Calculation of Tc of Superconducting Elements with the Roeser–Huber Formalism

Abstract

The superconducting transition temperature, Tc, can be calculated for practically all superconducting elements using the Roeser–Huber formalism. Superconductivity is treated as a resonance effect between the charge carrier wave, i.e., the Cooper pairs, and a characteristic distance, x, in the crystal structure. To calculate Tc for element superconductors, only x and information on the electronic configuration is required. Here, we lay out the principles to find the characteristic lengths, which may require us to sum up the results stemming from several possible paths in the case of more complicated crystal structures. In this way, we establish a non-trivial relation between superconductivity and the respective crystal structure. The model enables a detailed study of polymorphic elements showing superconductivity in different types of crystal structures like Hg or La, or the calculation of Tc under applied pressure. Using the Roeser–Huber approach, the structure-dependent different Tc’s of practically all superconducting elements can nicely be reproduced, demonstrating the usefulness of this approach offering an easy and relatively simple calculation procedure, which can be straightforwardly incorporated in machine-learning approaches.