# Effect of Nanodisks at Different Positions on the Fano Resonance of Graphene Heptamers
## 3 Simulation Results and Discussions  
### The Effect of the Chemical Potential of the Central Nanodisk on Fano Resonance  
Usually, Fano resonance can be obtained by two approaches [26]. One approach is to destroy the symmetry of the structure [33; 34]. Another approach is to introduce additional nanoparticles without changing the symmetry [35; 36]. In order to study the formation of Fano resonance of graphene heptamers with \(D_{6h}\) symmetry, nanoclusters with/without the central nanodisk are calculated respectively. Figure 2a shows the structure of the hexamer without the center disk and the distribution of the chemical potential. Six nanodisks with same chemical potential setting at 0.5 eV are evenly placed on the satellite orbit. Strikingly, there is only a pronounced resonance peak in extinction spectrum when the wavelength ranges from 4.6 \(\upmu\)m to 4.9 \(\upmu\)m, as shown in Figure 2b. This peak is labeled as A and the corresponding electric field \(|\)E\(|\) distribution is presented in Figure 2c. For peak A, the hot spots distribute evenly on the edge of all nanodisks. Simultaneously, a single nanodisk was calculated to investigate the coupling strength between ring nanodisks, as shown in Figure 2d. A single nanodisk at different positions in the ring has the same distribution of electromagnetic field without coupling between nanodisks [12]. However, the PMs, consisting of these single nanodisks, show uneven electromagnetic field distribution because of the coupling effect of the electromagnetic field, which means that the contribution of some nanodisks to the collective behavior is different [16; 35]. By comparing the amplitudes of a single nanodisk and hexamer, it is clearly seen that the coupling between nanodisks can greatly enhance the amplitude of the resonance peak. In the hexamer, the amplitude of the resonance peak is 1096.511 nm\({}^{2}\) (see Figure 2b), while the counterpart of the single nanodisk is 7.792 nm\({}^{2}\) (see Figure 2d). Therefore, the coupling of plasmons between the nanodisks can increase the strength by at least two orders of magnitude. Also, it makes the resonance peak red shift. However, an intriguing phenomenon appears when a central graphene nanodisk is added into this structure. The surface plasmon mode of the central nanodisk couples with the satellite nanodisks through near-field interaction, which results in a new local plasmon hybridization mode. In order to exclude the effect of the distances between nanodisks on the collective behavior, \(R_{2}\) is kept at 90 nm and d is kept at 10 nm. When the chemical potential of the central nanodisk is consistent with the satellite nanodisks, two plasmonic resonance peaks and a dip appear in the extinction spectrum, as represented in the top of Figure 3b. Two peaks from left to right in the extinction spectrum are marked as B and C, respectively. The electric-field intensity distribution of peak B is given in Figure 3c. Figure 2: (**a**) There are only six graphene nanodisks with same chemical potential (\(\mu_{\text{c1}}\)) on satellite orbits. (**b**) A pronounced peak in the extinction spectrum of the graphene hexamer appears when the incident plane light wavelength ranges from 4.6 \(\upmu\)m to 4.9 \(\upmu\)m. (**c**) The electric field (\(|\)E\(|\)) distribution of A. (**d**) The calculated extinction spectrum of a single nanodisk in the ring (left panel). Simultaneously, the central nanodisk is also considered (right panel). In contrast to the peak A, this collective behavior of the hexamer and the heptamer demonstrates striking similarities. For convenience, this mode is referred to mode I. However, compared with peak B, peak C shows a different phenomenon, indicating that the satellite nanodisks couple strongly with the central nanodisk. Hot points at peak C are transferred to the gap between the central nanodisk and the satellite nanodisks, which show another mode relative to peak A and peak B. This mode is defined as mode II.