Symmetry-breaking perturbations in the Jahn-Teller-Hubbard model

We study the effect of symmetry-breaking perturbations in the multiorbital Hubbard model coupled to anisotropic Jahn-Teller phonons, which is relevant for the description of fulleride superconductors. This system is often approximated by a model with static antiferromagnetic (AFM) Hund's coupling, in which the coupling to the Jahn-Teller phonon is effectively described, but the retardation effect associated with phonon propagation is neglected. We compare the properties of the models with static AFM Hund's coupling and dynamical Jahn-Teller electron-phonon interaction by means of the Eliashberg theory. Considering the susceptibilities for the spin, magnetic orbital, electric orbital, and superconductivity, we reveal a qualitatively different behavior between the two models in the case of the magnetic orbital susceptibility. We further study the effect of a magnetic field on the $s$-wave spin-singlet superconducting state. In the presence of the field, the magnetic orbital susceptibility becomes nonzero due to a combination of multiorbital and retardation effects, while the spin susceptibility remains zero at low temperatures. By analyzing this phenomenon both numerically and analytically, we clarify that odd-frequency pairs induced by the magnetic field play a crucial role in the spin and orbital magnetic susceptibilities. Thus, the magnetic degrees of freedom produce interesting behaviors in the presence of retardation effects associated with electron-phonon coupling.