Origin of the enhanced Nb3Sn performance by combined Hf and Ta doping

Coexistence of superconductivity and charge density wave instability in A15-Nb3Sn

A15-type compound Nb3Sn has attracted much attention due to its relatively high critical temperature and critical field of superconductivity, making it a leading material for superconducting applications. In this study, we investigate the structural instability and superconductivity of Nb3Sn under hydrostatic pressure using first-principles calculations. We determine the electronic properties, phonon dispersion, electron-phonon coupling and the superconducting gap for Nb3Sn at pressures ranging from ambient to 9 GPa. Our results show that a significant electron density is present near the Fermi level due to the van Hove singularity, indicating the strong electron-phonon coupling. The phonon dispersion of Nb3Sn exhibits Kohn anomalies at three different wave vectors at a lower temperature. Moreover, above a pressure of 6 GPa, the charge density wave (CDW) instability disappeared, suggesting that pressure inhibits the CDW phase. The superconducting temperature is predicted to be TC = 18.62 K under ambient conditions, which is well consistent with the experimental results. We find that both the CDW and superconducting orders respond to pressure, with their transition temperatures decreasing as the pressure increases below 6 GPa. Above 6 GPa, the superconducting transition temperature increases slowly with pressure. Our results suggest that the instability in Nb3Sn is driven by the softening of the phonon modes due to the CDW caused by strong electron-phonon coupling. Therefore, the CDW phase and superconducting phase of Nb3Sn coexist at low pressure.

Characteristic Length for Pinning Force Density in Nb3Sn

The pinning force density, Fp, is one of the main parameters that characterize the resilience of a superconductor to carrying a dissipative-free transport current in an applied magnetic field. Kramer (1973) and Dew-Hughes (1974) proposed a widely used scaling law for this quantity, where one of the parameters is the pinning force density maximum, Fp,max, which represents the maximal performance of a given superconductor in an applied magnetic field at a given temperature. Since the late 1970s to the present, several research groups have reported experimental data on the dependence of Fp,max on the average grain size, d, in Nb₃Sn-based conductors. Fp,maxd datasets were analyzed and a scaling law for the dependence Fp,maxd=A×ln1/d+B was proposed. Despite the fact that this scaling law is widely accepted, it has several problems; for instance, according to this law, at T=4.2 K and d≥650 nm, Nb₃Sn should lose its superconductivity, which is in striking contrast to experiments. Here, we reanalyzed the full inventory of publicly available Fp,maxd data for Nb₃Sn conductors and found that the dependence can be described by the exponential law, in which the characteristic length, δ, varies within a remarkably narrow range of δ=175±13 nm for samples fabricated using different technologies. The interpretation of this result is based on the idea that the in-field supercurrent flows within a thin surface layer (thickness of δ) near grain boundary surfaces (similar to London's law, where the self-field supercurrent flows within a thin surface layer with a thickness of the London penetration depth, λ, and the surface is a superconductor-vacuum surface). An alternative interpretation is that δ represents the characteristic length of the exponential decay flux pinning potential from the dominant defects in Nb₃Sn superconductors, which are grain boundaries.