  Heusler compounds have always attracted a great deal of attention from
researchers thanks to a wealth of interesting properties for technological
applications. They are intermetallic ductile compounds, and some of them have
been found to be superconducting. With this in mind, we perform an extensive
study of the superconducting and elastic properties of the cubic (full-)Heusler
family. Starting from thermodynamically stable compounds, we use ab initio
methods for the calculation of the phonon spectra, electron-phonon couplings,
superconducting critical temperatures and elastic tensors. By analyzing the
statistical distributions of these properties and comparing them to
anti-perovskites we recognize universal behaviors that should be common to all
conventional superconductors while others turn out to be specific to the
material family. The resulting data is used to train interpretable and
predictive machine learning models, that are used to extend our knowledge of
superconductivity in Heuslers and to provide an interpretation of our results.
In total, we discover a total of 8 hypothetical materials with critical
temperatures above 10 K, to be compared with the current record of Tc = 4.7 K
in this family. Furthermore, we expect most of these materials to be highly
ductile, making them potential candidates for the manufacture of wires and
tapes for superconducting magnets.
