A theory of the strain-dependent critical field in Nb$_{3}$Sn, based on anharmonic phonon generation

We propose a theory to explain the strain dependence of the critical properties in A15 superconductors. Starting from the strong-coupling formula for the critical temperature, and assuming that the strain sensitivity stems mostly from the electron-phonon alpha F-2 function, we link the strain dependence of the critical properties to a widening of alpha F-2. This widening is attributed to the nonlinear generation of phonons, which takes place in the anharmonic deformation potential induced by the strain. Based on the theory of sum- and difference-frequency wave generation in nonlinear media, we obtain an explicit connection between the widening of alpha F-2 and the anharmonic energy. The resulting model is fit to experimental datasets for Nb$_{3}$Sn, and the anharmonic energy extracted from the fits is compared with first-principles calculations.