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Here, we report Landau regulation in Raman modes for geometric graphenestructures including single-wall carbon nanotubes (SWNTs). First-principlescalculations show that radial-tangential Raman modes (RTMs) (comprising radialand tangential Eigenvectors) appear in order, following radial breading mode(RBM) (~150 cm-1). RTMs reveal two degenerated or non-degenerated frequenciesper node and extend upto G (~1590 cm-1). In Raman measurements for SWNTs, wedemonstrate the existence of RTMs at ~180-1440 cm-1, which have been partiallyinterpreted as RBM band for ~180-300 cm-1 and intermediate frequency mode for600-1300 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 graphenestructures of ~2.0-2.2 nm in diameter. The sequential appearance of RBM and RTMand the revelation of the double degeneracy are due to Landau regulationworking on spatial variation of the radial and tangential Eigenvectors. Ourfindings provide a further way of understanding the nature of low dimensionalmaterials utilizing Raman spectroscopy.

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