A Density-Functional-Perturbation-Theory Study of Superconducting Nb3Sn Under Uniaxial-Strain

The effects of strain on superconducting Nb$_3$Sn are of great interest because they cause significant changes in the performance of these materials during both cool-down and energisation of high field magnets and they give us an insight into the basic superconducting mechanism. There is a lot of experimental data describing these effects because this material is to be used in ITER, but a detailed first-principles understanding is not yet available. In this computational study, a unit cell of Nb$_3$Sn was subjected to a range of uni-axial strains and allowed to relax fully within a periodic density functional perturbation theory (DFPT) scheme. First order DFPT was then used to calculate the effects of electron-phonon coupling at each strain. The data obtained are compared with experimental measurements on single crystals as well as on wires made using both the ``powder in tube'' and ``bronze route'' methods. The calculated values for the strain dependence of the critical temperature ($T_C$) agree to within 20\% with the experimental data and the peak in $T_C$ found under compression may help improve our understanding of the experimental result that $T_C$ of the tetragonal phase is higher than that of the cubic phase.