Thermodynamic approach for enhancing superconducting critical current performance

The addition of artificial pinning centers has led to an impressive increase in critical current density ($J_{\rm c}$) in a superconductor, enabling record-breaking all-superconducting magnets and other applications. $J_{\rm c}$ has reached $\sim 0.2$-$0.3$ $J_{\rm d}$, where $J_{\rm d}$ is the depairing current density, and the numerical factor depends on the pinning optimization. By modifying $\lambda$ and/or $\xi$, the penetration depth and coherence length, respectively, we can increase $J_{\rm d}$. For (Y$_{0.77}$Gd$_{0.23}$)Ba$_2$Cu$_3$O$_y$ ((Y,Gd)123) we achieve this by controlling the carrier density, which is related to $\lambda$ and $\xi$. We also tune $\lambda$ and $\xi$ by controlling the chemical pressure in the Fe-based superconductors, BaFe$_2$(As$_{1-x}$P$_x$)$_2$ films. The variation of $\lambda$ and $\xi$ leads to an intrinsic improvement of $J_{\rm c}$, via $J_{\rm d}$, obtaining extremely high values of $J_{\rm c}$ of $130$ MA/cm$^2$ and $8.0$ MA/cm$^2$ at $4.2$ K, consistent with an enhancement of $J_{\rm d}$ of a factor of $2$ for both incoherent nanoparticle-doped (Y,Gd)123 coated conductors (CCs) and BaFe$_2$(As$_{1-x}$P$_x$)$_2$ films, showing that this new material design is useful to achieving high critical current densities for a wide array of superconductors. The remarkably high vortex-pinning force in combination with this thermodynamic and pinning optimization route for the (Y,Gd)123 CCs reached $\sim 3.17$ TN/m$^3$ at $4.2$ K and 18 T (${\bf H}\parallel c$), the highest values ever reported in any superconductor.