Dynamical mean-field theory for pairing and metal-insulator transitions in the Holstein model away from half-filling

We investigate the pairing and metal-insulator transitions of the Holstein model away from half-filling in infinite dimensions. The Holstein model treats the electron-phonon coupling g on a site and can be mapped to the attractive Hubbard model as the phonon frequency ω₀ increases to infinity. Here, we focus on the normal state in which the superconducting order is not allowed, and present the phase diagram within the dynamical mean-field theory in combination with Wilson's numerical renormalization group technique. We present the first order pairing transition between the Fermi liquid metal (M) and a non-Fermi liquid spin gap metal (SGM) of bound pairs and a metal-insulator transition between M and a spin gap bipolaron insulator (BPI) via coexisting regions. Along the phase boundary of the coexisting M and SGM region, a soft phonon mode coupled to the pairing instibility appears and the quasiparticle weight of the M phase vanishes.