We calculate, to second order in the scattering length between two fermions, the Landau quasiparticle interaction for a low-density mixture of two fermion species with unequal densities at temperature zero. From the Landau parameters we evaluate the energy density and find agreement with the result of Kanno [Prog. Theor. Phys. 44, 813 (1970)0033-068X10.1143/PTP.44.813]. The calculations are then extended to the case of two fermion components with different total densities, each with two spin components, a situation of interest in nuclear physics and astrophysics, where the species are neutrons and protons. An interesting finding is that, for low proton concentrations, x≪1, the leading term in the energy density, beyond the x5/3 contribution from the kinetic energy and the x2 one due to the two-body interaction in the mean-field approximation, varies as x7/3lnx. This is to be contrasted with the higher powers of x implicit in many phenomenological energy-density functionals employed in nuclear physics, such as those of the Skyrme type.