Dimers in Two-Dimensional ${}_{}{}^3{}_{}{}^{}He$- ${}_{}{}^4{}_{}{}^{}He$ Mixtures

Ground-state properties of two-dimensional ${}^3\mathrm{He}-{}^4\mathrm{He}$ 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 ${}^3\mathrm{He}$ dimers in low-concentration mixtures with ${}^4\mathrm{He}$. The binding energy of dimers ranges from milli- to microkelvins with increasing ${}^4\mathrm{He}$ density. By comparing the ${}^3\mathrm{He}$ impurity chemical potential in ${}^4\mathrm{He}$ with the one in pure ${}^3\mathrm{He}$ we conclude that at finite pressures ${}^3\mathrm{He}$ dimers form a mixture with ${}^4\mathrm{He}$ with a maximum solubility of $\approx 3\%$.