Interplay of orbital-selective Mott criticality and flat-band physics in La$_3$Ni$_2$O$_6$

Superconductivity in nickelates apparently takes place in two different Ni oxidation regimes, namely either for infinite-layer-type compounds close to Ni$^{+}$, or for Ruddlesden-Popper materials close to Ni$^{2+}$. The reduced La$_3$Ni$_2$O$_6$ bilayer with a nominal Ni$^{1.5+}$ oxidation state may therefore serve as a normal-state mediator between the two known families of $3d^8$-like and $3d^9$-like superconducting nickelates. Using first-principles many-body theory, we explain its experimental 50\,meV charge gap as originating from a new type of correlated (quasi-)insulator. Flat-band electrons of Ni-$d_{z^2}$ character become localized from scattering with orbital-selective Mott-localized Ni-$d_{x^2-y^2}$ electrons, by trading in residual hopping energy for a gain in local exchange energy in a ferromagnetic Kondo-lattice scenario. Most importantly, the flat-band electrons offer another route to unconventional superconductivity in nickelates at ambient pressure.