Superfluid Density of He II in the Critical Region

Abstract

The superfluid density of liquid ${\mathrm{He}}^{4}$ near the $\ensuremath{\lambda}$ point has been measured using the oscillating-disk-pile technique. From accurate measurements of the period of oscillation as a function of the temperature difference ${T}_{\ensuremath{\lambda}}\ensuremath{-}T$, the superfluid density ${\ensuremath{\rho}}_{s}$ is found to obey the power-law expression ${\ensuremath{\rho}}_{s}=1.43\ensuremath{\rho}{({T}_{\ensuremath{\lambda}}\ensuremath{-}T)}^{\ensuremath{\zeta}}$ with $\ensuremath{\zeta}=0.666\ifmmode\pm\else\textpm\fi{}0.006$. This power-law dependence closely resembles that found in other systems near a symmetry-breaking higher-order phase transition. In particular, Josephson has shown for He II that the value $\ensuremath{\zeta}=\frac{2}{3}$ is a direct consequence of a logarithmically divergent specific heat ($\ensuremath{\sim}\mathrm{ln}|{T}_{\ensuremath{\lambda}}\ensuremath{-}T|$). Thermodynamic and scaling arguments suggest that the coherence length in He II varies as ${({T}_{\ensuremath{\lambda}}\ensuremath{-}T)}^{\ensuremath{-}\ensuremath{\zeta}}$. Our result for the superfluid critical exponent $\ensuremath{\zeta}$, together with the superfluid-specific-heat data of Kellers, Fairbank, and Buckingham, are consistent with the validity of the Widom-Kadanoff-Josephson scaling laws.