Preformed pair induced quantum phase transition in fulleride superconductivity

Abstract There continues to be enormous interest in the BCS to BEC transition. While the BCS and BEC “end points” seem to be well‐established, in the intermediate region—home to fulleride and high temperature superconductors—considerable extrapolation of the models must be done as there still is no exact theory. Last year we reported a revealing reinterpretation of the Boson–Fermion model (BFM) by comparing it to the “cold” atom formulation. While the ground and singly excited states appear to remain continuous in all models we have examined, the collective modes due to a Feshbach resonance (tuned by doping) cause a breakdown of the Migdal theorem, thereby transforming the nature of the superconductivity. 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 (Squire and March, Int J Quantum Chem 2007, 107, 3013) of a quantum critical point in the fulleride phase diagram is passed. The result is a quantum phase transition between BCS and BEC superconductivity (SC) in the BFM. We discuss features of the resonance and the experimentally observed preformed pair formation in fullerides, essential to the BFM, and often speculated since the work of Nozieres and Schmitt–Rink (J Low Temp Phys 1985, 59, 980). Here we present arguments to establish a model of the preformed pair which can be favorably compared with a circular charge density wave (CDW) isolated on a fulleride molecule due to Coulomb splitting of the Jahn–Teller active H g vibrational modes. Our conclusions are: (1) the doping of two electrons into triply degenerate t 1u orbitals results in the experimentally observed singlet state (CDW); and (2) this CDW (preformed pair) results in suppression of BCS SC and enables the Feshbach resonance. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008