Aspects of BCS to BEC “Crossover” as illustrated by fulleride superconductivity

Abstract The pioneering works by Eagles, Leggett, and Nozieres/Schmitt‐Rink [Eagles, Phys Rev, 1969, 186, 456; Leggett, In: Modern Trends in the Theory of Condensed Matter, Springer‐Verlag: Berlin, 1980; Nozieres and Schmitt‐Rink, Low Temp Phys, 1985, 59, 980] (reviewed and augmented by Randeria [Randeria, Bose‐Einstein Condensation, Cambridge University Press, Cambridge, 1995, p 255]) emphasize that in the limits of the models studied both at T = 0 and T ≠ 0, the “cross‐over” from a BCS‐type to a BEC‐type superconductor is continuous. The BCS and BEC “end points” seem to be well‐established. However, 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. Yet, considerable current literature is devoted to what appears to be more “singular‐type phenomena” such as quantum critical points, “stripe” formation, insulator to superconductor phase transitions, loss of validity of the Fermi liquid theory, etc. Using a connection we have made with “cold” atom fermion‐boson crossover theory [Chen, Stajic, Levin, 2005, e‐print cond‐mat/0508603], we can establish that the resonance previously discussed [Squire and March, Int J Quant Chem, 2006, 106, 3343] is a result of the crossing of the fermion band by the boson band. While the ground state appears to remain continuous, the paired energy gap becomes transformed. We discuss features of the resonance and the experimentally observed pre‐formed “BEC Cooper pair” formation, essential to the boson‐fermion resonance theory. In addition some of the various singular phenomena discussed above can be put more into perspective. Finally, in both limits the relation of characteristic lengths to the inverse Fermi momentum is strongly emphasized, as is the role of the chemical potential near the pseudogap regime. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007