Effects of frequency mixing on Shapiro-step formations in sliding charge-density-waves

A one-dimensional charge-density wave (CDW) is driven to slide by a dc electric field, carrying an electric current. In an additional ac field with frequency ωex, it is known that the sliding CDW can be synchronized to ωex, leading to the occurrence of Shapiro steps in the I–V characteristics. Motivated by a recent experiment where ac fields with two frequencies ωex and ωex′ are simultaneously applied, we theoretically investigate the effects of frequency mixing on the Shapiro-step formation. Based on the Fukuyama–Lee–Rice model, we show that in addition to the main steps induced by ωex, satellite steps characterized by ωex′ emerge. It is also found that with increasing the ac-field strength for ωex′, each step width first exhibits a damped oscillation as in the one-frequency case and then exhibits a non-monotonic behavior. The origin of these behaviors and the relevance to the associated experiment are also discussed.