We study the instabilities towards (exotic) superconductivity of mixtures of 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 $2\ifmmode\times\else\texttimes\fi{}2$ in size, but this nevertheless allows us to study the pairing instabilities, and their possible divergence, in the $s\ensuremath{-}$ and d-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.
In superconducting phases, repulsive interactions between the electrons usually lead to higher-angular momentum Cooper pairing. Here, the authors employ the weak-coupling renormalization group approach to study unconventional superconducting phases emerging in the extended, repulsive Hubbard model on paradigmatic two-dimensional lattices. Among their findings are extended regions of chiral topological superconductivity on the square, triangular, and honeycomb lattices. They provide detailed superconducting phase diagrams as well as the coupling strengths that quantify the corresponding critical temperatures depending on the band-structure parameters, band filling, and interaction parameters. The importance of the resolution and accuracy of the numerical integration for the method is discussed and a way to higher numerical efficiency provided.