Superconductivity in single- and multi-band Hubbard models: can we optimise them?

We can capture various unconventional high-Tc superconductors basically either with single-band models or multiband ones. We can theoretically explore how we can optimise them for higher Tc's. There, "multiband" should not be confused with "multiorbital" systems, for which I shall compare merits and demerits of the two classes from both quantum many-body algorithms and materials-science points of view. For the former, I shall mention the dynamical vertex approximation to fathom the correlation between the electronic structure and the superconductivity and to search for enhanced Tc's. For the latter, I shall present various ideas that include "flat-band" superconductivity.