Shapiro steps at the sliding of charge density waves: oscillations, frequency mixing, and features in high electric fields

Recent results on the synchronization of the sliding of charge density waves with a radio-frequency electric field, which is manifested in the appearance of Shapiro steps on current–voltage characteristics have been reviewed. Oscillations of the widths of Shapiro steps depending on the amplitude of the radio-frequency field have been studied experimentally and the periodicity of oscillations in the displacement of a charge density wave in the half-cycle of the radio-frequency field has been demonstrated. It has been shown that the width of Shapiro steps can be related to the position of the return point of the charge density wave with respect to the periodic pinning potential. It has been demonstrated how the proposed approach allows one to obtain the form of a current–voltage characteristic measured under the application of the radio-frequency field and to describe Shapiro steps at the frequency mixing on the charge density wave. An original experiment has been described to determine the amplitude of oscillations of the charge density wave in the periodic pinning potential using a radio-frequency lock-in detector. The comparison of the experimental result with the calculation has revealed the effect of the periodic pinning potential on the amplitude of oscillations in the synchronization regime when the action of the periodic pinning potential is not averaged. The synchronization of the charge density wave in high electric fields when its sliding can be characterized by a certain mobility has also been considered. An analogy of the found relations with similar relations for a Josephson junction and a si-ngle-channel quantum wire has been demonstrated.