  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.
