Floquet Spectrum and Transport through an Irradiated Graphene Ribbon

Abstract

Graphene subject to a spatially uniform, circularly-polarized electric field supports a Floquet spectrum with properties akin to those of a topological insulator, including non-vanishing Chern numbers associated with bulk bands and current-carrying edge states. Transport properties of this system however are complicated by the non-equilibrium occupations of the Floquet states. We address this by considering transport in a two-terminal ribbon geometry for which the leads have well-defined chemical potentials, with an irradiated central scattering region. We demonstrate the presence of edge states, which for infinite mass boundary conditions may be associated with only one of the two valleys. At low frequencies, the bulk DC conductivity near zero energy is shown to be dominated by a series of states with very narrow anticrossings, leading to super-diffusive behavior. For very long ribbons, a ballistic regime emerges in which edge state transport dominates.

Topological Floquet spectrum in three dimensions via a two-photon resonance

“…(12). We consider a finite slab with homogeneous boundary conditions at z = 0, L and a driving electric field polarized in thex direction.…”

“…The Floquet spectrum of a periodically driven system was shown to exhibit a variety of topological phases 7 . For instance, graphene is expected to exhibit a quantum Hall effect when subjected to radiation 9,12,13 ; a spin-orbit coupled semiconductor heterostructure (such as HgTe/CdTe wells), can be turned topological using microwave-teraHertz radiation 10 , and vice versa 14,15 .…”

Floquet topological insulators

“…Nevertheless, an appropriate formalism needs to be used to compute DC Hall response functions in presence of steady states described as Floquet states [28,30].…”

“…It is also possible to open gaps at the Dirac point of graphene and even drive graphene into the topological Haldane phase by simple irradiation with suitably chosen parameters [20,[26][27][28][29]. Therefore, DC transport is expected to be drastically modified under such irradiation [28,30].…”

Engineering anomalous quantum Hall plateaus and antichiral states with ac fields

“…One of the most promising consists in periodically driving the system in order to achieve a topological phase transition [6][7][8][9][10][11]. Proposals with a time periodic driving in semiconductors [6,12], optical lattices [13], or graphene [7,[14][15][16][17][18] have been suggested to achieve various dynamical generalizations of static topological phases, called Floquet topological phases [12], and have been recently observed in photonic crystals [19]. Importantly for our purposes, the previous studies for the honeycomb lattice were restricted either to numerical calculations in finite-size systems, where the physical mechanism driving the topological phase transitions was not clear, or to very high frequencies and low-energy approximations, where most of the phase diagram remained unknown.…”