8 research outputs found
Floquet analysis of pulsed Dirac systems: A way to simulate rippled graphene
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
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.Comment: 16 pages, 1 figure. Suggestions and comments are welcom