Unconventional superconductivity in the extended Hubbard model: Weak-coupling renormalization group

TL;DR

This paper uses weak-coupling renormalization group methods to explore unconventional and topological superconducting phases in extended Hubbard models on various 2D lattices, revealing diverse pairing symmetries and phase diagrams.

Contribution

It introduces a comprehensive analysis of superconducting phases considering longer-range hoppings and non-local interactions, including detailed phase diagrams for multiple lattice types.

Findings

Superconducting solutions found for all irreducible representations.

Identification of extended regions of chiral topological superconductivity.

Quantitative relation between coupling strengths and critical temperatures.

Abstract

We employ the weak-coupling renormalization group approach to study unconventional superconducting phases emerging in the extended, repulsive Hubbard model on paradigmatic two-dimensional lattices. Repulsive interactions usually lead to higher-angular momentum Cooper pairing. By considering not only longer-ranged hoppings, but also non-local electron-electron interactions, we are able to find superconducting solutions for all irreducible representations on the square and hexagonal lattices, including extended regions of chiral topological superconductivity. For the square, triangular and honeycomb lattices, we provide detailed superconducting phase diagrams as well as the coupling strengths which quantify the corresponding critical temperatures depending on the bandstructure parameters, band filling, and interaction parameters. We discuss the sensitivity of the method with respect to the numerical resolution of the integration grid and the patching scheme. Eventually we show how to efficiently reach a high numerical accuracy.