Strain dependence of critical superconducting properties of Nb3Sn with different intrinsic strains based on a semi-phenomenological approach

A semi-phenomenological approach, which combined the microscopic properties calculated by first-principles and macroscopic critical characteristics determined from empirical relations, is suggested to investigate the superconducting critical properties of the low temperature superconductor Nb3Sn with different intrinsic strain modes like uniaxial tension, shear and torsion deformations. Firstly, the microscopic properties of the electronic structure and density of state for Nb3Sn are numerically obtained by first-principles calculations using density-functional theory in the generalized gradient approximation. These are further incorporate with the macroscopic empirical relation of the unified scaling law for predicting critical parameters of the strained Nb3Sn superconductor. The superconducting critical profiles of critical temperature, magnetic field and current, in such a way, are achieved for Nb3Sn under different strains. The predictions on the critical parameters of the superconductor bulk in uniaxial tension/compression state exhibit obvious degradations and bell-shaped curves with maximum critical values at zero strain and a slight asymmetry between the tensile and compressive strains, which show quite good agreements with the experimental data. As for Nb3Sn under shear and torsion deformations, the similar degradations on critical parameters also are presented which are monotonously decreased with the applied strains. The first-principles calculations and results in this work are based on an assumption which the superconducting critical properties from the strain-induced variations in the electronic density of states. Furthermore, the modified critical surfaces of Nb3Sn, determined by the critical temperature, current and magnetic field dependence upon the applied different strains are depicted. The present study will be helpful to identify the scaling relation for the critical parameters and understanding the origin of strain sensitivity in Nb3Sn conductors.