Size-dependent Kosterlitz-Thouless superfluid transition in thinHe4films adsorbed on porous glasses

We report the first quantitative study of the size-dependent suprefluid transition in ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ films adsorbed on porous glasses with pore diameters d from 50 to 10 000 Å. ${\mathit{T}}_{\mathit{c}}$ for the submonolayer films decreases as d increases up to d=2900 Å, whereas ${\mathit{T}}_{\mathit{c}}$ for the full-pore liquid increases with d. The d dependence of ${\mathit{T}}_{\mathit{c}}$ 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 ${\mathit{a}}_0$=25±12 Å from the fit by letting the 2D coherence length ${\xi }_2^{+}$(${\mathit{T}}_{\mathit{c}}$)=πd/2. .AE