Fig. 1. (a) The three-dimensional schematic of slow light waveguide, with a single layer of graphene nanodisks at the top. The graphene is exposed to air on the top, the background material is SiO₂, and the substrate material is Si. Different graphene nanodisks are applied with different bias voltages: V₁(t), V₂(t) and V₃(t). The diagram on the right shows how voltage is applied. (b) The graphene nanodisk’s external bias voltage changes periodically with time

Fig. 2. (a) Schematic diagram of graphene plasmon time crystal structure. (b) Energy band diagrams of graphene plasmon time crystals at four different moments in a cycle of external bias voltage change

Fig. 3. (a) When μ_c3=0.6 eV, the relationship between ∆μ_c and t. (d) A region composed of 5×10 graphene plasmon time crystals. P is the position of the excitation source. (b), (c), (e) and (f) Screenshots of four moments in the propagation process at the time nodes of =3.20 e⁻¹²s, =4.16 e⁻¹²s, =5.82 e⁻¹²s and =8.24 e⁻¹²s, respectively (a) 当 =0.6 eV时， 与t的关系。(d) 5×10石墨烯等离激元时间晶体组成的一个区域，P是激发源的位置。(b)，(c)，(e)和(f)是传播过程中4个时刻的截图，时间节点分别是 =3.20 e⁻¹²s, =4.16 e⁻¹²s, =5.82 e⁻¹²s和 =8.24 e⁻¹²s

Fig. 4. The phase distributions of Left-handed Circularly Polarized (LCP) and Right-handed Circularly Polarized (RCP) of the time crystal appear at point K, which are expressed as the component of the electric field in the direction Z and the in-plane Poynting vector (P_x, P_y). (a) and (d) the phase distribution diagram of point K at the time of =0.1 eV; (b) and (e) the phase distribution diagram of point K at the time of =0.12 eV; (c) and (f) the phase distribution diagram of point K at the time =0.14 eV 时间晶体在K点分别出现了左旋圆极化(LCP)和右旋圆极化(RCP)的相位分布，表示为电场在Z方向上的分量和面内坡印亭矢量(P_x, P_y)。(a)和(d)是在 =0.1 eV时刻，K点的相位分布图；(b)和(e)是在 =0.12 eV时刻，K点的相位分布图；(c)和(f)在 =0.14 eV时刻，K点的相位分布图

Fig. 5. (a) Schematic diagram of the Zigzag interface based on graphene plasmon time crystals, in which the bottom is the calculation model of the finite period super cell unit and the simulation electric field distribution results. (b) The dispersion curves of the Zigzag interface mode at different times

Fig. 6. (a) The boundary mode dispersion curve supported by the topological boundary under different . (b) The relationship between group velocity and frequency under different (a) 不同 下拓扑边界所支持的边界模色散曲线。(b)不同 下群速度随频率的变化关系图

Fig. 7. (a, d, g) Screenshots of the electric field intensity distribution at t₁, t₂ and t₃. (b, e, h) Cross-sectional electric field diagrams at the Zigzag boundary at different time t. (c, f, j) The changing process of the electric field at the capture point of light energy