Inhomogeneous broadening and the Kosterlitz-Thouless transition

Torsional-oscillator studies of very thin He4 films have found nonuniversal behavior of the superfluid response as a function of coverage. The temperature width of the superfluid transition region is nonmonotonic in the areal density n and exhibits cusplike variations at half of the layering period. We explore the assumption that this additional broadening is caused by macroscopic inhomogeneities in the substrate potential; such a theory for inhomogeneous broadening can be constructed from the Kosterlitz-Nelson relation between the superfluid areal density ns and the transition temperature Tc by determining the theoretical ''sensitivity'' S of ns to variations in the strength of the substrate potential. For substrate models that are atomically uniform, a simple microscopic hypernetted-chain calculation (without either ''elementary diagrams'' or three-body correlations, but with an optimized Jastrow function) finds this sensitivity always to be of the same sign, and yields reasonable order-of-magnitude agreement with experiment. However, models for which the sensitivity does not change sign appear to be incapable of yielding either the cusps or the half-periodicity of the data. We suggest that these properties may occur with a more recently developed (and more sophisticated) version of hypernetted-chain theory, wherein "elementary diagrams" and three-body correlations are incorporated.