## 3 Results and Discussions
From Figure 6b, we can evaluate that when external voltages are changed from 0.9 to 14 V, the Fermi energy is tuned from 0.05 to 0.20 eV, thus the group delay of the metamaterial can be reduced from 3.3 to 0.5 ps. Therefore, the active modulation of the slow light effect can be realized, which is highly desirable in terahertz communication. To further investigate the influence of the graphene layer, the responses of the metamaterial with the width of the graphene strip increasing from 22 to 42 \(\upmu\)m are calculated and depicted in Figure 7. The Fermi energy is fixed at 0.05 eV. The transmission amplitude of the whole transparency window declines gradually when the size of the graphene layer is increased. Intriguingly, there exists a remarkable difference between the two circumstances when the strip width is more and less than the U-shaped ring length \(l_{2}\). The transparency window remains noticeable regardless of degradation as the strip width is less than \(l_{2}\). However, if the width is larger than \(l_{2}\), the amplitude of the transparency dips sharply rises and the EIT effect almost disappears. As the U-shaped ring and the substrate are completely separated by the graphene layer, the complete interaction between the bright resonator and the graphene strip destroys the radiative mode. This destruction accounts for the sharp increase of transmission dips and the vanishing of the EIT window. As can be inferred from the transmission spectra in Figure 7, the strip width of the graphene layer can also have a significant impact on the slow light effect. Figure 8 shows the variations of the group delay spectra with different strip widths. It is interesting to see that the group delay manifests a slight increase from 3.6 to 3.7 ps as the strip width rises from 27 to 32 \(\upmu\)m. The enhanced interaction between the graphene layer and the U-shaped ring arising from the wider strip may account for the larger group delay. As the strip width becomes larger than U-shaped ring length, the group delay sharply declines to a much smaller value of 1.4 ps, which coincides with the vanishing trend of the  
Figure 6: (**a**) The group delay of the hybrid metamaterial with and without the graphene layer; (**b**) the approximate relation between the gate voltages and the Fermi energy. transparency window depicted in Figure 1:0 The slow light effect disappears when the strip width further increases to 42 \(\upmu\)m. Therefore, the optical buffering performance of the hybrid structure can be completely switched through changing the width of the graphene strip. As is well known, the carrier mobility is a critical index of graphene quality, which is closely related to the surface conductivity. In practice, it is a variable dependent on the production process. Here, the effect of the carrier mobility on the spectral response of the EIT metamaterial is investigated, which has seldom been reported as far as we know. The Fermi energy of the graphene strip is fixed at 0.10 eV. Figure 9a shows the transmission spectra of the proposed structure with carrier mobility \(\mu\) in the graphene varying from 2000 to 4000 cm\({}^{2}\) V\({}^{-1}\) s\({}^{-1}\). It can be seen that as \(\mu\) increases, the transparency peak declines slightly while the amplitude of transmission dips gradually rises, indicating the weakening of the EIT phenomenon. This trend is similar with the circumstance when the Fermi energy is increased, since the surface conductivity is enhanced with higher carrier mobility. Moreover, the group delay spectra with different carrier mobility are calculated, as depicted in Figure 9b. A noticeable decrease in the group delay can be observed, and the maximum value is reduced from 2.1 to 1.4 ps as \(\mu\) increases from 2000 to 4000 cm\({}^{2}\) V\({}^{-1}\) s\({}^{-1}\). It is worth noting that larger variations of the carrier mobility can lead to more drastic fluctuations in both the transmission and the group delay spectra.