Finite-size scaling of the superfluid density of He4 confined between silicon wafers

We report measurements of the superfluid density of He4 confined between two Si wafers. These are the first measurements of helium confined in a sufficiently well-defined planar geometry to show a crossover from three-dimensional-like to finite-size to two-dimensional behavior. Data for confinement in 0.106, 0.509, 2.8, and 3.9-m-thickness cells are analyzed for scaling with the exponent of the bulk correlation length, . We find that this scaling does not work: An exponent different from is required. We discuss these results in light of finite-size scaling predictions and earlier measurements.