Entropy of solidHe4: The possible role of a dislocation-induced glass

Solid ${}^4\mathrm{He}$ is viewed as a nearly perfect Debye solid. Yet recent calorimetry indicates that its low-temperature specific heat has both cubic and linear contributions. These features appear in the same temperature range $(T\sim 200\mathrm{mK})$ where measurements of the torsional oscillator period suggest a supersolid transition. We analyze the specific heat to compare the measured with the estimated entropy for a proposed supersolid transition with 1% superfluid fraction. We find that the experimental entropy is substantially less than the calculated entropy. We suggest that the low-temperature linear term in the specific heat is due to a glassy state that develops at low temperatures and is caused by a distribution of tunneling systems in the crystal. It is proposed that small scale dislocation loops produce those tunneling systems. We argue that the reported mass decoupling is consistent with an increase in the oscillator frequency, as expected for a glasslike transition.