Excitonic Stripe Order in the Two-Orbital Hubbard-Kanamori Model
Excitonic condensation and stripe formation are two distinct manifestations of electronic correlations. While excitonic order naturally arises in multi-orbital systems, stripe order is a prominent feature of doped correlated-electron models. Here, we investigate an excitonic analogue of stripe order in the two--orbital Hubbard-Kanamori model on the square lattice, characterized by a spatial modulation of inter-orbital particle-hole coherence and, in the orbital-parity-symmetric limit, spontaneous breaking of a relative orbital $\mathbb{Z}_2$ symmetry. Using unrestricted real-space Hartree-Fock calculations complemented by random-phase-approximation instability analysis, we determine how the Kanamori interactions select different excitonic channels. The sign of Hund's exchange controls the spin character of the condensate: ferromagnetic Hund coupling favors triplet excitonic order, whereas antiferromagnetic Hund coupling stabilizes singlet excitonic order. Upon doping, commensurate excitonic density waves develop incommensurate textures, including excitonic stripes and, in the triplet sector, spiral excitonic density waves. We further show that crystal-field splitting strongly reorganizes the excitonic instability by modifying inter-orbital nesting and can stabilize triplet excitonic order even in the absence of pair hopping. Our results establish excitonic stripes as a distinct symmetry-broken state of multi-orbital correlated systems and identify microscopic routes for their stabilization.