We consider mechanisms which can account for the observed rapid decrease of the critical current density J(c)(theta) with the misorientation angle theta through grain boundaries (GB's) in high-T-c superconductors (HTS's). We show that the J(c)(theta) dependence is mostly determined by the decrease of the current-carrying cross section by insulating dislocation cores and by progressive local suppression of the superconducting order parameter psi near GB's as theta increases. The insulating regions near the dislocation cores result from a strain-induced local transition to the insulating antiferromagnetic phase of HTS's. The structure of the nonsuperconducting core regions and current channels in GB's is strongly affected by the anisotropy of the strain dependence of T-c which is essentially different for YBa2Cu3O7 and Bi-based HTS's. We propose a mechanism of the progressive superconductivity suppression on GB's with a due to an excess ion charge on the GB's which shifts the chemical potential in the layer of the order of screening length I-D near the GB's. The local suppression of psi is amplified by the proximity of all HTS's to a metal-insulator transition, by their low carrier density and extended saddle point singularities in the electron density of states near the Fermi surface. Taking into account these mechanisms, we calculated J(c)(theta) analytically by solving the Ginzburg-Landau equation. The model well describes the observed quasiexponential decrease of J(c)(theta) with theta for many HTS's. The d-wave symmetry of the order parameter weakly affects J(c)(theta) in the region of small theta and cannot account for the observed drop of J(c)(theta) by several orders of magnitude as theta increases from 0 to theta similar or equal to 20 degrees - 40 degrees. [References: 111]
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