Effect of the temperature, external magnetic field, and transport current on electrical properties, vortex structure evolution processes, and phase transitions in subsystems of superconducting grains and “weak links” of granular two-level high-temperature superconductor YBa$_{2}$Cu$_{3}$O$_{7-\delta}$

The temperature dependences of the resistivity of granular high-temperature superconductor YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ $\rho(T)$ are measured at various transverse external magnetic fields $0\le\mathbf{H}_{\operatorname{ext}}\le$ 100 Oe in the temperature range from the resistivity onset temperature $T_\rho$ = 0 to the superconducting transition critical temperature $T_c$ at the transport current density from 50 to 2000 mA/cm$^2$. The effect of the external magnetic field and transport current density on the kinetics of phase transitions in both subsystems of granular two-level HTSC ($T=T_{c2J}$, $T_{c1g}$, $T_{c}$) is determined. The feasibility of the topological phase transition, i.e., the Berezinsky–Kosterlitz–Thouless transition, in the Josephson medium at $T_{c2J}<T_{\operatorname{BKT}}<T_{c1g}$ “in transport current” is established, and its feasibility conditions are studied.