Dipolar and charged localized excitons in carbon nanotubes

We study both experimentally and theoretically the fundamental interplay of exciton localization and polarization in semiconducting single-walled carbon nanotubes. From Stark spectroscopy of individual carbon nanotubes at cryogenic temperatures, we identify localized excitons as permanent electric dipoles with dipole moments of up to $1e\AA$. Moreover, we demonstrate field-effect doping of localized excitons with an additional charge which results in defect-localized trions. Our findings, in qualitative agreement with theoretical calculations, not only provide fundamental insight into the microscopic nature of localized excitons in carbon nanotubes, they also signify their potential for sensing applications and may serve as guidelines for molecular engineering of exciton-localizing quantum dots in other atomically thin semiconductors including transition metal dichalcogenides.

Figure 1

(a) Schematic layout of the experiment: carbon nanotubes, dispersed in between insulating oxide layers (${\mathrm{SiO}}_2$ and ${\mathrm{Al}}_2{\mathrm{O}}_3$), were subjected to a transverse electric field by applying a gate voltage $V_g$ to the semitransparent top gate (NiCr) with respect to the back gate ($p$-doped Si). The response of individual nanotubes to the electric field was studied with confocal excitation (laser) and detection of the photoluminescence (PL) at the temperature of liquid helium (4.2 K). (b) and (c) Photoluminescence spectra of individual nanotubes with single-peak ($X$) and double-peak ($X,X^{*}$) emission spectra at $V_g=0$ V.

Figure 2

(a) The transverse electric field (with orientation indicated by the inset schematics) was varied via the gate voltage from zero to $+V_{\max }$, then to $-V_{\max }$ and back to zero again according to the zigzag ramp with temporal progress in sequential steps along the $x$ axis as indicated by the arrow. (b) and (c) False-color plots of the photoluminescence from nanotubes in Fig. 1 in response to the field ramp shown in (a). In the regions of low intensity, the peak maxima are shown as blue circles where peak fitting converged; the intensity in the lower panel of (c) was magnified by a factor of 10. The red solid lines are linear fits to the dispersion with slopes determined by the corresponding permanent dipole moments $p$. (d) Histogram of the absolute values of dipole moments extracted from linear fits as in (b) and (c) for nanotubes with emission energy in the range $1.35\text{–}1.43$ eV. (e) For the majority of nanotubes with double-peak emission, the signs of dipole moments of the $X$ and $X^{*}$ states, $p_X$ and $p_{X^{*}}$, were anticorrelated (data in the grey-shaded quadrants).

Figure 3

Electric field dispersions of the two bright states (blue and dark blue data points in the upper and lower panels) associated with an oxygen-defect in ether-d configuration. The orientation of the defect with respect to the electric field is indicated in the inset schematics of the right and left panels. The numbers give the slopes in units of the permanent dipole moment, $e\AA$, extracted from linear fitting (solid lines) performed separately for positive and negative electric fields. The dashed line is a guide to the eye.

Figure 4

(a) Logarithmic false-color plot of the photoluminescence evolution in response to a field ramp as in Fig. 2 with peak-voltage values of $\pm 30$ V. The narrow peaks are Raman sidebands of the excitation laser at 1.484 eV amplified by the logarithmic color scale. In addition to the $X$ and $X^{*}$ peaks, trion ($T$) satellite emission appears at negative gate voltages. (b) Photoluminescence spectra at $V_g=0$ and $-10$ V (grey, magnified by a factor of 5). The distribution of trion binding energies, as given by the energy splitting ${\mathrm{\Delta }}_{{\mathrm{TX}}^{*}}$ between the $T$ and $X^{*}$ peaks of all nanotubes with trion satellites, is shown in the inset.