(Color online) (a) Zero-temperature phase diagram of the checkerboard Hubbard model for small and (b) of on the checkerboard lattice. The two superconducting phases both have -wave symmetry and no nodal quasi-particles, but one is BCS-like (-BCS) and the other is a Bose condensate of preformed two-particle bound states (-BEC). The dashed lines indicate a crossover between them rather than a sharp phase transition. The two Fermi liquid phases (FL and ) are distinguished by the quantum numbers of the quasi-particles. The dotted curve with arrows in (b) represents the effective trajectory corresponding to the Hubbard model with fixed as a function of increasing .Reuse & Permissions
Figure 2
Schematic finite temperature phase diagram of the checkerboard model. Notice that this figure is not drawn to scale and the x-axis has been offset from zero. As in Fig. 1a, there is a crossover within the superconducting phase from a -BEC to a -BCS limit. For large enough there is a FL phase. Above , indicated by the top dashed curve, the effective theory breaks down. The lower dashed curve, , signifies the crossover between a normal Bose liquid of preformed pairs for and a high temperature state with little electron pairing for . The range is a pseudo-gap regime. This can be a broad regime since the energy scale of coherence between preformed pairs would be down to as indicated by the solid curve.Reuse & Permissions