Floquet Spectrum and Transport through an Irradiated Graphene Ribbon

Graphene subject to a spatially uniform, circularly polarized electric field supports a Floquet spectrum with properties akin to those of a topological insulator. The transport properties of this system, however, are complicated by the nonequilibrium 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 superdiffusive behavior. For very long ribbons, a ballistic regime emerges in which edge state transport dominates.

Figure 1

Schematic diagram of device geometry.

Figure 2

(a) Tight-binding Floquet spectrum as a function of $k_x$ for a graphene ribbon oriented in the zigzag direction, subject to a circularly polarized electric field of magnitude $E_0$ with $e{E}_{0}a/\hslash \omega =0.5$, $\hslash \omega /t=3.0$, where $a$ is the Bravais lattice constant and $t$ the hopping parameter. (b), (c) Spectra from Dirac equation with infinite mass boundary conditions, corresponding to two different valleys. Only one valley carries edge states. Frequency $\omega a/v_{\mathrm{F}}=5$, electric field amplitude $E_0/\hslash \omega =1$, ribbon width $W=45a$.

Figure 3

Conductance vs $L$ for several different bandwidths: $q_{n_{\max }}W=\pi n_{\max }$, with $n_{\max }=10$ (blue asterisks), 15 (lavender open squares), 25 (aqua closed squares). For these plots, $W=20a$, $\omega a/v_{\mathrm{F}}=5$, and number of time steps is 13. Note approximate power law behavior $G\sim L^{-b}$ with $b\approx 0.65$ for $L<W$. For comparison, results for $E_0=0$ displayed as red crosses, displaying $G\sim 1/L$ behavior for $L<W$. Inset: Illustration of ${\epsilon }_{\alpha }$ vs $k_x$ for infinite system with periodic boundary conditions, showing Floquet copies of spectrum and resulting avoided crossings for $k_x\ne 0$.