Third and fourth optical transitions in semiconducting carbon nanotubes.

TLDR: This work establishes the diameter and chiral angle dependence of the poorly studied third and fourth optical transitions in semiconducting tubes and explains the result showing strongly bound excitons in the first and second transitions and a delocalized electron wave function in the third transition.

Abstract: We have studied the optical transition energies of single-wall carbon nanotubes over broad diameter (0.7–2.3 nm) and energy (1.26 –2.71 eV) ranges, using their radial breathing mode Raman spectra. We establish the diameter and chiral angle dependence of the poorly studied third and fourth optical transitions in semiconducting tubes. Comparative analysis between the higher lying transitions and the first and second transitions show two different diameter scalings. Quantum mechanical calculations explain the result showing strongly bound excitons in the first and second transitions and a delocalized electron wave function in the third transition. In carbon nanotubes [1], quantum confinement is responsible for 1D van Hove singularities in the electronic density of states and unusually strong many-body (electron-electron and electron-hole) interactions [2]. Current understanding of the photophysical properties of semiconducting carbon nanotubes [2 –7] are based mostly on experimental results for the first (E S ) and second (E S ) optical transitions (S superscript stands for semiconducting, while M will be used for metallic tubes), based on a set of fewer than 40 SWNTs (characterized by their (n, m) indices [1]) in the diameter range from 0.7 to 1.3 nm [8– 13]. Efforts have been made to extend these results to larger diameter tubes, and to establish the third (E S ) and fourth (E S ) transitions [14,15]. E S and E S are important for the optics of large diameter semiconducting single-wall carbon nanotubes (SWNTs), since for dt > 1: 3n m, E S is already in the infrared range [8–11]. Here we measure the optical properties of SWNTs over broad diameter (0.7–2.3 nm) and energy (1.26 –2.71 eV) ranges. We probe over 200 different SWNT species, about 378 different optical transition energies, going up to the fourth optical transition of semiconducting SWNTs, thus establishing the (n, m) dependence of the poorly studied E S and E S transitions. Surprisingly, we find that E S and E S follow a different (blue-shifted) diameter scaling when compared with E S and E S . These results are supported by electronic structure calculations showing that E S and E S are described by bound exciton states, whereas the E S transitions correspond to a delocalized exciton or to an unbound electron-hole pair. The sample consists of as-grown vertically aligned SWNTs, synthesized by the chemical vapor deposition method from alcohol, on top of a quartz substrate. Transmission Electron Microscopy shows a rather homogeneous sample formed by isolated SWNTs and very small