On the Commensurate Phase in the Second Layer of Helium on Graphite: A New Quantum Phase?

The second-layer phase diagrams of $^4$He and $^3$He adsorbed on graphite are investigated from heat-capacity measurements below 2 K at densities where He films solidify due to strong correlations and a periodic potential created by underlayers. In contrast to a recent first-principles simulation, we observed large heat-capacity anomalies in both isotopes which indicate unambiguously the existence of a distinct phase stabilized by the weak periodic potential, most likely a commensurate solid, over an extended density region between liquid and incommensurate solid phases. We propose novel states of matter including a quantum solid with $\it{zero}$-$\it{point~defectons}$ for this phase where exotic ground states such as supersolid or gapless quantum spin-liquid are expected.