Band-structure effects on superconductivity in Hubbard models

TL;DR

This paper investigates how different band structures affect superconductivity in the Hubbard model, revealing transitions in pairing symmetry and potential relevance to various materials like cuprates and iron-based superconductors.

Contribution

It provides a detailed analysis of band-structure effects on pairing symmetry and transition temperatures in the weak-coupling limit of the Hubbard model, highlighting new phase transitions and degeneracies.

Findings

Smooth evolution from d-wave to near-degenerate p- and d-wave states with nematicity

Phase transition from d-wave to s±-wave in bilayer systems

Charge-density-wave order alters pairing symmetry from d_{x^2-y^2} to d_{xy}

Abstract

We study the influence of the band structure on the symmetry and superconducting transition temperature in the (solvable) weak-coupling limit of the repulsive Hubbard model. Among other results we find: 1) As a function of increasing nematicity, starting from the square lattice (zero nematicity) limit where nodal d-wave state is strongly preferred, there is a smooth evolution to the quasi-1D limit, where a striking near-degeneracy is found between a p-wave- and a d-wave-type paired states with accidental nodes on the quasi-one-dimensional Fermi surfaces---a situation which may be relevant to the Bechgaard salts. 2) In a bilayer system, we find a phase transition as a function of increasing bilayer coupling from a d-wave to an $s_{\pm}$-wave state reminiscent of the iron-based superconductors. 3) When an antinodal gap is produced by charge-density-wave order, not only is the pairing scale reduced, but the symmetry of the pairs switches from $d_{x^2-y^2} to $d_{xy}$; in the context of the cuprates, this suggests that were the pseudo-gap entirely due to a competing order, this would likely cause a corresponding symmetry change of the superconducting order (which is not seen in experiment).