Local Plaquette Physics as Key Ingredient of High-Temperature Superconductivity in Cuprates

Abstract

A major pathway towards understanding complex systems is given by exactly solvable reference systems that contain the essential physics of the system. For the $t-t^{\prime }-U$ Hubbard model, the four-site plaquette is known to have a quantum critical point in the $U-\mu$ space where states with electron occupations $N=2,3,4$ per plaquette are degenerate [Phys. Rev. B {\bf 94}, 125133 (2016)]. We show that such a critical point in the lattice causes an instability in the particle-particle singlet d-wave channel and manifests some of the essential elements of the cuprate superconductivity. For this purpose we design an efficient superperturbation theory -- based on the dual fermion approach -- with the critical plaquette as the reference system. Thus, the perturbation theory already contains the relevant d-wave fluctuations from the beginning via the two-particle correlations of the plaquette. We find that d-wave superconductivity remains a leading instability channel under reasonably broad range of parameters. The next-nearest-neighbour hopping $t^{\prime }$ is shown to play a crucial role in a formation of strongly bound electronic bipolarons whose coherence at lower temperature results in superconductivity. The physics of the pseudogap within the developed picture is also discussed.

arXiv comment25 pages, 28 figures

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