Strong pairing from doping-induced Feshbach resonance and second Fermi liquid through doping a bilayer spin-one Mott insulator: application to La$_3$Ni$_2$O$_7$: Part II

We study the physics of doping a bilayer spin-one Mott insulator with S = 1 moment formed by d_{z^2} and d_{x^2−y^2} orbitals, motivated by the superconducting La_3Ni_2O_7. We argue that the minimal model should be the type II t-J model proposed by the two of us. Through DMRG calculation of the model in a two-leg ladder configuration (Lz = 2, Ly = 1, Lx → ∞), we find that the pairing gap increases with hole doping x (per site per layer) across x = 0.5 and then decreases, in contrast to the conventional one-orbital t-J model. To capture the essential physics, we propose a new t-J model (dubbed as the ESD-t-J model) containing empty, singly occupied, and doubly occupied states of holes at each rung. Through a generalized slave boson theory, we obtain the phase diagram for the square lattice in the entire range of doping x ∈ [0, 1]. We identify two distinct symmetric and featureless Fermi liquids as normal states: (1) A conventional Fermi liquid (FL) in the x > 0.5 regime with Fermi surface volume per spin per layer AF S = (1−x )/2 . (2) A second Fermi liquid (sFL) in the range x ∈ (0, 0.5) with Fermi surface volume AF S = − x/2 . The sFL phase can be viewed as a symmetric pseudogap metal and is beyond any weak coupling description. In the underdoped regime with x close to 0 or 1, we also obtain an effective fermion-boson model with a gapped virtual cooper pair, which causes pairing instability of the sFL and FL phase with the inter-layer s ′ -wave pairing symmetry. Moving towards the overdoped regime around x = 0.5, the energy of the gapped cooper pair must go down due to filling constraint and induces a Feshbach resonance and the Bardeen–Cooper–Schrieffer (BCS) to the Bose–Einstein condensation (BEC) crossover tuned by doping.