Strain-dependence of the superconducting critical temperature Tc in Al and Nb simple crystals from first-principles

In the past 20 years, efforts have been devoted to predict the critical current density $J_{c}$ of superconducting magnets based on the Nb$_{3}$Sn compound. The use of Nb$_{3}$Sn magnets for high-field applications has highlighted the dependence of $J_{c}$ on strain. We present calculations of the $T_{c}$-dependence of Al and Nb crystals on pressure, uni-axial and shear strains using the DFT \textit{PWscf} package from the Quantum-ESPRESSO distribution to evaluate the phonon linewidth and the \textit{el-ph} coupling parameter using very dense \textbf{\textit{k}}-space samplings of the IBZ. The superconducting critical T$_{c}$ is calculated by using the McMillan formula as a fit to the solution of the Migdal-Eliashberg equations. Favourable comparisons with available experimental data have been obtained and will be presented. The modelling of the $T_{c}$-dependence on strain in Nb$_{3}$Sn crystals is an ongoing effort. The potential for modelling the $T_{c}$-dependence on strain in Nb$_{3}$Sn is discussed. In this regard, recent advances in the implementation of the Wannier formalism give access to the sampling of the dense \textbf{\textit{k}}-point grids required to calculate fully-converged electron-phonon coupling quantities. This approach opens the possibility to extend the study of the $T_{c}$-dependence on strain to unit cells characterized by a higher number of atoms or electronic complexity.