Ground-state properties of two-dimensional 3He- 4He mixtures are studied at zero temperature. A general argument based on the long-ranged attraction of the phonon exchange is given for the existence of 3He dimers in low-concentration mixtures with 4He. The binding energy of dimers ranges from milli- to microkelvins with increasing 4He density. By comparing the 3He impurity chemical potential in 4He with the one in pure 3He we conclude that at finite pressures 3He dimers form a mixture with 4He with a maximum solubility of approximately 3%.
We calculate the phase diagram of 3 He-4 He mixtures in two dimensions as a function of density and 3 He concentration. A number of features distinguish this system significantly from its three-dimensional counterpart. Specifically, we find that the 3 He phase consists, at low 3 He concentrations and positive pressures, of loosely bound dimers. The dimerized liquid phase separates at a 3 He concentration of 2-3 % because the chemical potential of the 3 He component in the mixture exceeds the chemical potential in the pure phase. Atomic 3 He-4 He 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 3 He concentration is accompanied by a divergence of the 3 He hydrodynamic effective mass, and the magnetic susceptibility vanishes. We verify, wherever possible, that our results are consistent with simulation data and exact estimates.
We have studied the ground state properties of two-dimensional 3 He -4 He mixtures at zero temperature. 3 He atoms with opposite spins form loosely bound dimers in free space and in low concentration mixtures with 4 He . The binding energy of the dimer ranges from milli-Kelvins near the saturation density to micro-Kelvins at the solidification density. The radius of such a weakly bound dimer is tens of Ångstöms. We also calculate the phase diagram of the mixture. The maximum solubility of 3 He ≈7% is determined by comparing chemical potentials in the pure and mixed fluids. The upper stability limit of the super-saturated mixture is obtained from the second derivative of the enthalpy. It becomes negative at the concentration 10-15% depending of the pressure, indicating a softening of the concentration-fluctuation mode. We also find an indication of the phase transition from the dimerized to atomic mixture.
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