  Full or empty narrow bands near the Fermi level are known to enhance
superconductivity by promoting scattering processes and spin fluctuations.
Here, we demonstrate that doublon-holon fluctuations in systems with
half-filled narrow bands can similarly boost the superconducting $T_c$. We
study the half-filled attractive bilayer Hubbard model on the square lattice
using dynamical mean-field theory. The band structure of the noninteracting
system contains a wide band formed by bonding orbitals and a narrow band formed
by antibonding orbitals, with bandwidths tunable by the inter-layer hopping.
The shrinking of the narrow band can lead to a substantial increase in the
superconducting order parameter and phase stiffness in the wide band. At the
same time, the coupling to the wide band allows the narrow band to remain
superconducting -- and to reach the largest order parameter -- in the flat band
limit. We develop an anomalous worm sampling method to study superconductivity
in the limit of vanishing effective hopping. By analyzing the histogram of the
local eigenstates, we clarify how the interplay between different interaction
terms in the bonding/antibonding basis promotes pair fluctuations and
superconductivity.
