Tuning the Optically Bright and Dark States of Doped Graphene Quantum Dots

Employing a combination of the many-body configuration-interaction method described by an extended Hubbard model and first-principles calculations, we predict the emergence of high oscillator strength at the near-IR region which originates from the Davydov type of splitting in doped graphene quantum dots (GQDs). Incorporation of the strain in GQDs promotes closely spaced bright states that are pertinent to coherent excitation. Controlling the destructive interference of the functionalized-nanographene quantum states, the dark states can be tuned towards the red end, ensuring that the system is a good candidate for a photocell. On the other hand, the coherent states can be tailored to concentrate the light at a very high intensity, resulting in an opportunity for a photonic device.

Figure 1

(a) Schematic of constructive and destructive interfering states. (b) Absorption spectra of C30 acene GQDs calculated by TD-DFT using the B3LYP functional. (Inset) Edge-state absorption. (c) With an increase in size, edge-state absorption energy gets redshifted more steadily compared to coherent-state ($\beta$) absorption. For edge states, the oscillator strengths remain more or less the same but, for the coherent states, the strengths increase steadily (when taken from the ZINDO calculation).

Figure 2

(a) Variation of oscillator strength $(\times 10)$ and absorption energy of acene GQDs with C30 at different $U/t$ values in a many-body calculation. (b) The transition-energy states get more blueshifted and become more closely spaced having a greater number of states moderate to high oscillator strength $(\times 10)$ at a high $U/t$ ratio, whereas for a low $U/t$ value, bright states are redshifted and are more separated. (c) Emergence of high oscillator strength at the near-IR region due to partial dipole–partial dipole coupling in substituted GQDs.

Figure 3

The orientation of boron and nitrogen in GQDs dictates the alignments of partial dipoles, resulting in either an attractive or a repulsive potential of dipolar coupling. Our DFT calculations show that, for an attractive partial dipole–partial dipole potential, the coherent states are more redshifted than the incoherent states, whereas for a repulsive potential, the incoherent states are in the red end to result either repulsive (a),(c) or attractive (b),(d) potential of dipolar coupling.

Figure 4

(a) For the same sequence of GQD shown in Fig. 3, the optical transition determined by a many-body calculation depends, in a similar fashion, on DFT. The emergence of high oscillator strength $(\times 10)$ in the lower energy is observed due to the dipole-dipole interaction. (b) Schematic of the hybrid QDs and energy states involved in the electron transfer. The relative position of the dark state at lower energy compared to the bright state in GQDs can make the composite efficient in electron transfer by taking either an electron from another excited QD (CT1) or for GQD excitation. An electron from the bright state can go through phonon relaxation to the dark state [CT2(i)], prohibiting the radiative loss and enhancing the electron transfer [CT2(ii)].

Figure 5

Schematic showing, in substituted GQDs, that the attractive dipolar kind of potential will move the coherent state in the red end relative to the incoherent state, whereas the repulsive dipolar kind of potential will operate in the reverse manner.