Theoretical study of the critical current of YBa₂Cu₃O_7-_δ bicrystals with hole-deficient grain boundaries

We develop a theory of the critical current across grain boundaries in YBa2Cu3O7-delta 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 degrees misorientation angle about [100] which is known to be strongly coupled for the purposes of current now, and a 31 degrees 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.