Absence of a BCS-BEC crossover in the cuprate superconductors

Abstract

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, $\hat{I}¼$. We identify an accurate method of determining the change of $\hat{I}¼$ in the cuprate high temperature superconductors from angle-resolved-photoemission data (along the "nodal" direction), and show that $\hat{I}¼$ 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).

6 pages, 5 figures