Effective Masses in Zr-Doped Superconducting Ceramic SrTiO3

An analysis is made of published experimental results on superconducting transition temperature as a function of carrier concentration and on magnetic field penetration depths in Zr-doped ceramic SrTi${\mathrm{O}}_3$. From the penetration-depth results it is deduced that the ratio of effective masses $m_3$ and $m_1$ for 3% and 1% of Ti ions replaced by Zr satisfies $\left(\frac{m_3}{m_1}\right)\simeq 1.48$ if Zr ions are the main scattering centers. Using a model involving screened electron-electron interaction via intervalley phonons of energy 0.0497 eV modified by intervalley Coulomb repulsion and by intravalley effects, it is shown that the transition-temperature data can be fitted fairly well with mass changes of the above magnitude, provided that the ratio of phonon-induced to Coulomb intervalley interactions is postulated to increase by about 5% for each percent of Zr doping. It is argued that the large mass increases may imply that a crossing of levels associated with small and large mass states is taking place as Zr is added. The possibility of superconductivity at very low carrier concentrations in specimens with 3% Zr content is discussed.