Multiterminal Conductance of a Floquet Topological Insulator

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.

Figure 1

(a) Scheme of a setup where a laser of frequency $\mathrm{\Omega }$ illuminates part of a sample in a six-terminal configuration. (b) Six-terminal setup with arrows representing one of the possible directions for the currents induced at zero bias voltage (pumped currents) on each lead. (c) Six-terminal configuration in a hexagonal arrangement. For a graphene sample, this high symmetry configuration gives a vanishing pumped current.

Figure 2

(a) Quasienergy dispersion for a zigzag graphene ribbon of width $W=125a$ illuminated by a circularly polarized laser of frequency $\hslash \mathrm{\Omega }=1.5{\gamma }_0$ and intensity $z=0.15$. The color scale encodes the weight of the states on the time-averaged DOS at energy $E$: white for no weight and black for maximum weight. Replicas with $-2\le n\le 2$ are considered. (b) Conductance in a two-terminal setup where a section of the infinite zigzag ribbon of length $L=420a$ is illuminated. Full (blue) circles correspond to the pristine system while the empty (red) circles are for a ribbon with 15 vacancies distributed at random. Symmetry breaking due to defects leads to a pumped current ${\mathcal{I}}_P$ (inset).

Figure 3

Results for the setup of Fig. 1; parameters are as in Fig. 2. (a) Conductance. (b) Hall resistance (see insets); empty (blue) circles are for leads without additional doping, and (black) triangles and full circles are for $n$-doped leads (on-site energies are shifted by $0.75{\gamma }_0$ and $1.25{\gamma }_0$, respectively).

Figure 4

(a) Detail of the Hall resistance in the hexagonal setup close to the Dirac point. Triangles (squares) are for laser intensity parametrized by $z=0.15$ ($z=0.25$). The results are for $\hslash \mathrm{\Omega }=1.5{\gamma }_0$, and zigzag terminated leads ($W=99a$, $L=300a$) with on-site energies are shifted by $1.5{\gamma }_0$. The full quasienergy spectra for these intensities are shown in (b) and (c). Chiral edge states other than those shown in the projection on the Floquet channel $n=0$ in Fig. 2 also develop but do not impact $R_{xy}$.