The Zitterbewegung Study Of Dirac Points In Two - Dimensional Phononic Crystals

Phononic crystal is a kind of composite material, in which the elastic moduluschanges periodically. So we can use its periodic elastic structure to modulate acousticwaves which propagate in it. In recent years, the research on phononic crystal hasattracted general attentions and wide interests in many research communities.Zitterbewegung (ZB) originally means the trembling motion of relativistic freeelectron, however, not long ago, there were some researches show that ZB also occursin phononic crystal, which means that the wave packet propagating in phononiccrystal may be oscillating. So, in this paper, we analyzed the main factors and theireffects which affect ZB in phononic crystal. In order to simplify the discussion, thetwo dimensional (2D) phononic crystal is taken as a case study.First, the effects of2D phononic crystal’s rectangular lattice structure onacoustic ZB were discussed in detail. In this study we considered eight kinds ofrectangular lattices, and for the eight kinds of rectangular lattices, their symmetriesare reduced gradually. The effects were concluded through analyzing the oscillationfrequency, transient character and the maximum amplitude of ZB.Then, the influences of wave packet’s propagation direction and its position atthe initial time on acoustic ZB were researched in2D square lattice phononic crystal.For comparison purposes, we also considered another rectangular lattice structure inthis study. For the propagation direction of wave packet, we considered the directionsof ΓΧ、ΧΜ and ΓΜ, which are the three important directions of wave vector in thefirst Brillouin zone. In addition, without losing comprehensiveness, for each directionof ΓΧ、ΧΜ and ΓΜ, the wave packet’s center is arranged at the subterminal positionor the middle position at the initial time.Next, the effects of scatterer’s shape on acoustic ZB were studied in2D squarelattice phononic crystal. This work involves seven kinds of scatterers which have thedifferent geometrical symmetries, that is, triangular prism, tetragonal prism, hexagonal prism, octagonal prism, cylinder and two kinds of elliptic cylinder.Similarly, we also analyzed the effects from the oscillation frequency, transientcharacter and the maximum amplitude of ZB.Finally, take the2D square lattice phononic crystal whose scatterers aretetragonal prism, for example, the effects of rotation operation on acoustic ZB werediscussed form the above-mentioned three aspects.Through these studies, some regular conclusions about ZB can be obtained,which will be helpful for the further theoretical and experimental research. What’smore, this work may provide some enlightenment for the study on ZB in other fields.