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Fluidity in Domain Walls in Dilute $^3$He-$^4$He Films on Graphite: Possible 1D Fermi Fluid and Dirac Fermions in Helium Film

The heat capacity of a small amount of $^3$He atoms dissolved in submonolayer $^4$He film has been measured. The measured heat capacity is finite and suggests that $^3$He atoms are mobile at an areal density regime higher than that of the $\sqrt{3}\times\sqrt{3}$ phase, where $^4$He films are believed to be solid. At higher areal densities, the measured heat capacity is proportional to $T^2$ and depends on the amounts of $^3$He atoms. These behaviors are anomalous to that of a two-dimensional Fermi fluid, and cannot be explained by uniform melting of $^4$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 $^3$He atoms gather into 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.