A glassy contribution to the heat capacity of hcp $^4$He solids

TL;DR

This paper models the low-temperature specific heat of hcp solid helium-4 by incorporating two-level tunneling states alongside phonons, explaining excess heat capacity and linear terms observed experimentally.

Contribution

It introduces a cutoff in the two-level tunneling density of states to accurately describe the excess specific heat in solid helium-4 at very low temperatures.

Findings

Agreement with experimental specific heat data

Presence of ppm-level two-level tunneling systems

Independence from supersolidity hypothesis

Abstract

We model the low-temperature specific heat of solid $^4$He in the hexagonal closed packed structure by invoking two-level tunneling states in addition to the usual phonon contribution of a Debye crystal for temperatures far below the Debye temperature, $T < \Theta_D/50$. By introducing a cutoff energy in the two-level tunneling density of states, we can describe the excess specific heat observed in solid hcp $^4$He, as well as the low-temperature linear term in the specific heat. Agreement is found with recent measurements of the temperature behavior of both specific heat and pressure. These results suggest the presence of a very small fraction, at the parts-per-million (ppm) level, of two-level tunneling systems in solid $^4$He, irrespective of the existence of supersolidity.