Heterogeneous surfaces and superfluid onset

Nonuniformity of substrate properties can be detected in the physical adsorption of common molecular gases including helium. Effects due to binding-energy variation extend beyond the first adsorbed layer, usually to thicknesses of many layers. We qualitatively describe reasons for this persistence and show how its form and range are related to the spatial variation of the binding energy. Heterogeneity can play an important role in the appearance of superfluidity in thin films of He4. It is argued that heterogeneity has been a more serious perturbation in superfluid-onset experiments than is generally recognized; that heterogeneity can account for the lack of agreement between experiments which use different techniques and/or substrates; that the experimental disagreements have hindered development of a satisfactory theory of superfluidity in thin films. We derive a thermodynamic formula relating the shifts of onset temperature with thickness to the lateral scale of the thickness variations caused by substrate heterogeneity, and illustrate its application in simple examples. The sensitivity of superfluid onset to heterogeneity might be exploited for surface characterization, yielding important information that is not presently obtainable by other methods. As a separate benefit, it can lead to a clearer understanding of superfluidity. Specific experimental tests are suggested.