Effects of periodic kicking on dispersion and wave packet dynamics in graphene

TL;DR

This paper investigates how periodic delta-function kicks influence the energy-momentum dispersion in graphene, revealing various novel dispersion types and dynamical localization effects through analytical and numerical methods.

Contribution

It introduces a comprehensive analysis of Floquet dispersion modifications in graphene under periodic kicks, including analytical derivations and numerical demonstrations of diverse dispersion regimes.

Findings

Dispersion can become linear, anisotropic, or quadratic depending on kicking parameters.

Dynamical localization leads to completely flat dispersion.

Numerical simulations confirm analytical predictions.

Abstract

We study the effects of $\delta$-function periodic kicks on the Floquet energy-momentum dispersion in graphene. We find that a rich variety of dispersions can appear depending on the parameters of the kicking: at certain points in the Brillouin zone, the dispersion can become linear but anisotropic, linear in one direction and quadratic in the perpendicular direction, gapped with a quadratic dispersion, or completely flat (called dynamical localization). We show all these results analytically and demonstrate them numerically through the dynamics of wave packets propagating in graphene. We propose experimental methods for producing these effects.