The effects of disorder on the normal state and superconducting properties of Nb$_3$Sn

The effect of disorder on the normal state resistivity and the superconducting properties of Nb${}_{3}$Sn is explored in a combination of ab initio calculations and microscopic theory. The crystal symmetry is calculated to be preferentially tetragonal at a normal state resistivity below 27.0 ± 1.4 $\mu {\rm{\Omega }}\mathrm{cm}$, and preferentially cubic above this value, which is shown to be consistent with the experimentally observed transition point. The phonon density of states, the Eliashberg spectrum ${\alpha }^{2}(\omega )F(\omega )$, the electron–phonon coupling constant, the characteristic frequency, the critical temperature T c, and the upper critical magnetic field at 0 K ${H}_{{\rm{c}}2}(0)$ are calculated over a large normal state resistivity range and shown to be consistent with experimental observations. The high degree of consistency between the calculation results and experimental observations is a strong indication that the calculation approach utilized here, a combination of ab initio calculations and microscopic theory, is a useful tool for understanding the superconducting and normal state properties of Nb${}_{3}$Sn.