  Motivated by the presence of an extremely small electron pocket in the
electronic band structure of infinite-layer (IL) nickelate superconductors, we
systematically explore the superconducting (SC) properties of a two-dimensional
Hubbard model influenced by an additional conduction band with small occupancy
(dry Fermi sea). Our dynamic cluster quantum Monte Carlo calculations
demonstrated the unusual impact of this additional dry metallic layer, which
shifts the SC dome of the correlated Hubbard layer towards the overdoped
regime, namely the $d$-wave SC can be enhanced (suppressed) in the overdoped
(underdoped) regime. Simultaneously, the pseudogap (PG) crossover line shifts
to the same higher doping regime as well. Our analysis revealed the interplay
of the effective pairing interaction, pair-field susceptibility, and
antiferromagnetic spin fluctuation in the underlying non-monotonic physics. We
postulate on the physical picture of SC dome shift in terms of the Kondo-type
electron-hole binding in the case of a dry additional conduction band. Our
investigation provided valuable new insights on tuning the SC properties via
external dry bands.
