## 2 Proposed Structure and Simulation Method  
A representative unit cell of the proposed metamaterial, based on two orthogonally twisted SRRs, is vividly illustrated in Figure 1. The meta-atoms unit are made of aluminum (Al), with \(t_{Al}=200\) nm being the thickness, and a silicon (with refractive index 3.42) substrate is assembled at the bottom. The proposed concept of a metal-graphene metamaterial can be realized by the different types of structures, but in this paper, this simple SRR structure is selected due to the perfect electrical interplay between its split-gap and the active graphene layer material [18; 24]. The linearly y-polarized plane wave along the negative z direction is adopted as incident light all through the paper. The right and left SRRs are termed as SRR1 and SRR2, respectively. The SRR1, acting as the bright resonator, strongly coupled with the incident THz wave. However, the SRR2 is not excited by the incident wave due to its symmetric structure with respect to the exciting electric field, thus acting as the dark resonator. By near-field coupling, an obvious PIT resonance is obtained via the destructive interference between the bright and dark mode in the unit cell composed of the SRR1 and the SRR2. For tuning the PIT resonance, a continuous monolayer graphene ribbon is placed under the split gap of SRR1. In this work, the tunability of the proposed structure was studied numerically by using the finite-difference time-domain (FDTD) method. The unit cell was simulated under the periodic boundary conditions in the x-y plane. The perfectly matched layer boundary condition, maintaining computational convergence, was employed for the z direction. In the calculations, the mesh accuracy 4 is used to keep a balance between simulation time, memory requirements and accuracy. The simulation time is set to 800 picoseconds. In order to detect the transmission characteristics, a frequency-domain power monitor was placed under the substrate. The simulation is carried out on a small computing workstation, which has 64 Gigabytes memory and 16 central processing units. The permittivity of  
Figure 1: (**a**) Schematic representation of the tunable plasma-induced transparency (PIT) metamaterial and the normal incident plane wave configuration. (**b**) Top view (from z axis) for the unit cell, the geometrical structure parameters are: \(Px=100\)\(\upmu\)m, \(Py=50\)\(\upmu\)m, \(l=36\)\(\upmu\)m, \(w=6\)\(\upmu\)m, \(s=1\)\(\upmu\)m, \(g=2\)\(\upmu\)m.  
Al, \(\varepsilon_{Al}(\omega)\), characterizing the optical properties at the THz frequencies, can be determined using the Drude model [25],  
\[\varepsilon_{Al}(\omega)=\varepsilon_{\infty}-\frac{\omega_{p}^{2}}{\omega^{2}+i \omega\gamma}, \tag{1}\]  
where we assume that \(\omega_{p}=2\pi\times 3.57\times 10^{15}\) s\({}^{-1}\) and \(\gamma=2\pi\times 1.98\times 10^{13}\) s\({}^{-1}\), for the plasma frequency and the damping constant, respectively. In terahertz range, the surface conductivity of graphene, \(\sigma_{gna}(\omega)\), regarding as a function of angular frequency, \(\omega\), can be described using the Drude-like model [26; 27]:  
\[\sigma_{gna}(\omega)=\frac{e^{2}E_{F}}{\pi\hbar^{2}}\frac{i}{\omega+i/\tau}, \tag{2}\]  
where \(e\) is the basic unit charge, \(\hbar\) is the reduced [PERSON]'s constant, \(\tau=uE_{F}/\left(ev_{F}^{2}\right)\) is a parameter describing the carrier relaxation time, with \(E_{F}\) being the Fermi energy of graphene. In this paper, the Fermi velocity \(v_{F}=1.1\times 10^{6}\) m/s and the carrier mobility \(u=3000\) cm\({}^{2}/\left(\)V\(\cdot\)s\(\right)\) are assumed, which are realistic for the monolayer graphene material [28]. Thus, as shown in Figure 2, the conductivity of graphene can be tuned as function of Fermi energy. According to the expression \(E_{F}\propto\sqrt{V_{g}}\)[29], the Fermi energy can be flexibly controlled by applying the external gate voltage \(V_{g}\). Using the above strategy, an electric control of resonator response can be realized by varying the optical conductivity of the graphene layer.