Pairing in the Peierls/Su-Schrieffer-Heeger(SSH) model: From light spinful bipolarons to self-trapping of hard-core pairs and repulsive bipolarons

It is widely accepted that strong particle-phonon coupling generally makes the resulting polarons and bipolarons heavy, with masses increasing smoothly with the coupling strength with no self-trapping transitions. This is the characteristic behaviour in the Holstein and Fr{\"o}hlich models. Here, we study the one-dimensional Peierls/Su-Schrieffer-Heeger(SSH) model necessary for describing coupling of hopping to breathing-mode distortions in certain oxides, polyenes and quantum simulators based on ultracold lattice systems. We show that the Peierls interactions bind polarons into light bipolarons, which could undergo Bose-Einstein condensation at high temperatures. This proves that phonon-mediated high-Tc superconductivity is possible. We also find that for particles with hard-core statistics, interactions mediated by Peierls phonons are repulsive. The interplay of hard-core statistics and phonon-mediated hopping leads to a transition characterized by flattening of the bipolaron dispersion, suggestive of self-trapping. The repulsive phonon-mediated interactions also lead to a repulsively bound bipolaron state appearing above the two-polaron continuum. These results provide a specific path to utilize Peierls coupling to control superconductivity and quantum transport.