Strong exciton-plasmon coupling in semiconducting carbon nanotubes

We study theoretically the interactions of excitonic states with surface electromagnetic modes of small-diameter $\left(\lesssim 1\text{nm}\right)$ semiconducting single-walled carbon nanotubes. We show that these interactions can result in strong exciton-surface-plasmon coupling. The exciton absorption line shape exhibits Rabi splitting $\sim 0.1\text{eV}$ as the exciton energy is tuned to the nearest interband surface-plasmon resonance of the nanotube. We also show that the quantum confined Stark effect may be used as a tool to control the exciton binding energy and the nanotube band gap in carbon nanotubes in order, e.g., to bring the exciton total energy in resonance with the nearest interband plasmon mode. The exciton-plasmon Rabi splitting we predict here for an individual carbon nanotube is close in its magnitude to that previously reported for hybrid plasmonic nanostructures artificially fabricated of organic semiconductors on metallic films. We expect this effect to open up paths to new tunable optoelectronic device applications of semiconducting carbon nanotubes.

Figure 1

(Color online) The geometry of the problem.

Figure 2

(Color online) Schematic of the two transversely quantized azimuthal electron-hole subbands (left) and the first-interband ground-internal-state exciton energy (right) in a small-diameter semiconducting carbon nanotube. Subbands with indices $j=1$ and 2 are shown, along with the optically allowed (exciton-related) interband transitions (Ref. 53). See text for notations.

Figure 3

(Color online) [(a) and (b)] Calculated dimensionless (see text) axial surface conductivities for the (11,0) and (10,0) CNs. The dimensionless energy is defined as $\left[\text{Energy}\right]/2{\gamma }_0$, according to Eq. (17).

Figure 4

(Color online) [(a) and (b)] Surface-plasmon DOS and conductivities (left panels) and lowest bright exciton dispersion when coupled to plasmons (right panels) in (11,0) and (10,0) CNs, respectively. The dimensionless energy is defined as $\left[\text{Energy}\right]/2{\gamma }_0$, according to Eq. (17). See text for the dimensionless quasimomentum.

Figure 5

(Color online) (a) Calculated binding energies of the first bright exciton in the (11,0) and (10,0) CNs as functions of the perpendicular electrostatic field applied. Solid lines are the numerical solutions to Eq. (34), dashed lines are the quadratic approximations as given by Eq. (35). (b) Field dependence of the effective cutoff Coulomb potential (31) in the (11,0) CN. The dimensionless energy is defined as $\left[\text{Energy}\right]/2{\gamma }_0$, according to Eq. (17).

Figure 6

(Color online) [(a) and (b)] Calculated dependences of the first bright exciton parameters in the (11,0) and (10,0) CNs, respectively, on the electrostatic field applied perpendicular to the nanotube axis. The dimensionless energy is defined as $\left[\text{Energy}\right]/2{\gamma }_0$, according to Eq. (17). The energy is measured from the top of the first unperturbed hole subband.

Figure 7

(Color online) [(a) and (b)] Exciton absorption-emission line shapes as the exciton energies are tuned to the nearest plasmon resonance energies (vertical dashed lines in here; see Fig. 3 and left panels in Fig. 4) in the (11,0) and (10,0) nanotubes, respectively. The dimensionless energy is defined as $\left[\text{Energy}\right]/2{\gamma }_0$ according to Eq. (17).

Figure 8

(Color online) The dimensionless function (D13) with the zero-field cutoff parameter (D14). See text for details.