Octupolar Weyl superconductivity from electron-electron interaction

Weyl topological superconductivity (TSC) is an exotic superconducting state featuring topologically protected point gap nodes and Bogoliubov-Majorana Fermi arcs. However, its realization remains rare, often requiring complicated band structures or fine-tuned spin-orbit coupling. Here, we propose a universal and robust mechanism to generate Weyl TSC relying solely on 3D cubic lattice symmetry under repulsive electron-electron interaction. Standard group theory combined with Ginzburg-Landau analysis reveals that generalizing the [Formula: see text]-wave pairing in the 2D square lattice, typically driven by repulsive interactions, to a 3 dimensional (3D) cubic lattice naturally yields a chiral [Formula: see text] state. Unlike other time-reversal symmetry breaking pairings such as [Formula: see text] (for example, [Formula: see text]He-A) and [Formula: see text] under planar hexagonal symmetry, Cooper pairs with such a symmetry do not possess a net orbital angular momentum (OAM). Instead, they develop an octupolar [Formula: see text] component of OAM, which results in eight nodal points along the body diagonal directions, exhibiting an alternating distribution of monopole charges [Formula: see text]. This naturally constitutes an octupolar Weyl TSC with non-trivial topology. Employing the single-orbital cubic Hubbard model as a prototype, we utilize a weak-coupling approach within the random-phase approximation, along with a strong-coupling analysis based on slave-boson mean-field theory and variational Monte Carlo simulations. Our numerical results consistently confirm the emergence of the [Formula: see text] Weyl TSC, highlighting the universality of this interaction-driven symmetry-protected mechanism. This finding simplifies the search for Weyl TSC, suggesting potential realization in cubic-lattice correlated superconductors and in cold-atom quantum simulation of the 3D Hubbard model upon suppression of its Néel antiferromagnetic phase.