Visualization of a Berezinskii–Kosterlitz–Thouless topological phase transition in a Josephson medium: detection of an anomalous temperature dependence of the magnetoresistance of YBa$_2$Cu$_3$O$_{7-\delta}$ granular high-temperature superconductors

The possibility of implementing a Berezinskii–Kosterlitz–Thouless topological phase transition in a Josephson medium of two-level high-temperature superconductors induced by a magnetic field has been studied. The effect of temperature and external magnetic field on the transport properties of the YBa$_2$Cu$_3$O$_{7-\delta}$ granular high-temperature superconductor considered as a model object is studied experimentally. For the first time, an anomalous behavior of the magnetoresistance isotherms is detected in a narrow range of temperature and external magnetic field indicating a topological phase transition in the Josephson medium of granular high-temperature superconductors.