Why Does Maximum T_c Occur at the Crossover From Weak to Strong Electron–phonon Coupling in High-temperature Superconductors?

Abstract

In cuprate superconductors, a pronounced maximum of superconducting ${T}_{c}^{max}$ is observed in compounds that have an in-plane Cu–O distance ${a}_{Cu-O}$ close to $\sim 1.92$ angstroms. On the other hand, direct measurements of the electron–phonon coupling $\lambda \langle {\omega }^{2}\rangle$ as a function of ${a}_{Cu-O}$ show a clear linear correlation, implying that ${T}_{c}^{max}$ is a strongly non-linear function of $\lambda \langle {\omega }^{2}\rangle$. Conventional superconductivity theories based on the electron–phonon interaction predict a monotonic dependence of ${T}_{c}^{max}$ on $\lambda \langle {\omega }^{2}\rangle$, which makes them incompatible with the observed behavior. The observed crossover behavior as a function of $\lambda \langle {\omega }^{2}\rangle$ suggests that ${T}_{c}^{max}$ occurs at the crossover from weak to strong coupling, which is also associated with the onset of carrier localization. A coexistence, with a dynamical exchange of localized and itinerant carriers in a two-component superconductivity scenario are in agreement with the observed anomalous behavior and are suggested to be the key to understanding the mechanism for achieving high ${T}_{c}^{max}$.