model. Several unusual and previously unreported features appear in both cases. Numerical estimates of the critical current densities are in favorable agreement with corresponding experiments.