  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.
