Thermal-noise-induced resistance and supercurrent correlation function in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ grain-boundary Josephson junctions

Thermal noise is known to cause a finite resistance ${\mathit{R}}_{\mathit{p}}$ of overdamped Josephson junctions even in the zero-current limit. By extending the treatment of Ambegaokar and Halperin the magnetic-field dependence of this resistance is analyzed for arbitrary current-phase relations. We show that the measurement of the magnetic-field dependence of ${\mathit{R}}_{\mathit{p}}$ allows the determination of the magnetic-field dependence of the critical current in the temperature regime where thermal-noise rounding effects prevent the application of the usual methods. Applying this technique the correlation function of the supercurrent distribution of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ grain-boundary junctions could be determined with a spatial resolution of 130 nm. The correlation function indicates that the supercurrent distribution along the grain boundary is spatially nonuniform on a sub-μm scale.