Stable Phase Locking in Long Intrinsic Josephson Junctions at Zero-Field Steps of IV-Characteristics

Due to high values of energy gaps of high-temperature superconductors, wavelengths of Josephson generation of intrinsic Josephson junctions in these superconductors are in the range from several tens of micrometers to hundreds micrometers. Therefore, high-temperature superconductors are promising sources of submilimeter waves. Linear dimensions of samples of intrinsic Josephson junctions are inside this range of wavelengths. Because of the influence of modes of geometrical resonances, self-induced steps (so-called zero-field steps) appear in IV-characteristics of samples. We studied numerically the phase locking phenomenon at zero-field steps. We developed a model of a long junction in which the long junction is divided to a number of small parts. We investigated IV-characteristics and stability of the solution of dynamic equations of all parts of one separate long intrinsic junction with homogeneous distribution of critical currents. Our stability analysis was based on the modified Floquet exponents approach. We found the stable solution at frequencies of geometrical resonances which corresponded to zero-field steps in IV-characteristics. We investigated stability of the solution of dynamic equations for two long junctions which interacted inductively with each other. We proved the existence of stable phase-locking of all long junctions at zero-field steps. The developed model can be used for the explanation of experiments on coherent emission of intrinsic Josephson junctions.