Enhanced correlations and superconductivity in weakly interacting partially flat-band systems: A determinantal quantum Monte Carlo study

Motivated by recent experiments realizing correlated phenomena and superconductivity in two-dimensional (2D) van der Waals devices, we consider the general problem of whether correlation effects may be enhanced by modifying band structure while keeping a fixed weak interaction strength. Using determinantal quantum Monte Carlo, we study the 2D Hubbard model for two different band structures: a regular nearest-neighbor tight-binding model and a partially flat-band structure containing a nondispersing region, with identical total noninteracting bandwidth ${W}_{\mathrm{tot}}$. For both repulsive and attractive weak interactions ($|U|\ensuremath{\ll}{W}_{\mathrm{tot}}$), correlated phenomena are significantly stronger in the partially flat model. In the repulsive case, even with $U$ being an order of magnitude smaller than ${W}_{\mathrm{tot}}$, we find the presence of a Mott insulating state near half filling of the flat region in momentum space. In the attractive case, where generically the ground state is superconducting, the partially flat model exhibits significantly enhanced superconducting transition temperatures. These results suggest the possibility of engineering correlation effects in materials by tuning the noninteracting electronic dispersion.