Using surface plasmonics to turn on fullerene's dark excitons

Using our recently proposed Bethe-Salpeter $G_0{W}_0$ formulation, we explore the optical absorption spectra of fullerene (${\mathrm{C}}_{60}$) near coinage metal surfaces (Cu, Ag, and Au). We pay special attention to how the surface plasmon ${\omega }_S$ influences the optical activity of fullerene. We find that the lower-energy fullerene excitons at $3.77$ and $4.8$ eV only weakly interact with the surface plasmon. However, we find that the surface plasmon strongly interacts with the most intense fullerene $\pi$ exciton, i.e., the dipolar mode at $\hslash {\omega }_{+}\approx 6.5$ eV, and the quadrupolar mode at $\hslash {\omega }_{-}\approx 6.8$ eV. When fullerene is close to a copper surface ($z_0\approx 5.3$ Å), the dipolar mode ${\omega }_{+}$ and “localized” surface plasmons in the molecule/surface interface hybridize to form two coupled modes which both absorb light. As a result, the molecule gains an additional optically active mode. Moreover, in resonance, when ${\omega }_S\approx {\omega }_{\pm }$, the strong interaction with the surface plasmon destroys the ${\omega }_{-}$ quadrupolar character and it becomes an optically active mode. In this case, the molecule gains two additional very intense optically active modes. Further, we find that this resonance condition, ${\omega }_S\approx {\omega }_{\pm }$, is satisfied by silver and gold metal surfaces.

Figure 1

Schematic depicting $x$-polarized incident light of energy $\hslash \omega$ being absorbed by a fullerene molecule at a height $z_0$ above a metal surface.

Figure 2

Calculated HOMO-LUMO gap of fullerene in eV as a function of the height $z_0$ in Å above a metal surface using (black dots) the full dynamical $G_0{W}_0$ correction of Eqs. (28) and (29), (red squares) image theory of Eq. (32), and (blue diamonds) a HOMO and LUMO corrected by the image potential ($\pm e^2/4z_0$). The gas-phase result (black dashed line) is provided for comparison.

Figure 3

Optical absorption intensity for an isolated fullerene molecule as a function of the incident $x$-polarized light's energy $\hslash \omega$ in eV. The calculated spectrum (black solid line) is compared with the measured spectrum from Ref. [51].

Figure 4

Fullerene optical absorption intensity as a function of the incident $x$-polarized light's energy $\hslash \omega$ in eV and the molecule's height $z_0$ in Å above a copper surface ($r_s\approx 2.7a_0$).

Figure 5

Fullerene optical absorption intensity as a function of the inverse coupling constant $V^{-1}$ in eV${}^{-1}$ obtained from the point polarizable dipole model of Eqs. (20, 21, 22). Dipole frequencies are chosen to be $\hslash {\omega }_{\pi }\approx 6.50$ eV and $\hslash {\omega }_S\approx 7.51$ eV, respectively.

Figure 6

Fullerene optical absorption intensity as a function of the incident $x$-polarized light's energy $\hslash \omega$ in eV and the molecule's height $z_0$ in Å above a silver or gold surface ($r_s\approx 3.0a_0$).

Figure 7

Dipole energy loss spectra as a function of the energy $\hslash \omega$ in eV of an $x$-polarized driving dipole placed at 6.35 Å (black solid line) above, (red dashed line) in a symmetric configuration, and (blue dash-dotted line) in an antisymmetric configuration above and below the molecule's centroid.

Figure 8

Induced charge density distributions of (a) an isolated fullerene molecule's dipolar and quadrupolar modes ${\omega }_{+}$ and ${\omega }_{-}$, respectively, and (b) the fullerene/metal surface coupled modes ${\omega }_1$, ${\omega }_2$, and ${\omega }_3$.