Acoustic Study Of Dirac 's Flicker In Two - Dimensional Phononic Crystals Based On Electrorheological Materials

Zitterbewegung(ZB) refers to the rapid trembling motion of a free Dirac electron, originating from the interference between the states of Dirac electron with positive and negative energy. It is difficult to observe the ZB oscillations of a Dirac electron, since the amplitude of ZB is approximately up to the Compton wavelength,12h/ mc10 m-?, which is extremely short. Recently, some studies have approved the existence of ZB oscillations when the acoustic waves propagate in phononic crystals.Electrorheological(ER)materials are widely used in the industrial field, thanks to it’s special property of visco-elastic changed by the applying electric field. Thus, the possibility of band gaps controlled by applied electric field also can be realized while the ER materials are introduced into the phononic crystals and act as a matrix.In this paper, based on two-dimensional(2D) phononic crystals consisting of epoxy circular cylinders embedded in an ER matrix, the ZB phenomenon is investigated mainly in the tunable two-dimensional phononic crystals, and the study includes the following three aspects.Firstly, considering the in-of-plane propagation of elastic waves in 2D phononic crystals with ER materials, this oscillatory behavior is still presented and the oscillatory period and amplitude of the acoustic ZB can be controlled by external voltages.Secondly, the band structure of the elastic wave oblique incidence to such a phononic crystal with ER materials are studied. By comparing with the cases reported previously, we found that, the entire band structure shift to high frequency slowly with the increasing of oblique incident angle. This can solve the problem of the disappearance of the band gap with the oblique incidence angle of elastic waves increases, which caused by the movements of the whole band structure to highfrequency range.Finally, the effects of out-of-plane propagation of elastic waves were investigated in2 D square lattice phonoic crystals. We analyzed the conditions of ZB in the case of elastic wave oblique incidence were analyzed and found that, the ZB oscillation can be observedobviously when the wave vector component parallel to rodsz? is less than 1, while the the wave vectorz? is greater than 2, this oscillatory behavior is actually generated sub-wave-packets and disappearing acts instead of ZB oscillatory behavior.This work can provide a theoretical and experimental basis on probing ZB behavior intelligently, meanwhile, it also has important significance for the study of the ZB phenomenon in other fields.