Floquet analysis of pulsed Dirac systems: A way to simulate rippled graphene

TL;DR

This paper proposes a method using high-frequency periodic driving in optical lattices to simulate rippled graphene's curved space effects, enabling the study of geometric influences on electronic properties without physical deformation.

Contribution

It introduces a Floquet engineering approach to mimic curved space effects in Dirac systems through tailored pulsed driving schemes in optical lattices.

Findings

Effective Hamiltonian simulates curvature effects.

Curvature influences electronic properties like LDOS.

Method enables studying geometry effects without physical deformation.

Abstract

The low energy continuum limit of graphene is effectively known to be modeled using Dirac equation in (2+1) dimensions. We consider the possibility of using modulated high frequency periodic driving of a two-dimension system (optical lattice) to simulate properties of rippled graphene. We suggest that the Dirac Hamiltonian in a curved background space can also be effectively simulated by a suitable driving scheme in optical lattice. The time dependent system yields, in the approximate limit of high frequency pulsing, an effective time independent Hamiltonian that governs the time evolution, except for an initial and a final kick. We use a specific form of 4-phase pulsed forcing with suitably tuned choice of modulating operators to mimic the effects of curvature. The extent of curvature is found to be directly related to $\omega^{-1}$ the time period of the driving field at the leading order. We apply the method to engineer the effects of curved background space. We find that the imprint of curvilinear geometry modifies the electronic properties, such as LDOS, significantly. We suggest that this method shall be useful in studying the response of various properties of such systems to non-trivial geometry without requiring any actual physical deformations.