An Exactly Solvable Model of Phase-Fluctuating Superconductivity in Cuprates: The Role of Partially Flat Bands

TL;DR

This paper presents an exactly solvable Hubbard-like model for cuprates that captures phase fluctuations and the pseudogap phase, revealing the role of flat bands in shaping the superconducting dome and phase stability.

Contribution

It introduces a novel exactly solvable model incorporating phase fluctuations and flat bands, providing insights into the doping-dependent superconductivity in cuprates.

Findings

Dome-shaped d-wave superconducting region with optimal doping near quantum critical point.

Partially flat band influences phase fluctuations, stabilizing d_{x^2-y^2}-wave pairing.

Discontinuity in the superconducting dome indicates a transition in phase fluctuation strength.

Abstract

Utilizing an exactly solvable Hubbard-like model that exhibits a pseudogap (PG) phase and a partially flat band, we perform self-consistent microscopic calculations of the superconductivity (SC) in cuprates, incorporating both thermal and zero-point superconducting phase fluctuations in the presence of long-range Coulomb interactions. The results reveal an important role of the partially flat band in determining phase-fluctuating SC as well as several key features that are consistent with experimental observations. Specifically, we find a dome-shaped $d$-wave superconducting region in the temperature-doping phase diagram with the optimal doping point located near the quantum critical point between the PG and the metallic phases. Near the optimal doping, the partially flat band suppresses and amplifies the fluctuation-induced destructing effect on the $d_{x^2-y^2}$- and $d_{xy}$-wave pairing, respectively, ensuring an absolutely dominant $d_{x^2-y^2}$-wave SC. While the phase fluctuations of the $d_{x^2-y^2}$-wave SC are relatively weak around optimal doping, they become significant in both underdoped and overdoped regimes. We then identify a discontinuity on the superconducting dome in underdoped regime that results from a transition from a strong- to a weak-phase-fluctuating state as doping approaches the optimal point.