Weak-coupling superconductivity in an anisotropic three-dimensional repulsive Hubbard model

TL;DR

This paper explores the phase diagram of a weakly coupled three-dimensional repulsive Hubbard model, revealing multiple superconducting phases, including Weyl superconductors with broken time-reversal symmetry.

Contribution

It provides a comprehensive analysis of the superconducting phases in a 3D Hubbard model, identifying new competing order parameters and the emergence of Weyl superconductivity.

Findings

Identification of five types of p- and d-wave orders.

Discovery of Weyl superconductors with broken time-reversal symmetry.

Phase diagram connecting 2D and 3D Hubbard models.

Abstract

We study a three-dimensional single-band repulsive Hubbard model at weak coupling. We establish the superconducting phase diagram in the parameter space of the chemical potential and the out-of-plane hopping strength. The model continuously connects the Hubbard model in two and three dimensions. We confirm previously-established results in these limits, and identify a rich structure of competing order parameters in between. Specifically, we find five types of $p$- and $d$-wave orders. In several regions of the phase diagram, even when the Fermi surface is a corrugated cylinder, the ground state is a time-reversal-symmetry-breaking superconductor with nodes, i.e. a Weyl superconductor.