Calculation of the Superconducting Transition Temperature

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Abstract
An explicit expression is derived for the superconducting transition temperature in an isotropic super-conductor. The calculation includes three improvements over previous work. Firstly, strong-coupling effects are included; secondly, both normal and umklapp contributions are evaluated in detail in calculating the electron-phonon interaction; and thirdly, a more realistic approximation to the lattice is obtained by including a Coulomb pseudopotential and correcting the jellium ionic plasma frequency with the use of the measured sound velocity. The theory is applied to the case of the lanthanum selenide system, in which one can vary the electron concentration independently of other material parameters and measure the superconducting transition temperature as a function of this variation. The theory accounts very well for the observed transition temperatures over the whole measured range from 1 to 10°K.