Hysteresis jumps of the surface reactance of a layered superconductor as the incident wave amplitude varies

Abstract

The nonlinear response of a layered superconductor to symmetric (in magnetic field) electromagnetic excitation has been theoretically investigated. An ambiguous dependence of the phase of the reflected signal on the amplitude H0 of the irradiating wave is predicted. This causes hysteresis jumps in the dependence of the surface reactance of the superconductor on H0. If the frequency of the irradiating field is close to the Josephson plasma frequency, this unusual nonlinear effect can be observed when the amplitudes of the ac field are not very strong. The conditions for the appearance of hysteresis are obtained. Expressions for the phase shift of the reflected wave are derived, using the coupled sine-Gordon equations. Moreover, a class of solutions of these equations that are discontinuous in the coordinate are studied that correspond to a continuous spatial distribution of the magnetic field in the superconductor. Such solutions result in the appearance of additional branches in the dependence of the phase shift of the reflected wave on the incident wave amplitude.