Strong Pairing Originated from an Emergent $\mathbb{Z}_2$ Berry Phase in La$_3$Ni$_2$O$_7$

The recent discovery of high-temperature superconductivity in La$_3$Ni$_2$O$_7$ offers a fresh platform for exploring unconventional pairing mechanisms. Starting with the basic argument that the electrons in $d_{z^2}$ orbitals nearly form local moments, we examine the effect of the Hubbard interaction $U$ on the binding strength of Cooper pairs based on a single-orbital bilayer model with intralayer hopping $t_{\|}$ and interlayer super-exchange $J_{\perp}$. By extensive density matrix renormalization group calculations, we observe a remarkable enhancement in binding energy as much as $10$-$20$ times larger with $U/t_\|$ increasing from $0$ to $12$ at $J_{\perp}/t_\|\sim 1$. We demonstrate that such a substantial enhancement stems from a kinetic-energy-driven mechanism. Specifically, a $\mathbb{Z}_2$ Berry phase will emerge at large $U$ due to the Hilbert space restriction (Mottness), which strongly suppresses the mobility of single particle propagation as compared to $U=0$. However, the kinetic energy of the electrons (holes) can be greatly restored by forming an interlayer spin-singlet pairing, which naturally results in a superconducting state even for relatively small $J_\perp$. An effective hard-core bosonic model is further proposed to estimate the superconducting transition temperature at the mean-field level.