Observation of Drastic Electronic-Structure Change in a One-Dimensional Moiré Superlattice

We report the first experimental observation of a strong-coupling effect in a one-dimensional moiré superlattice. We study one-dimensional double-wall carbon nanotubes (DWCNTs) in which van der Waals–coupled two single nanotubes form a one-dimensional moiré superlattice. We experimentally combine Rayleigh scattering spectroscopy and electron beam diffraction on the same individual DWCNTs to probe the optical transitions of the structure-identified DWCNTs in the visible spectral range. Among more than 30 structure-identified DWCNTs examined, we experimentally observed and identified a drastic change of the optical transition spectrum in a DWCNT with chirality (12,11)@(17,16). The origin of the marked change is attributed to the strong intertube coupling effect in the moiré superlattice formed by two nearly armchair nanotubes. Our numerical simulation is consistent with the experimental findings.

Figure 1

Rayleigh scattering spectra of two typical structure-identified DWCNTs with weak coupling. (a) Spectrum for DWCNT (15,13)@(21,17). (b) Spectrum for DWCNT (22,4)@(23,18). In both (a) and (b), red and blue arrows mark the optical transitions for inner and outer nanotubes, respectively. The experimental data are presented by red open circles. Each fitted optical transition is presented with a black curve, and the overall fitted spectrum is shown by a solid green line.

Figure 2

Structure characterization of a DWCNT (12,11)@(17,16) showing a strong-coupling effect. (a) TEM image of the DWCNT. Dashed lines indicate the walls of two constituent nanotubes. The scale bar is $\sim 2\mathrm{nm}$. (b) Experimental electron diffraction pattern. (c) Simulated electron diffraction pattern of a DWCNT with chirality (12,11)@(17,16). Two yellow arrows indicate the position of the equatorial line in the diffraction pattern. The dashed lines are eye guidance to show one of the key identities between the experiment and simulation.

Figure 3

Rayleigh spectrum of DWCNT (12,11)@(17,16) showing a strong-coupling effect. Experimental data are shown in the solid black line. Dashed red and blue lines indicate the expected optical transition energies for pristine inner and outer nanotubes, respectively.

Figure 4

Theoretical calculation of DWCNT (12,11)@(17,16) within a tight-binding and effective continuum model. (a) Calculated band structure of two pristine nanotubes (12,11) in red and (17,16) in blue in a DWCNT without intertube coupling. (b) Calculated band structure of coupled DWCNT (12,11)@(17,16). (c) Calculated optical absorption spectra for a pristine inner nanotube (dashed red line), a pristine outer nanotube (dashed blue line) and the coupled DWCNT (solid black line). Optical transitions from pristine inner and outer nanotubes are specified (e.g., $S_{33}$, $S_{44}$, etc.). Different transitions for the coupled DWCNT in (c) are denoted by different markers which originate from interband transitions as indicated with the same markers in the calculated band structure in (b). Note that the peak at $\sim 2.4\mathrm{eV}$ (solid black line) is comprised of multiple peaks that are very close in energy. $a$ in the horizontal axises in (a) and (b) denotes the graphene lattice constant.