Engineering Intrinsic and Extrinsic Quantum Interference in Electronic States of Carbon Nanotubes Measured By Resonant Raman Scattering
Authors: Haroz Erik H. 
Published: February 2020

Examination of Raman resonant excitation profiles (REPs) of the radial breathing mode (RBM) and G-band phonons has provided a wealth of new insights into the coupling between electrons/excitons and phonons in single-wall carbon nanotubes. Very recently, new measurements of the REPs of the G-band phonon on highly pure, single semiconducting species SWCNT samples displayed a high degree of asymmetry when comparing the Raman intensity at the incident and scattered Raman resonances for either the first or second optical transitions. The REP asymmetry is due to a self-interference between Condon and non-Condon terms in Raman polarizability, where the effect of the non-Condon term becomes visible in the weak exciton-phonon coupling regime. This results in the observation that the Raman intensity at the scattered resonance is always lower in intensity than that of the incident resonance, a consequence of the failure of the Franck-Condon approximation. This is contrary to the symmetrical G-band REP expected by theory and observed for RBM REPs. At even higher energy optical transitions, quantum interference can occur between a pair of closely spaced electronic transitions, such as the third and fourth transitions in certain semiconducting species, where the scattered resonance of the lower energy optical transition interferes constructively or destructively with the incident resonance of the higher energy optical transition. This is on top of the already underlying self-interference effects stemming from the non-Condon contribution, creating a highly complex and rich energy structure for SWCNT Raman measurements of high energy phonon modes.
Here, we examine the origin of these deviations from the expected symmetrical REPs for exciton-mediated, one-phonon Raman processes in SWCNTs, by expanding the previous measurements on the RBM and G-band phonons to include additional pure SWCNT species as a function of chiral angle, diameter, and electronic type. We measured the intrinsic non-Condon-induced self-interference of the G-band in the “metallic” family of SWCNTs, consisting of the so-called armchair and narrow-gap semiconductor (NGS)-type nanotube species. Specifically, we examined the diameter dependence of REP asymmetry of armchairs ranging from (5,5) to (8,8), as well as the NGS-species (7,4). The addition of these particular nanotube structures allows the examination of the effect of electronic type on REP behavior, where the unique linear band structure of armchair and quasi-linear band structure of NGS species produces additional electron-phonon coupling resonances through the so-called Kohn anomaly, further enhancing the observed REP asymmetry due to non-Condon-based self-interference. Preliminary data already suggests that armchair species exhibit the largest degree of G-band REP asymmetry relative to other species. Furthermore, NGS-type SWCNT species, such as the (7,4), possess the additional trigonal warping splitting term in their band structure, which causes each optical transition to split into two, allowing for additional quantum interference between upper and lower branch transitions.
To further explore and control the degree of quantum interference between transitions possible, we applied mechanical uniaxial strain to single-chirality SWCNTs embedded in stretchable polymer films to further induce and enhance quantum interference for chiralities such as the (12,4), (8,6) and (7,4) and measured their RBM and G-band REPs as a function of strain. Theoretical calculations predict that the application of a few percent uniaxial strain will cause the third and fourth optical transitions in certain type-I semiconductor species and the trigonal-warping split transitions in NGS-type tubes to move toward one another in energy, thereby inducing quantum interference. In this situation, interference can be manipulated and, in some cases where quantum interference did not previously exist, created artificially, allowing a broader range of REP asymmetries to be examined.