Edge-state signature in optical absorption of nanographenes: Tight-binding method and time-dependent density functional theory calculations

The optical absorption of triangular nanographenes with well-defined edge structure, that is, zigzag- and armchair-type edges, is studied using the tight-binding method within the Hückel approximation. The absorption spectra of zigzag triangular nanographenes exhibit rich peak structures originating from the excitations associated with the edge states, while those of armchair ones do not. The main feature in the absorption spectra is reproduced by time-dependent density functional theory calculations within a real-time scheme. By varying the size of the nanographenes, we elucidate the role of the edge states in the optical absorption, which becomes conspicuous when the graphene size is on a nanometer scale. Our finding in this paper provides a way to capture the edge-state signature by optical experiments with visible light.

Figure 1

Structures of (a) zigzag nanographene with $N_z=6$ and (b) armchair nanographene with $N_a=4$. The edge carbon atoms are indicated by solid circles on each side.

Figure 2

(Color online) Density of states of zigzag TNGs with $N_z$=(a) 4, (b) 10, and (c) 50. Dashed curves represent the DOS of 2D graphene. These DOSs are normalized by the number of carbon atoms in the system.

Figure 3

(Color online) Optical absorption cross sections of zigzag TNGs with $N_z$=(a) 4, (b) 10, and (c) 50 calculated by the tight-binding method. Dashed curves represent the DOS of 2D graphene. The inset of (a) is the cross section of zigzag TNGs with $N_z=4$ calculated by the TDDFT method.

Figure 4

The ratio of the oscillator strength associated with the edge states to the total oscillator strength of zigzag TNGs as a function of $N_z$. The curve is a guide to the eye.