Melting curve of $^4$He: no sign of the supersolid transition down to 10 mK

TL;DR

This study precisely measured the melting curve of $^4$He from 10 to 400 mK, finding no evidence of a supersolid transition down to 10 mK, and confirmed the expected $T^4$-dependence in the relevant temperature range.

Contribution

The paper provides high-accuracy melting curve data for $^4$He and shows no signs of supersolidity, challenging previous claims of a supersolid transition at low temperatures.

Findings

Melting curve follows $T^4$-dependence between 80 and 400 mK.

No signs of supersolid transition down to 10 mK.

Observed deviations below 80 mK are not related to supersolidity.

Abstract

We have measured the melting curve of $^4$He in the temperature range from 10 to 400 mK with the accuracy of about 0.5 $\mu$bar. Crystals of different quality show the expected $T^4$-dependence in the range from 80 to 400 mK without any sign of the supersolid transition, and the coefficient is in excellent agreement with available data on the sound velocity in liquid $^4$He and on the Debye temperature of solid $^4$He. Below 80 mK we have observed a small deviation from $T^4$-dependence which however cannot be attributed to the supersolid transition because instead of decrease the entropy of the solid rather remains constant, about $2.5\times10^{-6}$ $R$