Why Does Maximum Tc 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 \({T}_{c}^{max}\).