Size-dependent Kosterlitz-Thouless superfluid transition in thin 4He films adsorbed on porous glasses.

We report the first quantitative study of the size-dependent suprefluid transition in {sup 4}He films adsorbed on porous glasses with pore diameters {ital d} from 50 to 10 000 A. {ital T}{sub {ital c}} for the submonolayer films decreases as {ital d} increases up to {ital d}=2900 A, whereas {ital T}{sub {ital c}} for the full-pore liquid increases with {ital d}. The {ital d} dependence of {ital T}{sub {ital c}} and the dissipation at the transition for the films reveal that the vortex-pair unbinding on length scales smaller than the pore sizes determines the superfluid transition. We obtain the diameter of vortex core {ital a}{sub 0}=25{plus minus}12 A from the fit by letting the 2D coherence length {xi}{sub 2}{sup +}({ital T}{sub {ital c}})={pi}{ital d}/2.