Theoretical study of the critical current of YBa2Cu3O7−δ bicrystals with hole-deficient grain boundaries

We develop a theory of the critical current across grain boundaries in YBa₂Cu₃O_7−δ bicrystals. Experiments have shown that there is hole depletion near a boundary and the concentration profiles have been determined for specific cases. These results mean that the critical temperature is a function of distance from the boundary. Taking this function from experiment as input into the theory, we study two specific boundaries: a boundary with a 7° misorientation angle about 100] which is known to be strongly coupled for the purposes of current flow, and a 31° boundary which is known to be weakly coupled. Using Ginzburg-Landau theory, we determine the dependence of the critical current density (j_c) on temperature and the spatial dependence of the order parameter for these boundaries. The results show that the oxygen depletion can account for a major portion of the change from weak to strong coupling of boundaries as the misorientation angle is increased.