Electromagnetic, atomic-structure and chemistry changes induced by Ca-doping of low-angle $YBa_2Cu_3O_{7-\delta}$ grain boundaries

Practical high temperature superconductors must be textured to minimize the reduction of the critical current density $J_{gb}$ at misoriented grain boundaries. Partial substitution of Ca for Y in $YBa_2Cu_3O_{7-\delta}$ has shown significant improvement in $J_{gb}$ but the mechanisms are still not well understood. Here we report atomic-scale, structural and analytical electron microscopy combined with transport measurements on $7^{\circ}$ $[001]$-tilt $Y_{0.7}Ca_{0.3}Ba_2Cu_3O_{7-\delta}$ and $YBa_2Cu_3O_{7-\delta}$ grain boundaries, where the dislocation cores are well separated. We show that the enhanced carrier density, higher $J_{gb}$ and weaker superconductivity depression at the Ca-doped boundary result from a strong, non-monotonic Ca segregation and structural rearrangements on a scale of ~1 nm near the dislocation cores. We propose a model of the formation of $Ca^{2+}$ solute atmospheres in the strain and electric fields of the grain boundary and show that Ca doping expands the dislocation cores yet enhances $J_{gb}$ by improving the screening and local hole concentration.