Fermi Arc Reconstruction in Synthetic Photonic Lattice

The chiral surface states of Weyl semimetals have an open Fermi surface called a Fermi arc. At the interface between two Weyl semimetals, these Fermi arcs are predicted to hybridize and alter their connectivity. In this Letter, we numerically study a one-dimensional (1D) dielectric trilayer grating where the relative displacements between adjacent layers play the role of two synthetic momenta. The lattice emulates 3D crystals without time-reversal symmetry, including Weyl semimetal, nodal line semimetal, and Chern insulator. Besides showing the phase transition between Weyl semimetal and Chern insulator at telecom wavelength, this system allows us to observe the Fermi arc reconstruction between two Weyl semimetals, confirming the theoretical predictions.

Figure 1

Sketch of a 1D trilayer photonic grating with period $\mathrm{\Lambda }$. The relative displacements between adjacent layers are denoted by ${\delta }_1$ and ${\delta }_2$. The optical guided modes of interest couple with each other via intralayer diffraction and interlayer evanescent field, described by the coupling rates $U_l$ and $V_j$, respectively.

Figure 2

(a) Nodal points and lines of the spectrum obtained from the effective model with $U_1=U_2=U_3=V_1=V_2=1$. They are degeneracy points of energy bands shown in (b). The violet dashed line indicates the path for plotting the band structures in (b) and (c). The band structures obtained from the effective model (solid line) and PWE simulation (dashed line) are shown for (b) $U_1=U_2=U_3=V_1=V_2=1$ (a), and (c) $U_1=U_3=1$, $U_2=1.2$, $V_1=1.6$, and $V_2=0.6$. The six bands are labeled by numbers.

Figure 3

(a) Distance ${\mathrm{\Delta }}_W$ between the two Weyl points at $k=0$ when $U_1=U_3=1$ and $U_2=1.2$. The three domains in black are where bands (3) and (4) separate, and the lattice simulates a 3D CI. (b) and (c) show the Weyl point trajectories in the BZ while (d) and (e) show the Chern number computed in a 2D plane normal to $q_2$ when the interlayer coupling strengths vary along lines 1 and 2 of (a), respectively. In (b) and (c), $\chi$ is the Weyl point chirality.

Figure 4

Junction of two WSMs. (a) Sketch of the setup for simulation. The intralayer coupling strengths are $U_1=U_3=1$ and $U_2=1.2$. (b) Positions of Weyl points on each side. The yellow dots correspond to $(V_1,V_2)=(1.3,1)$ while the blue ones are for $(V_1,V_2)=(1,1.3)$. (c) Energy spectrum of the effective model (left) and the transmission spectrum obtained from FDTD simulation (right) of the systems in the diagonal plane $q_1=q_2$. The dashed lines indicate the frequencies for visualizing the isofrequency transmission over the synthetic BZ in (d). The inset of (d) shows the reconstructed FAs, with the dashed gray lines being the FAs before reconstruction.