Inter-orbital spin-triplet superconductivity from altermagnetic fluctuations

Abstract: Altermagnetic (AM) fluctuations are a new class of collinear spin fluctuations whose role in mediating superconductivity faces a fundamental tension: their $\Gamma$-point peak favors intra-orbital spin-triplet pairing, while their spin compensation favors inter-orbital singlets. Here, we demonstrate that inversion-symmetry-broken AM fluctuations generically resolve this competition in favor of spin-triplet pairing. As a proof of concept, we study a minimal two-orbital model with two van Hove singularities. The broken inversion symmetry induces momentum-orbital locking: the same orbital dominates at opposite momenta, enhancing the triplet channel. Crucially, a subdominant fluctuation channel arising from inter-van-Hove nesting provides an internal Josephson coupling that locks the phase difference between triplet pairs on different orbitals. We find this coupling changes sign ($+$ to $-$) upon a crossover from AM-dominant to ferromagnetic-dominant fluctuations. The resulting $\pi$-phase difference manifests as a $\tau_z$-type order parameter, $c_{k,1\uparrow}c_{-k,1\uparrow} - c_{k,2\uparrow}c_{-k,2\uparrow}$. Although intra-orbital in the original basis, its orbital-nontrivial character, as manifested by its equivalence to inter-orbital pairing under rotation, defines a general \textit{inter-orbital spin-triplet superconductivity}. This state is distinct from the $\tau_0$-triplet pairing mediated by ferromagnetic fluctuations, as evidenced by the canceled intra-orbital supercurrent in a Josephson junction between them.