One-way transport in laser-illuminated bilayer graphene: A Floquet isolator

We explore the Floquet band structure and electronic transport in laser-illuminated bilayer graphene ribbons. By using a bias voltage perpendicular to the graphene bilayer we show how to get one-way charge and valley transport among two unbiased leads. In contrast to quantum pumping, our proposal uses a different mechanism based on generating a nonreciprocal band structure with a built-in directionality. The Floquet states at one edge of a graphene layer become hybridized with the continuum on the other layer, so the resulting band structure allows for one-way transport as in an isolator. Our proof of concept may serve as a building block for devices exploiting one-way states.

Figure 1

(a) Scheme of the simplest ideal isolator (as discussed in Ref. [11]) where single-mode wires are connected to a sample. The scattering matrix is skewed, and transmission occurs only from left to right. (b) Scheme of the setup considered in this work to obtain an isolator effect: a laser-illuminated graphene sample connected to left and right electrodes, an inhomogeneous region with monolayer and bilayer graphene areas, and a third electrode on top. The bilayer area is biased perpendicularly to the graphene plane.

Figure 2

(a) and (b) The full dispersion for the electronic states of a bilayer graphene ribbon with a bias voltage and irradiated with a laser, where the interlayer coupling is off and on, respectively. (c) Scheme of a graphene bilayer with Bernal stacking and a bias voltage applied perpendicularly. (d)–(g) The same dispersion as in (b) with a color scale encoding the weight of the states on sites $A_1,B_1,A_2$, and $B_2$ for the Floquet replica $n=0$. The parameters are chosen with the aim of illustrating the proposed mechanism: $\mathrm{\Delta }=0.2,W=103a,\hslash \mathrm{\Omega }=3.5$, and $z=0.5$.

Figure 3

(a) Top: Scheme of the three-terminal setup where a bilayer sample is connected to three monolayer graphene leads, two of them on the lower layer (L and R) and a third one on the upper layer. Bottom: Transmission probabilities between the left (L) and right (R) leads as a function of the electronic energy. One can see a strong directionality in the energy region marked with a dashed box in Figs. 2 and 2. (b) Same as (a) for the case where the upper layer covers only half of the lower one, with rough edges and 1 ‰ vacancies. In this setup directional transport is achieved throughout the full gap as explained in the text. The laser parameters are as in Fig. 2, $W=103a$ and $l=500a$.

Figure 4

Transmission probabilities as a function of the energy of the incoming electrons. Here the lower layer is half covered, and the corresponding zigzag edge state is polarized on the $B_1$ sublattice. The “switch-off” mechanism is ineffective, at least for the pristine system in (a) where the directionality is almost lost. The situation changes dramatically when edge roughness and disorder are added to the same sample, as shown in (b). The remaining system parameters are chosen as in Fig. 3.

Figure 5

Numerical results for the transmission probabilities of the setups considered in the text for (a)–(d) the bilayer setup and (e)–(h) the half-covered bilayer setup. The results correspond to pristine systems [(a) and (e)] and samples with different realizations of disorder and edge roughness. The parameters are the same as in Fig. 3.

Figure 6

Transmission probabilities for the half-covered bilayer setup [(b) and (d)] with and [(a) and (c)] without disorder and edge roughness for two different values of the laser intensity given by the dimensionless parameter $z$. The remaining system parameters are chosen as in Fig. 3.