Floquet Weyl fermions in three-dimensional stacked graphene systems irradiated by circularly polarized light

Using Floquet theory, we illustrate that Floquet Weyl fermions can be created in three-dimensional stacked graphene systems irradiated by circularly polarized light. One or two semi-Dirac points can be formed due to overlapping of Floquet subbands. Each pair of Weyl points have a two-component semi-Dirac point parent, instead of a four-component Dirac point parent. Decreasing the light frequency will make the Weyl points move in the momentum space, and the Weyl points can approach to the Dirac points when the frequency becomes very small. The frequency-amplitude phase diagram is worked out. It is shown that there exist Fermi arcs in the surface Brillouin zones in semi-infinitely stacked and finitely multilayered graphene systems irradiated by circularly polarized light. The Floquet Weyl points emerging due to the overlap of Floquet subbands provide a new platform to study Weyl fermions.

Figure 1

A schematic of the three-dimensional stacked graphene model which can be built by stacking infinite graphene layers. Panel (a) shows the relation between the two nearest graphenes. The interlayer distance is eqivalent to $dsin\theta$. The sliding displacement between the nearest graphene layers, $a-dcos\theta$, is along the $x$ axis, which becomes clear by using the top view (b).

Figure 2

The band structure along the $k_y$ axis, with $k_x=k_z=0$. For the $A_{0}a$ values, there always exist two gapless Dirac points (denoted by green circles). For different frequencies, there can be one or two pairs of Weyl points astride ${\mathbf{k}}_0$ (red circles) and/or ${\mathbf{k}}_1$ (black circles). The $H_F$ matrix is truncated at $m=\pm 2$, and other parameters are set as $d=2a,\eta =\gamma /7$, and $\theta =4\pi /9$. (a) $A_{0}a=1,w=3.5\gamma$ (b) $A_{0}a=1,w=2.3\gamma$ (c) $A_{0}a=1,w=1.5\gamma$ (d) $A_{0}a=2,w=3.5\gamma$ (e) $A_{0}a=2,w=2\gamma$ (f) $A_{0}a=2,w=1.3\gamma$.

Figure 3

The band structures of the $m=0$ and $m=\pm 1$ subbands in the $k_z=0$ plane, with parameters $\eta =\gamma /7,A_{0}a=1.5,w=2\gamma ,d=2a$, and $\theta =4\pi /9$. Two pairs of Weyl points are symmetrical astride ${\mathbf{k}}_0$ and ${\mathbf{k}}_1$, respectively.

Figure 4

The phase diagram with experimentally achievable [31] parameters $d=2a,\eta =\gamma /7$, and $\theta =4\pi /9$. There are six phases: semimetal (SM), Weyl semimetal with one pair of Weyl fermions astride ${\mathbf{k}}_0$ (WSM1-A), Weyl semimetal with one pair of Weyl fermions astride ${\mathbf{k}}_1$ (WSM1-B), Weyl semimetal with two pairs of Weyl fermions (WSM2), ordinary insulator (I), and Weyl semimetal (WSM). The six triangles show the $(\omega /\gamma ,A_{0}a)$ values for the band structures shown in Fig. 2.

Figure 5

The frequency dependence of the Fermi arcs in the surface Brillouin zone: (a) no Fermi arc for $w\sim 3.5\gamma$ in the SM phase, (b) one Fermi arc near $(k_x,k_y)=(0,0)$ for $w\sim 2.3\gamma$ in the WSM1-A phase, and (c) two Fermi arcs near $(k_x,k_y)=(0,0)$ and $(0,\pi /a)$ for $w\sim 1.5\gamma$ in the WSM2 phase. Here the light amplitude is $A_{0}a<1$. (a) No Fermi arc in the SM phase.(b) One Fermi arc in the WSM1-A phase.(c) Two Fermi arcs in the WSM2 phase.