Asymmetry in Raman Resonant Excitation Profiles of Single-Wall Carbon Nanotubes: The Role of Kohn Anomaly, Optical Transition Order, and State-Mixing
More recently, these Raman REP studies were expanded to include metallic armchair species, (5,5) through (8,8), excited via E11M. Similar asymmetries to those of semiconducting SWCNTs were observed in the TO phonons of these armchair species while no asymmetry was observed for their respective RBM REPs, emphasizing the similarity in the excitonic nature of the optical states of these two electronic types of SWCNTs. In addition, a new model was developed in terms of a condensed matter formalism involving phonon-mediated state-mixing of dark and bright excitonic states to successfully explain the asymmetry in G-band phonon REPs of both semiconductor and armchair SWCNT species. Here, we extend our understanding of this optical phenomenon by considering the roles that Kohn anomaly, optical transition order and phonon-mediated state-mixing play in the degree of asymmetry observed for SWCNT phonon REPs.
To examine the effect of the Kohn anomaly, we measured G-band phonon REPs of another electronic type of SWCNT, known as narrow-gap semiconductors (NGS), such as the (7,4) and (10,4) species, whose electronic band structure is similar to that of metallic armchair SWCNTs with the exception of a small band gap on the order of 10 meV. Of special interest in NGS SWCNT structures are the LO phonons, which are strongly frequency-softened and broadened through the Kohn anomaly due to strong coupling of LO phonons with the two Fermi points. Such a strong interaction should further enhance the observed REP asymmetry due to non-Condon-based self-interference. Furthermore, NGS-type SWCNT species, such as the (7,4) and (10,4), possess the additional trigonal warping splitting term in their band structure, which causes each optical transition to split into two, allowing for potential quantum interference between upper and lower branch transitions which may produce further asymmetry.
To examine the role of optical transition order on REP asymmetry, we measured RBM and G-band REPs for multiple semiconducting chiralities such as (8,3), (9,1), (5,4), (7,6), (9,4), and (8,6) across multiple optical transitions ranging from E11S-E44S. Generally, the degree of asymmetry increased with increasing transition order for the same SWCNT species for the LO phonon. Additionally, we reexamined whether asymmetry exists in RBM REPs of semiconducting species excited via E11S, where the RBM phonon energy is greater than or equal to the electronic linewidth of the transition, allowing resolution of both incident and scattered resonances of the REP. This was not possible in previous measurements because the electronic linewidths of the optical transitions involved were greater than the RBM phonon energies.
Finally, to test the validity of the phonon-mediated state-mixing model, we prepared isotopically pure 12C- and 13C-samples of single chiralities (7,5), (7,6), and (7,7). Using these samples, excited via E22S for (7,5) and (7,6) and via E11M for (7,7), we compared the measured G-band phonon REPs for both isotopes of the same chirality. While 13C-SWCNTs look identical to their 12C-counterparts in terms of electronic band structure and optical transition energies, the phonons in their Raman spectra decrease in frequency by a factor of √(12/13) due to the isotope effect. If G-band phonon REP asymmetry is really due to mixing of dark and bright excitonic states, mediated by G-band or K-point phonons, which in turn causes quantum interference between excitonic states or transfer of oscillator strength from one excitonic state to another, then a change in the phonon energy mediating such an interaction should cause a visible change in the degree of asymmetry of the REP for the same chirality. The change in the degree of REP asymmetry provides a measure of the magnitude of state-mixing.