Evidence for a Self-Bound Liquid State and the Commensurate-Incommensurate Coexistence in 2D ${}^3$He on Graphite

We made heat-capacity measurements of two dimensional (2D) ${}^3$He adsorbed on graphite preplated with monolayer ${}^4$He in a wide temperature range (0.1 $\leq T \leq$ 80 mK) at densities higher than that for the 4/7 phase (= 6.8 nm${}^{-2}$). In the density range of 6.8 $\le \rho \le$ 8.1 nm${}^{-2}$, the 4/7 phase is stable against additional ${}^3$He atoms up to 20% and they are promoted into the third layer. We found evidence that such promoted atoms form a self-bound 2D Fermi liquid with an approximate density of 1 nm${}^{-2}$ from the measured density dependence of the $\gamma$-coefficient of heat capacity. We also show evidence for the first-order transition between the commensurate 4/7 phase and the ferromagnetic incommensurate phase in the second layer in the density range of 8.1 $\le \rho \le$ 9.5 nm${}^{-2}$.