The heat capacity of a small number of ${}^3\mathrm{He}$ atoms dissolved in a submonolayer ${}^4\mathrm{He}$ film has been measured. The measured heat capacity is finite and suggests that ${}^3\mathrm{He}$ atoms are mobile in an areal density regime higher than that of the $\sqrt{3}\times \sqrt{3}$ phase, where ${}^4\mathrm{He}$ films are believed to be solid. At higher areal densities, the measured heat capacity is proportional to $T^2$ and depends on the number of ${}^3\mathrm{He}$ atoms. These behaviors are anomalous to that of a two-dimensional Fermi fluid and cannot be explained by uniform melting of ${}^4\mathrm{He}$ films. One possible explanation for these anomalous behaviors is that helium atoms exhibit fluidity only inside the domain walls of the adsorption structure, and the dissolved ${}^3\mathrm{He}$ atoms gather in them and behave as a one-dimensional Fermi fluid or as Dirac fermions, depending on the structure of the domain walls. The behaviors of the measured heat capacity strongly suggest this possibility.

• Received 16 August 2022
• Revised 2 November 2022
• Accepted 23 December 2022

DOI:https://doi.org/10.1103/PhysRevB.107.L020505