Absence of a BCS-BEC crossover in the cuprate superconductors

We examine key aspects of the theory of the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) crossover, focusing on the temperature dependence of the chemical potential, mu. We identify an accurate method of determining the change of mu in the cuprate high temperature superconductors from angle-resolved-photoemission data (along the 'nodal' direction), and show that mu varies by less than a few percent of the Fermi energy over a range of temperatures from far below to several times above the superconducting transition temperature, T-c. This shows, unambiguously, that not only are these materials always on the BCS side of the crossover (which is a phase transition in the d-wave case), but are nowhere near the point of the crossover (where the chemical potential approaches the band bottom).