Studies on Isotope Shift Exponent and Pressure Coefficient for Extended Superconductors within BCS Formalism

A tight-binding model comprising a hopping and an attractive interaction term was considered for high temperature superconductors. Explicit calculations on the effects of isotopic substitution of atoms and application of pressure on the transition temperatures were made in this work. Exact analytical expressions for the isotope-shift exponent (α) and pressure coefficient $(γ_P)$ of transition temperature $(T_C)$ considering the isotopic mass and pressure dependence of the hopping and attractive interaction strengths from a minimal model describing superconductivity were obtained. Theoretical predictions for α and $γ_P$ with proper choice of parameters are found to be qualitatively consistent with the results of the experiments of high $T_C$ oxides. The results depend on the band dispersion chosen.