Heat capacity reveals a possible glass state in hcp $^4$He solids

We model the low-temperature specific heat of solid $^4$He 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 small fraction, at the parts-per-million(ppm) order, of two-level tunneling systems in solid $^4$He, irrespective of a possible existence of supersolidity.