Floquet engineering of low-energy dispersions and dynamical localization in a periodically kicked three-band system

TL;DR

This paper explores how periodic kicking in a three-band lattice system can engineer various low-energy dispersions and induce dynamical localization, revealing new ways to control quasienergy structures and wave packet dynamics.

Contribution

It demonstrates the ability to engineer diverse quasienergy dispersions and dynamical localization in a three-band system by tuning the kicking parameter, extending Floquet engineering beyond pseudospin-1/2 systems.

Findings

Different quasienergy dispersions can be achieved by tuning the kicking parameter.

Absolute flat quasienergy bands lead to wave packet localization.

Dynamical localization does not occur at intermediate alpha values.

Abstract

Much having learned about Floquet dynamics of pseudospin-$1/2$ system namely, graphene, we here address the stroboscopic properties of a periodically kicked {three-band fermionic system such as $\alpha$-T$_3$ lattice. This particular model provides an interpolation between graphene and dice lattice via the continuous tuning of the parameter $\alpha$ from 0 to 1.} In the case of dice lattice ($\alpha=1$), 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, Dirac type, semi-Dirac type, gapless line, 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 packet at stroboscopic times. We find a situation where absolute flat quasienergy bands lead to a complete dynamical localization of the wave packet. {Aditionally, we calculate the quasienergy spectrum numerically for $\alpha$-T$_3$ lattice. A periodic kick in a perpendicular (planar) direction breaks (preserves) the particle-hole symmetry for $0<\alpha<1$. Furthermore, it is also revealed that the dynamical localization of wave packet does not occur at any intermediate $\alpha \ne 0,\,1$.}