Finite-size scaling of the superfluid density ofHe4confined between silicon wafers

We report measurements of the superfluid density of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ 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-μm-thickness cells are analyzed for scaling with the exponent of the bulk correlation length, ν. We find that this scaling does not work: An exponent different from ν is required. We discuss these results in light of finite-size scaling predictions and earlier measurements.