Superconductivity from a long-range interaction: a crossover between the electron gas and the lattice model

TL;DR

This paper investigates how long-range electron-electron interactions influence superconductivity, revealing a crossover from lattice-specific pairing symmetries to behaviors akin to the electron gas, depending on band filling and interaction range.

Contribution

It introduces an extended Hubbard model with long-range interactions and analyzes the resulting superconducting pairing symmetries using a simplified fluctuation-exchange approximation.

Findings

Charge susceptibility becomes comparable to spin susceptibility at low fillings.

p and s wave pairings dominate in dilute regimes.

d-wave pairing remains dominant away from half filling.

Abstract

We explore how the superconductivity arising from the on-site electron-electron repulsion will change when the repulsion is changed to a long-ranged, 1/r-like one by introducing an extended Hubbard model with the repulsion extending to distant (12th) neighbors. With a simplified fluctuation-exchange approximation, we have found for the square lattice that (i) as the band filling becomes dilute enough, the charge susceptibility becomes comparable with the spin susceptibility, where p and then s pairings become dominant, in agreement with the result for the electron gas by Takada, while (ii) the d-wave, which reflects the lattice structure, dominates well away from the half filling. All these can be understood in terms of the spin and charge structures along with the shape and size of the Fermi surface.