Mathematical modeling of current-voltage characteristics of high-temperature superconductors with fractal boundaries of normal phase clusters

The fractality effect of the normal phase clusters' boundaries of a high-temperature superconductor ${YBa}_{2}{Cu}_{3}{O}_{7-x}$ (YBCO) on the magnetic flux creep is investigated. Experimental current-voltage and magnetoresistive characteristics of YBCO at the boiling point of nitrogen are obtained. Based on the model of intergranular clusters with fractal boundaries, an approximation of the experimental data is obtained after geometric-probability analysis of the photomicrographs of the samples. A model of the magnetoresistive state caused by flux creep is proposed for various transport currents, and experimental and empirical dependences of the fractal dimension of the normal YBCO phase cluster boundaries on the constant magnetic field are found. The magnetic field intensity is determined for a given fractal dimension, at which the vortex penetration into the granules begins. It is shown that the state of the samples corresponds to the metastable phase of the vortex glass. The connectivity index of the stall paths of the vortex bundles at the percolation threshold is calculated.