Floquet engineering of low-energy dispersions and dynamical localization in a periodically kicked three-band system
Lakpa Tamang, Tanay Nag, Tutul Biswas
Abstract
Although we know much about Floquet dynamics of pseudospin-$1/2$ systems, namely graphene, we here address the stroboscopic properties of a periodically kicked three-band fermionic system such as the $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{T}}_{3}$ lattice. This particular model provides an interpolation between graphene and dice lattice via the continuous tuning of the parameter $\ensuremath{\alpha}$ from 0 to 1. In the case of dice lattice ($\ensuremath{\alpha}=1$), we reveal that one can, in principle, engineer various types 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 quasienergy dispersions, for example, the Dirac type, semi-Dirac type, gapless line, and/or absolute flat quasienergy bands, depending on the specific values of the kicking parameter. Moreover, we numerically study the dynamics of a wave packet in dice lattice. The quasienergy dispersion allows us to understand the instantaneous structure of wave packets at stroboscopic times. We find a situation where absolute flat quasienergy bands lead to a complete dynamical localization of the wave packet. Additionally, we calculate the quasienergy spectrum numerically for the $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{T}}_{3}$ lattice. A periodic kick in a perpendicular (planar) direction breaks (preserves) the particle-hole symmetry for $0<\ensuremath{\alpha}<1$. Furthermore, it is also revealed that the dynamical localization of a wave packet does not occur at any intermediate $\ensuremath{\alpha}\ensuremath{\ne}0,\phantom{\rule{0.16em}{0ex}}1$.