Designer flat bands: Topology and enhancement of superconductivity

We construct quasi-one-dimensional topological and nontopological three-band lattices with a tunable band gap winding number of the flat band. Using full multiband mean field (MF) exact density matrix renormalization group (DMRG) calculations, we show explicitly how affects pairing superconductivity (SC) in Hubbard model attractive interactions. obtain excellent agreement between MF DMRG calculations. The SC weight ${D}_{s}$ on gapped topological, $W\ensuremath{\ne}0$, increases linearly interaction strength $U$ for low values slope that depends details compact localized state at $U=0$. As $U\ensuremath{\rightarrow}0$ ($W=0$), decays power law faster than quadratically but slower exponentially. In gapless case (flat touching above it), find (for both $W=0$ $W\ensuremath{\ne}0$) ${D}_{s}\ensuremath{\propto}{U}^{\ensuremath{\varphi}}$, $\ensuremath{\varphi}<1$. other words, $U$, thus favoring weak more case. Our results reestablish BCS quantum metric alone are insufficient to characterize coupling.