Phonon-mediated superconducting transitions in layered cuprate superconductors

Abstract

A phonon-mediated $d$-wave BCS-like model is presented for a homologous series of layered cuprate superconductors. We show that the dependence of both the superconducting transition temperature ${T}_{c}$ and oxygen isotope exponent $\ensuremath{\alpha}$ on the doping level, number of $\mathrm{Cu}{\mathrm{O}}_{2}$ layers, pressure, and cation disorder in the model superconducting series $\mathrm{Hg}{\mathrm{Ba}}_{2}{\mathrm{Ca}}_{n\ensuremath{-}1}{\mathrm{Cu}}_{n}{\mathrm{O}}_{2n+2+\ensuremath{\delta}}$ can be well reproduced within one single theoretical framework. We also find that the theoretical model accounts well for the superconducting transitions in other homologous series such as the bismuth- and thallium-based family. Our results suggest that the interlayer coupling plays an important role in the significant enhancement of ${T}_{c}$ and in the systematic reduction of $\ensuremath{\alpha}$ in a layered homologous series.