A Glassy Contribution to the Heat Capacity of hcp 4He Solids

We model the low-temperature specific heat of solid He-4 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 < I similar to (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 He-4, 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 He-4, irrespective of the existence of supersolidity.