Abstract
Two dimensional fluorescence spectroscopy on suspensions of carbon nanotubes probes the electronic excitations of carbon nanotubes with unprecedented resolution and reveals systematic deviations from the predictions of conventional one electron theories. We address these problems by formulating a theory of the scaling optical excitation energies with band index, tube radius and chiral angle. This reveals an unconventional scaling relation that arises from a singular self energy contribution to the quasiparticle dispersion relation in the two dimensional graphene sheet. Self energy and excitonic effects from the long range part of the Coulomb interaction for the one dimensional nanotube are separately strong but they largely cancel, exposing the physics of the two dimensional interacting system.
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