Superfluid density in He-3 film

The size effect on the superfluid density rho(s) of He-3 films with thickne ss of the order of the coherence length is discussed on the basis of the qu asi-classical Green's function method. We formulate a linear response theor y in He-3 films where the ABM state is stabilized owing to the size effect. This study is motivated by the third sound experiment recently reported by Schechter et al. In this experiment, the superfluid density rho(s) has bee n obtained for films with thicknesses in the range 92-281 nm. We show that when we assume the scattering from the substrate to be diffusive and that f rom the free surface of He-3 to be specular, our results reproduce well the temperature dependence of rho(s) measured for films thinner than 174 nm, w hile the data for thicker films deviate from our ABM results. (C) 2000 Else vier Science B.V. All rights reserved.