Phases of ³he-⁴He mixtures in two dimensions

We calculate the phase diagram of ³He-⁴He mixtures in two dimensions as a function of density and ³He concentration. A number of features distinguish this system significantly from its three-dimensional counterpart. Specifically, we find that the ³He phase consists, at low ³He concentrations and positive pressures, of loosely bound dimers. The dimerized liquid phase separates at a ³He concentration of 2-3% because the chemical potential of the ³He component in the mixture exceeds the chemical potential in the pure phase. Atomic ³He-⁴He mixtures can be found only in a metastable state in a concentration regime above 3%, where the mixture is stable against infinitesimal concentration fluctuations. The softening of concentration-fluctuation modes with decreasing ³He concentration is accompanied by a divergence of the ³He hydrodynamic effective mass, and the magnetic susceptibility vanishes. We verify, wherever possible, that our results are consistent with simulation data and exact estimates.