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. Moreover, 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 2D Fermi fluid, and cannot be explained by uniform melting. One possible explanation for these anomalous behaviors is that helium atoms exhibit fluidity inside the domain walls of the adsorption structure, and the dissolved $^3$He atoms 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.