This paper studies the normal (non‑superconducting) state of a model for bilayer nickelate materials and finds a new kind of pseudogap metal and a nearby quantum critical point with non‑Fermi‑liquid behavior. The work is theoretical. The authors use a simplified microscopic model and a numerical technique to map how the electronic state changes when they vary an interlayer spin coupling and the number of charge carriers (doping). A “pseudogap” here means a depletion of low‑energy electronic states without the usual signs of symmetry breaking.

The model, called a double Kondo lattice, represents each unit cell as two layers. Each layer has an itinerant electron band coming from a dx2−y2 orbital and a localized spin‑1/2 moment from a dz2 orbital. Those two kinds of degrees of freedom are coupled on each site by a ferromagnetic Kondo‑type coupling (written JK = −2JH). The localized spins on the two layers are further coupled by an antiferromagnetic interlayer exchange J⊥. The authors solve this model with single‑site dynamical mean‑field theory (DMFT) combined with a numerical renormalization group (NRG) impurity solver. This method gives controlled access to low‑energy spectral functions while treating interactions that are local within the unit cell.

The main result is a phase diagram with two distinct metallic Fermi liquid states when interlayer tunneling t⊥ is set to zero. In the overdoped region the system is a conventional Fermi liquid with a large Fermi surface. In the underdoped region it becomes a pseudogap metal that the authors call a “second Fermi liquid” (sFL). The sFL shows small hole pockets, very heavy quasiparticles (small quasiparticle residue and large effective mass), and a clear pseudogap in the spectral function. Remarkably, the sFL violates the perturbative form of the Luttinger theorem (a constraint linking Fermi surface volume to particle density) even though the calculation does not show symmetry breaking or fractionalized excitations. The transition between the two metals is continuous at t⊥=0 and sits in the universality class related to a two‑channel, two‑spin Kondo impurity model. The authors also present an intuitive ancilla‑fermion picture in which the auxiliary fermion acts like a spin‑polaron and produces a Kondo‑like resonance seen directly in the DMFT spectral data.