Flat-Band Enhanced Antiferromagnetic Fluctuations and Unconventional Superconductivity in Pressurized CsCr$_3$Sb$_5$

The interrelationship between flat bands and correlated phenomena such as unconventional superconductivity stands as an intriguing subject in condensed matter physics. Here, by first-principles calculations and random phase approximation analyses, we investigate the electronic structure, superconducting instability, as well as roles of the incipient flat bands in kagome superconductor CsCr$_3$Sb$_5$. Our calculations reveal strong antiferromagnetic spin fluctuations in CsCr$_3$Sb$_5$, which mediates two sets of spin-singlet superconducting orders with $s_{\pm}$- and ($d_{xy}$, $d_{x^2-y^2}$)-wave symmetries. Under the dominance of local Coulomb interactions, the unoccupied incipient flat bands are shown to be crucial for the momentum dependence of spin fluctuations and thus the superconductivity. Our further analyses unveil a sublattice-momentum-coupling-driven mechanism for this momentum-dependent enhancement of the fluctuations, which provides us a new perspective for future studies of geometrically frustrated systems.