Quantum Phase Transition Induced by a Preformed Pair in a Boson-Fermion Model of Fulleride Superconductivity

There continues to be enormous interest in the BCS to BEC transition as there still is no exact theory. We recently reported a revealing reinterpretation of the condensed phase Boson-Fermion Model (BFM) by comparing it to a cold atom formulation [1]. While the ground and singly excited states appear to remain continuous in all models we have examined, the collective modes contain a singularity due to a Feshbach resonance (tuned by doping) causing a breakdown of the Migdal theorem. As a result of vertex corrections, there is a fundamental change in the nature of the superconductivity due to the formation of preformed pairs as the previously suggested location [1] of a quantum critical point in the fulleride phase diagram is passed. The result is a quantum phase transition (QPT) between BCS and BEC-like (or Feshbach resonance) superconductivity (SC). We discuss features of the resonance and the role of the experimentally observed preformed pair formation in fullerides, essential to the Boson-Fermion Model (BFM), and often speculated since the work of Nozieres and Schmitt-Rink [17]. Here, we present arguments to establish a model of the preformed pair which can be favorably compared to a circular charge density wave (CDW) isolated on a fulleride molecule. The binding is much larger than a Cooper pair. The CDW seems to be stabalized by splitting of the Jahn-Teller active vibrational modes to reduce Coulomb repulsions. Our conclusions are: 1) the doping of two electrons into triply degenerate orbitals results in the experimentally observed singlet state (CDW); and 2) this CDW (preformed pair) has a dual role as doping is varied: suppression of BCS SC and enabling a Feshbach resonance form of SC.