Superconductivity in Inhomogeneous Hubbard Models

TL;DR

This paper investigates the low temperature phases of highly inhomogeneous Hubbard models, revealing a transition from semiconductor-like behavior to nodeless d-wave superconductivity and eventually to a Fermi liquid as interaction strength varies.

Contribution

It introduces a controlled perturbative method to analyze inhomogeneous Hubbard models and uncovers distinct superconducting and metallic phases depending on the model and interaction strength.

Findings

Dimerized model behaves like a doped semiconductor with smooth parameters.

Checkerboard model exhibits nodeless d-wave superconductivity for certain U.

Transition to Fermi liquid phase at large U > U_c.

Abstract

We present a controlled perturbative approach to the low temperature phase diagram of highly inhomogeneous Hubbard models in the limit of small coupling, $t'$, between clusters. We apply this to the dimerized and checkerboard models. The dimerized model is found to behave like a doped semiconductor, with a Fermi-liquid groundstate with parameters ({\it e.g.} the effective mass) which are smooth functions of the Hubbard interaction, $U$. By contrast, the checkerboard model has a nodeless d-wave superconducting state (preformed pair condensate, $d$-BEC) for $0 < U < U_c$, which smoothly crosses over to an intermediate BCS-like superconducting phase ($d$-BCS), also with no nodal quasi-particles, for $|U - U_c| < {\cal O}(t^\prime)$, which gives way to a Fermi liquid phase at large $U > U_c = 4.58$.