Unified Quantification of Quantum Defects in Small-Diameter Single-Walled Carbon Nanotubes by Raman Spectroscopy

The covalent functionalization of single-walled carbon nanotubes (SWCNTs) with luminescent quantum defects enables their application as near-infrared single-photon sources, as optical sensors, and for in-vivo tissue imaging. Tuning the emission wavelength and defect density are crucial for these applications. While the former can be controlled by different synthetic protocols and is easily measured, defect densities are still determined as relative rather than absolute values, limiting the comparability between different nanotube batches and chiralities. Here, we present an absolute and unified quantification metric for the defect density in SWCNT samples based on Raman spectroscopy. It is applicable to a range of small-diameter nanotubes and for arbitrary laser wavelengths. We observe a clear inverse correlation of the D/G$^{+}$ ratio increase with nanotube diameter, indicating that curvature effects contribute significantly to the defect-activation of Raman modes. Correlation of intermediate frequency modes with defect densities further corroborates their activation by defects and provides additional quantitative metrics for the characterization of functionalized SWCNTs.