# Effect of Nanodisks at Different Positions on the Fano Resonance of Graphene Heptamers
## 3 Simulation Results and Discussions
### The Effect of the Top and Bottom Nanodisks in the Ring on Collective Behaviors  
In order to further research the influence of the changes of the nanodisk on collective behavior, we vary the upper left nanodisk and the lower left nanodisk. The distributions of chemical potential and radius are depicted in Figure 6a,b, respectively. When the chemical potential labeled as \(\mu_{c4}\) gradually increases, the Fano resonance phenomenon is weakened and gradually disappears, which is shown in Figure 6c. Compared with Figure 5c, it can be seen that the Fano resonance disappears much faster than the change of the chemical potential in the upper left nanodisk. In Figure 5c, the Fano resonance disappears when the chemical potential changes to 0.8 eV. However, in Figure 6c, the Fano resonance disappears when the chemical potential changes to 0.7 eV. The change of this situation is caused by the drastic variation of the dipole moment. For the change of radius, a series of extinction spectra with different radii are obtained by varying the radius of the upper left nanodisk and the lower left nanodisk, as presented in Figure 6d. It can be seen that the decrease of the radius makes the Fano resonance gradually disappear. When the radius is reduced to 10 nm, the Fano resonance disappears completely. However, when the nanodisks are completely absent, the extinction spectrum is almost the same as when the radius is 10 nm. This highlights that when the nanodisk is small enough, the nanodisk becomes an isolated particle, and its effect on the collective behavior is negligible. Moreover, the variation of chemical potential and radius does not lead to the change of mode I and mode II. The electric field distributions of the two modes are depicted in Figure 6e. The electric distribution of the plasmonic resonance peak A\({}_{1}\) of mode I shows that the chemical potentials of the upper left nanodisk and the lower left nanodisk not only affect themselves, but also have a great influence on the leftmost nanodisk. When the chemical potentials of the upper left nanodisk and the lower left nanodisk are greater than other nanodisks, the near-field distributions of nanodisks next to them are enhanced [27]. Moreover, the leftmost nanodisk is right in the middle of these two nanodisks, the near-field distribution of the leftmost nanodisk is enhanced. Because the plasmonic peak A\({}_{1}\) belongs to mode I, the enhanced hot spots are evenly distributed around the nanodisk. However, it is observable from the near-field distribution of the plasmonic peak B\({}_{1}\) belonging to mode II that the hot spots on the leftmost nanodisk are mainly distributed between the central nanodisk and the leftmost nanodisk. Figure 5: (**a**) The chemical potential of the upper left nanodisk is labeled as \(\mu_{c3}\). (**b**) The radius of the upper left nanodisk is marked as \(R_{3}\). (**c**) The Fano dip disappears gradually when \(\mu_{c3}\) is varied from 0.5 eV to 0.8 eV. (**d**) The extinction spectra with the change of radius. In order to more comprehensively study the influence of the nanodisks at different positions on the collective behavior, we also modified the parameters of the upper left nanodisk and the lower right nanodisk. The distributions of chemical potential and radius are shown in Figures 7a and 7b, respectively. For the change of chemical potential, it is seen that when the chemical potential is 0.7 eV, the Fano resonance disappears, which is depicted in Figure 7c. Compared with the variation of the upper left nanodisk, the change of Fano resonance in the extinction spectra is similar, except that the Fano resonance disappears faster when the two nanodisks are modified. When \(\mu_{\mathrm{C}}\) increases, the dipole moments of two nanodisks decrease, which causes the net dipole moment of the ring to decrease rapidly. Therefore, it can be seen that the influence of the number of nanodisks on the Fano resonance is different. Fast modulation of Fano resonance is achievable by changing the number of nanodisks in the ring.