Test for BCS-BEC Crossover in the Cuprate Superconductors

TL;DR

This paper proposes a test based on coherence length measurements to determine if cuprate superconductors exhibit BCS-BEC crossover behavior, aiming to clarify their fundamental pairing mechanism.

Contribution

It introduces a concrete experimental prediction linking coherence length behavior to BCS-BEC crossover in cuprates, encouraging systematic measurements.

Findings

Coherence length behavior near $T_c$ can indicate BCS-BEC crossover presence.

Measurements across the phase diagram can locate cuprates within the crossover spectrum.

The paper motivates further experiments to characterize $\xi_0^{ ext{coh}}$ in cuprates.

Abstract

In this paper we address the question of whether high-temperature superconductors have anything in common with BCS-BEC crossover theory. Towards this goal, we present a proposal and related predictions which provide a concrete test for the applicability of this theoretical framework. These predictions characterize the behavior of the Ginzburg-Landau coherence length, $\xi_0^{\text{coh}}$, near the transition temperature $T_{\text{c}}$, and across the entire superconducting $T_{\text{c}}$ dome in the phase diagram. That we are lacking a systematic characterization of $\xi_0^{\text{coh}}$ in the entire class of cuprate superconductors is perhaps surprising, as it is one of the most fundamental properties of any superconductor. This paper is written to motivate further experiments and, thus, address this shortcoming. Here we show how measurements of $\xi_0^{\text{coh}}$ contain direct indications for whether or not the cuprates are associated with BCS-BEC crossover and, if so, where within the crossover spectrum a particular superconductor lies.