Superconductivity in the doped bilayer Hubbard model

TL;DR

This paper demonstrates that doping a valence bond crystal in a bilayer Hubbard model can induce superconductivity near the Mott transition, with a specific order parameter, extending over a significant doping range.

Contribution

It reveals the emergence of superconductivity in the doped bilayer Hubbard model near the Mott transition, using the Gutzwiller approximation, highlighting a potentially general phenomenon.

Findings

Superconductivity with $d_{z^2-r^2}$ order parameter is stabilized near the Mott insulator.

Superconductivity extends from half-filling to a critical doping level.

The behavior is consistent with that in two-leg Hubbard ladders.

Abstract

We study by the Gutzwiller approximation the melting of the valence bond crystal phase of a bilayer Hubbard model at sufficiently large inter-layer hopping. We find that a superconducting domain, with order parameter $d_{z^2-r^2}$, $z$ being the inter-layer direction and $r$ the intra-layer one, is stabilized variationally close to the half-filled non-magnetic 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.