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Electron-Hole Asymmetry in Single-Walled Carbon Nanotubes Probed by Direct Observation of Transverse Quasi-Dark Excitons

We studied the asymmetry between valence and conduction bands in single-walled carbon nanotubes (SWNTs) through the direct observation of spin-singlet transverse dark excitons using polarized photoluminescence excitation spectroscopy. The intrinsic electron-hole (e-h) asymmetry lifts the degeneracy of the transverse exciton wavefunctions at two equivalent K and K' valleys in momentum space, which gives finite oscillator strength to transverse dark exciton states. Chirality-dependent spectral weight transfer to transverse dark states was clearly observed, indicating that the degree of the e-h asymmetry depends on the specific nanotube structure. Based on comparison between theoretical and experimental results, we evaluated the band asymmetry parameters in graphene and various carbon nanotube structures.