Phases of 3He-4He mixtures in two dimensions

ABSTRACT 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.