In the presence of a circularly polarized mid-infrared radiation graphene develops dynamical band gaps in its quasi-energy band structure and becomes a Floquet insulator. Here we analyze how topologically protected edge states arise inside these gaps in the presence of an edge. Our results show that the gap appearing at $\hbar\Omega/2$, where $\hbar \Omega$ is the photon energy, is bridged by two chiral edge states whose propagation direction is set by the direction of the polarization of the radiation field. Therefore, both the propagation direction and the energy window where the states appear can be controlled externally. We present both analytical and numerical calculations that fully characterize these states. This is complemented by simple topological arguments that account for them and by numerical calculations for the case of semi-infinite sample, thereby eliminating finite size effects.Comment: 12 pages, 8 figures. Revised version, submitted to PR

We report on simulations of the dc conductance and quantum Hall response of a Floquet topological insulator using Floquet scattering theory. Our results reveal that laser-induced edge states lead to quantum Hall plateaus once imperfect matching with the nonilluminated leads is lessened. The magnitude of the Hall plateaus, however, is not directly related to the number and chirality of all the edge states at a given energy, as usual. Instead, the plateaus are dominated by those edge states adding to the time-averaged density of states. Therefore, the dc quantum Hall conductance of a Floquet topological insulator is not directly linked to topological invariants of the full Floquet bands.

We report on the emergence of laser-induced chiral edge states in graphene ribbons. Insights on the nature of these Floquet states is provided by an analytical solution which is complemented with numerical simulations of the transport properties. Guided by these results we show that graphene can be used for realizing non-equilibrium topological states with striking tunability: While the laser intensity can be used to control their velocity and decay length, changing the laser polarization switches their propagation direction. [12][13][14][15]. Endowing graphene with protected edge states would unite the best of both materials.Since graphene is a zero gap semiconductor a very first step is the creation of a bulk band-gap. Predictions indicate that a circularly polarized laser can do this task [16][17][18][19][20]-this was verified by a recent experiment at the surface of a TI [21]. Although laser induced band-gaps appear both at the Dirac point and away from it, the most promising ones are the latter [22], also called dynamical gaps [23], which occur at half the photon energy ( Ω) above/below the Dirac point and can be reached within an experimentally relevant set of parameters [19] (n ∼ 2.5 × 10 11 cm −2 for Ω = 100meV, λ ∼ 10µm). Once the bulk gap opens, one should look for Floquet edge states (FES). Such intriguing states were proposed in [24][25][26] and realized recently in photonic crystals [27] but experiments were not reported in condensed matter so far. Crafting FES within dynamical gaps in graphene would extend the realm of Floquet topological insulators (FTI) [24,28] and lead to a new playground for optoelectronics [12,29].Here we show how chiral edge states emerge at the dynamical bandgaps in graphene. To such end we use Floquet theory (FT) and combine numerics with an explicit analytical solution for the edge states. Our analysis reveals that these states decay exponentially towards the bulk with a decay length that depends only on the ratio of the field's frequency and its intensity. More importantly, these FES turn out to be chiral, i.e. all the states on each edge of the sample propagate in the same direction, like in one-way streets. Additional simulations