Abstract
We compute the zero-temperature equation of state of a mixture of two fermionic atomic species with repulsive interspecies interactions using second-order perturbation theory. We vary the interaction strength, the population, and the mass imbalance, and we analyze the competition between different states: homogeneous, partially separated, and fully separated. The canonical phase diagrams are determined for various mass ratios, including the experimentally relevant case of the $^{6}\mathrm{Li}$-$^{40}\mathrm{K}$ mixture. We find substantial differences with respect to the equal-mass case: phase separation occurs at weaker interaction strength, and the partially separated state can be stable even in the limit of a large majority of heavy atoms. We highlight the effects due to correlations by making comparisons with previous mean-field results.
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