Superconductivity in the two-dimensional $t$-$t'$-Hubbard model

TL;DR

This paper uses a renormalization group approach to identify conditions for d-wave superconductivity in the 2D Hubbard model, highlighting the importance of next-to-nearest neighbor hopping in pairing and competition with antiferromagnetism.

Contribution

It introduces a renormalization group method to analyze superconductivity in the 2D Hubbard model and elucidates the role of $t'$ in pairing and magnetic competition.

Findings

D-wave pairing instability occurs in the studied regime.

A sizable $t'$ enhances the pairing gap.

Superconductivity competes with antiferromagnetism depending on $t'$.

Abstract

Using a recently developed renormalization group method for fermionic superfluids, we determine conditions for d-wave superconductivity in the two-dimensional Hubbard model at moderate interaction strength, and we compute the pairing gap in the superconducting regime. A pairing instability signaled by a divergent flow in the Cooper channel leads to a superconducting state in all studied cases. The next-to-nearest neighbor hopping $t'$ plays a crucial role in the competition between antiferromagnetism and superconductivity. A sizable $t'$ is necessary to obtain a sizable pairing gap.