Vibrational Andreev bound states in magnetic molecules

We predict the existence of vibrational Andreev bound states in deformable magnetic molecules on superconducting surfaces. We discuss the Anderson impurity model with electron-phonon coupling to a realistic anharmonic vibrational mode that modulates the tunneling barrier and show that the vibronic features are spectroscopically most visibile near the transition point between the Kondo-screened singlet and the unscreened doublet ground state. We find competing tendencies between phonon hardening due to anharmonicity and softening due to coupling to electrons, contrary to the Anderson-Holstein model and other models with harmonic local phonon mode where the vibrational mode is always softened. In addition, we find that the singlet and doublet many-body states may experience very different effective phonon potentials.