Landau Raman Regulation Observed from Geometric Graphene Structures Including Single-Wall Carbon Nanotubes

Here, we report Landau regulation in Raman modes for geometric graphene structures including single-wall carbon nanotubes (SWNTs). First-principles calculations show that radial-tangential Raman modes (RTMs) (comprising radial and tangential Eigenvectors) appear in order, following radial breading mode (RBM) (~150 cm-1). RTMs reveal two degenerated or non-degenerated frequencies per node and extend upto G (~1590 cm-1). In Raman measurements for SWNTs, we demonstrate the existence of RTMs at ~180-1440 cm-1, which have been partially interpreted as RBM band for ~180-300 cm-1 and intermediate frequency mode for 600-1300 cm-1. We reinterpret the RBM band as a coalescent signature of RBM (~150-170 cm-1) and 1st node RTM (~170-190 cm-1) for geometric graphene structures of ~2.0-2.2 nm in diameter. The sequential appearance of RBM and RTM and the revelation of the double degeneracy are due to Landau regulation working on spatial variation of the radial and tangential Eigenvectors. Our findings provide a further way of understanding the nature of low dimensional materials utilizing Raman spectroscopy.