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

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.

16 pages, 1 figure. Suggestions and comments are welcome

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Cited by in corpus (8)

• Effects of periodic kicking on dispersion and wave packet dynamics in graphene
• Topological edge states on time-periodically strained armchair graphene nanoribbons
• Topological flat bands in time-periodically driven uniaxial strained graphene nanoribbons
• `Muhammad Ali effect' and incoherent destruction of Wannier-Stark localization in a stochastic field
• Topological phase-diagram of time-periodically rippled zigzag graphene nanoribbons
• Curvature-induced pseudogauge fields from time-dependent geometries in graphene
• Phase transition in a Aubry-Andre system with rapidly oscillating magnetic field
• Chiral Luttinger liquids in graphene tuned by irradiation