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

The superconducting transition temperature, T_c, can be calculated for practically all super-conducting 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 T_c 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 T_c under applied pressure. Using the Roeser–Huber approach, the structure-dependent different T_c ’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.