Properties of monolayer solid helium and its melting transition

High-resolution heat-capacity measurements of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ adsorbed on exfoliated graphite have explored the incommensurate solid phase and its melting transition. The characteristics of the solid and the melting peaks resemble earlier measurements on Grafoil but the new results reflect greater uniformity of the present substrate, higher experimental resolution, and detailed substrate characterization. For temperatures $T<\mathrm{}0.06\mathrm{}{T}_{\mathrm{peak}}$ the Debye temperatures are independent of $T$ with values approximately equal to previous results. In the range $0.06T_{\mathrm{peak}}<T<\mathrm{}{T}_{\mathrm{peak}}$ the heat capacity is increased by an exponential contribution attributed to the thermal activation of vacancies or dislocation pairs. Activation energies of the defects depend on density, and range from $20k_B$ to $27k_B$, in close agreement with nuclear-magnetic-resonance results and with estimates obtained from some computer-simulation studies. Peak temperatures are lower than the melting temperatures predicted by the theory of dislocation-mediated melting. Substrate characterization indicates variations in binding energy of 3.4 × ${10}^{-4\mathrm{}}$. These variations cause appreciable broadening of the melting peaks. We conclude that the experimental peaks are consistent with a first-order melting transition.