We study the instabilities towards (exotic) superconductivity of mixtures of $\text{spin-}1/2$ fermions coupled to scalar bosons on a two-dimensional square lattice with the dynamical cluster approximation (DCA) using a numerically exact continuous-time Monte-Carlo solver. The Bogoliubov bosons provide an effective phononic bath for the fermions and induce a nonlocal retarded interaction between the fermions, which can lead to (exotic) superconductivity. Because of the sign problem the biggest clusters we can study are limited to $2\times 2$ in size, but this nevertheless allows us to study the pairing instabilities, and their possible divergence, in the $s-$ and $d\text{-wave}$ channels as well as the competition with antiferromagnetic fluctuations. At fermionic half filling we find that the $d$ wave is stable when the mediated interaction by the bosons is of the same order as the bare fermionic repulsion. Its critical temperature can be made as high as the maximum one for $s$ wave, which opens perspectives for its detection in a cold atom experiment.

• Received 11 August 2015

DOI:https://doi.org/10.1103/PhysRevB.92.184505