Absence of a BCS-BEC crossover in the cuprate superconductors

TL;DR

This paper investigates the BCS-BEC crossover in cuprate superconductors, demonstrating through experimental data that these materials remain on the BCS side and do not approach the crossover regime.

Contribution

The study introduces an accurate method to determine the chemical potential change from ARPES data and conclusively shows cuprates are always on the BCS side of the crossover.

Findings

Chemical potential varies less than a few percent of the Fermi energy across temperatures.

Cuprates are always on the BCS side, not near the crossover point.

No evidence of BCS-BEC crossover in 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, $\mu$. 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).