Floquet engineering of low-energy dispersions and dynamical localization in a periodically kicked pseudospin-1 system

Much having learned about Floquet dynamics of pseudospin-$1/2$ system namely, graphene, we here address the stroboscopic properties of a periodically kicked pseudospin-1 fermionic system such as dice lattice that is alternatively known as $T_3$ lattice. Likewise graphene, we reveal that one can, in principle, engineer various type of low energy dispersions around some specific points in the Brillouin zone by tuning the kicking parameter in the Hamiltonian along a particular direction. Our analytical analysis shows that one can experience different quasi-energy dispersions for example, Dirac type, semi-Dirac type, gapless line, absolute flat quasi-energy bands, depending on the specific values of the kicking parameter. Moreover, we numerically study the dynamics of a wave packet in this system; the quasi-energy dispersion allows us to understand the instantaneous structure of wave-packet at stroboscopic times. We find a situation where absolute flat quasi-energy bands lead to a complete dynamical localization of the wavepacket.