Superconductivity in the doped bilayer Hubbard model

We study by the Gutzwiller approximation the melting of the valence-bond crystal phase of a bilayer Hubbard model at sufficiently large interlayer hopping. We find that a superconducting domain, with order parameter 𝑑𝑧2−𝑟2, 𝑧 being the interlayer direction and 𝑟 the intralayer one, is stabilized variationally close to the half-filled nonmagnetic Mott insulator. Superconductivity exists at half filling just at the border of the Mott transition and extends away from half filling into a whole region till a critical doping, beyond which it gives way to a normal-metal phase. This result suggests that superconductivity should be unavoidably met by liquefying a valence-bond crystal, at least when each layer is an infinite-coordination lattice and the Gutzwiller approximation becomes exact. Remarkably, this same behavior is well established in the other extreme of two-leg Hubbard ladders, showing it might be of quite general validity.