A15 compounds, HTSC and strong coupling superconductors

We suggest that it is possible to understand the origin of high T$_{C}$ in the framework of strong coupling theory of superconductors. An exploratory investigation of materials with promising structural or electronic motifs is presented. The electron-phonon coupling constant $\lambda $ has been calculated for A15 compounds assuming the width of the $\Gamma_{12}$ band as 80 meV. $\lambda $ has been found to be inversely proportional to the molecular weight. The analysis is based on the numerically derived equation for T$_{C}$ from strong coupling theory for superconductivity by McMillan. The Coulomb pseudopotential $\mu^{\ast }$ has been found to be negative for YBa$_{2}$Cu$_{3}$O$_{7}$. The T$_{C}$ of YBa$_{2}$(Cu$_{1-x}$Zn$_{x})_{3}$O$_{7}$ decreases linearly from 89 K to the nonsuperconducting state at a rate of about 15 K/at{\%} of Zn substitution. Similar analysis YBa$_{2}$(Cu$_{1-x}$Zn$_{x})_{3}$O$_{7}$ shows that $\mu^{\ast }$ changes sign from negative to positive as T$_{C}$ reduces. The isotope effect exponent $\alpha $ is found to go through a maximum as T$_{C}$ decreases and is found to be equal to 1/2 for x$=$0.026 which can be verified experimentally.