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.
Highlights
We use the Roeser–Huber formalism [1,2,3,4] to calculate the superconducting transition temperature, Tc, of the superconducting elements in ambient conditions as well as under pressure
A relatively simple calculation procedure like the Roeser–Huber formalism, which requires only knowledge of the crystal structure and the basic electronic configuration with no free parameters, has clear advantages when being incorporated as a test in machine learning approaches to find new superconducting materials [19,20,21], because there is only a limited number of crystal structures to be considered
The basic idea of the Roeser–Huber formalism is the view of superconductivity being a resonance effect between the charge carrier wave (Cooper pairs with the de Broglie wavelength, λcc ) moving through the crystal lattice and a characteristic distance, x, within the crystal unit cell
Summary
We use the Roeser–Huber formalism [1,2,3,4] to calculate the superconducting transition temperature, Tc , of the superconducting elements in ambient conditions as well as under pressure. A relatively simple calculation procedure like the Roeser–Huber formalism, which requires only knowledge of the crystal structure and the basic electronic configuration with no free parameters, has clear advantages when being incorporated as a test in machine learning approaches to find new superconducting materials [19,20,21], because there is only a limited number of crystal structures to be considered. Given are the abbreviations of the names, the transition temperatures, Tc , and the applied pressure or some extra info for each element. All data given are taken from Refs. [6,7,8,9,10,11,12,13]
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