Theoretical calculation of Tc for lead

2014 Using our ab initio band structure results, we calculate the transition temperature of Pb according to the Gaspari-Gyorffy theory. The calculated value is half the experimental one. The discrepancy is attributed to the rigid muffin tin approximation. A simple method with no adjustable parameters is developed to account for this approximation. The new transition temperature is in excellent agreement with experiment. LE JOURNAL DE PHYSIQUE LETTRES TOME 40, 15 JUIN 1979, Classification Physics Abstracts 74.55 74.70G 74.90 Following the work of McMillan [1], which relates in a practical way the superconducting transition temperature T~ to microscopic quantities, a large amount of research has been reported along those lines. In particular, the theory of Gaspari and Gyorffy [2, 3], which we employ here, was designed especially for transition metals. However, as we shall illustrate below, this theory properly corrected can give very good estimates of the electron-phonon interaction ’1 for normal metals like lead as well. The parameter ~, which together with the average phonon frequency w2 ~, [1, 4] defines 7~, can be expressed in the Gaspari-Gyorffy theory in terms of partial densities of states and phase shifts readily available from traditional band structure calculations. In the first stage of this work we have determined, within the Rigid Muffin Tin Approximation (RMTA), the quantity ’1 using our self-consistent ab initio band calculation. The latter includes relativistic effects, such as the mass velocity and Darwin corrections,