Optical Conductivity Signatures of Floquet Electronic Phases

The Floquet graphene antidot lattice is a hole-patterned graphene sheet driven periodically by electromagnetic radiation. Notably, the equilibrium semiconducting state in such a system can be steered through Floquet Dirac, selectively dynamically localized, or Floquet semi-Dirac electronic phases by applying circularly polarized near-IR radiation of suitable intensity [1]. We show that these features persist when the Dirac Hamiltonian approach we previously employed is upgraded to a tight binding model containing all 870 atoms in the supercell, with electromagnetic driving included via the Peierls substitution. In our analysis, we implement a gauge invariant procedure for reducing the full time-dependent Hamiltonian, current, and inverse effective mass operators to an effective four band model, enabling the efficient calculation of the low energy non-equilibrium properties for large nanostructures. On the basis of a Floquet formulation of linear response theory [2], the real and imaginary parts of the longitudinal and transverse components of the probe-frequency-dependent conductivity are computed and correlated with features in the band structures. In practice, the optical conductivity can be connected to the reflectance which, for 2D materials, can be determined experimentally using ellipsometry techniques [3].



[1] Floquet Graphene Antidot Lattices, A. Cupo et al., Phys. Rev. B, 104, 174304, 2021

[2] Linear Response Theory and Optical Conductivity of Floquet Topological Insulators, A. Kumar et al., Phys. Rev. B, 101, 174314, 2020

[3] Spectroscopic Ellipsometry for Low-Dimensional Materials and Heterostructures, S. Yoo and Q.-H. Park, 11(12): 2811–2825, Nanophotonics, 2022



This work was supported by the NSF under grant No. OIA-1921199.