Single bipolaronic Transition in Jahn-Teller Model

We investigate the bipolaronic crossover and the pairing transition for a two-orbital model with Jahn-Teller coupling to a two-fold degenerate phonon mode. The evolution from weak to strong coupling is reminiscent of the behavior of the single-band Holstein model: The polaron crossover in which the electrons and phonons become strongly entangled occurs for a weaker coupling than the binding of bipolarons, which gives rise to a metal-insulator transition. Interestingly, a single bipolaronic transition takes place also when the two bands have significantly different bandwidths, as opposed to the case of repulsive Hubbard-like interactions for which an orbital-selective Mott transition has been reported. This behavior is related to the inter-orbital nature of the Jahn-Teller coupling.