## 3 Results and Discussions  
The tunability of PIT resonance based on modifying the length parameter and relative distance of the SRRs have been widely studied by many groups [30; 31]. Figure 3a presents the transmission spectra with different split gaps g. The different arrays, identified by the split gap g, present broad resonances range at THz regime. With the increase of split gap from 1 \(\upmu\)m to 4 \(\upmu\)m, the transparent peak moved from 0.47 THz blue to 0.54 THz, and the amplitude of transparency peak decreases form 0.86 to 0.80. In the inductive-capacitive (LC) resonance of SRRs, the split gap has a capacitance effect. The capacitance effect decreases with the increase of split gap. From the expression analysis, \(f\propto 1/\sqrt{LC}\), the corresponding resonance frequency increases. The decrease of the transmission peak height indicates the reduction of the coupling between light and dark modes due to the smaller capacitance effect in the gap. Figure 2: The frequency dependent graphene surface conductivity with different Fermi energies: (**a**) real and (**b**) imaginary parts. Next, a continuous monolayer graphene ribbon, was integrated under the split gap of the bright resonator to obtain active control of PIT resonance, which was different than reported in literature [32, 33]. The common dark mode control method basically controls PIT resonance by adjusting the transparency peak. However, the bright-mode tuning scheme mainly regulates the PIT resonance by shifting the resonance dips on both sides of the transparency peak. The transmission spectra, as the function of Fermi energy, are plotted in Figure 3b. It is worth noting that the PIT line shape can be clearly modulated with increase of Fermi energy. For example, the resonance dips at 0.46 THz and 0.56 THz, amplitude increase from 0.64 to 0.83 and from 0.76 to 0.8, respectively. The transparent window gradually broadens, but the frequency of the transmission peak is almost constant. When \(E_{F}=0.8\) eV, the near-field coupling between the bright and dark resonators disappears, leaving only a broad and flat resonance dip caused by the bright resonator. The complete modulation of the PIT resonance can be realized by merely shifting the Fermi energy of graphene, due to the sensitivity of SRRs to the conductive graphene layer. Figure 3: The tunable transmission spectra for the proposed PIT metamaterial: (**a**) with different gaps \(\mathrm{g}=1\), \(2\), \(3\), \(4\) μm; (**b**) numerical simulation and (**c**) analytical calculation for different Fermi energies. The above modulation behaviors can be quantitatively described by the classical coupled two-particle model [34, 35]:  
\[\chi=\chi_{r}+i\chi_{i}\propto\frac{\omega-\omega_{2}+i\frac{\gamma_{2}}{2}}{ \Big{(}\omega-\omega_{1}+i\frac{\gamma_{1}}{2}\Big{)}\Big{(}\omega-\omega_{2}+i \frac{\gamma_{2}}{2}\Big{)}-\frac{\kappa^{2}}{4}} \tag{3}\]  
Here, bright and dark resonators are plotted by subscripts 1 and 2, respectively. \(\omega_{1}(\omega_{2})\) and \(\gamma_{1}(\gamma_{2})\) are the resonance angular frequency and the damping rate, respectively. The parameter \(\kappa\) is introduced to represent the coupling coefficient between the two resonators, and \(\delta=\omega_{2}-\omega_{1}\) represents the detuning of the resonance frequency of the dark mode from the bright mode. The imaginary part of susceptibility \(\chi_{i}\) determines the loss of energy in the system, thus, the transmission \(T(\omega)\) can be described through the formula \(T(\omega)=1-j\chi_{i}\), where \(j\) is a geometric parameter describing the coupling strength of the bright mode resonator with the incident light. The theoretical calculation results, shown in Figure 3c, are in good agreement with the simulated results except for slight deviations come from the effect related to the periodicity of the metamaterial [36].