title: Exciton hierarchies in gapped carbon nanotubes.
abstract: We present evidence that the strong electron-electron (e-e) interactions in gapped carbon nanotubes lead to finite hierarchies of excitons within a given nanotube subband. We study these hierarchies by employing a field theoretic reduction of the gapped carbon nanotube permitting e-e interactions to be treated exactly. We analyze this reduction by employing a Wilsonian-like numerical renormalization group. We are so able to determine the gap ratios of the one-photon excitons as a function of the effective strength of interactions. We also determine within the same subband the gaps of the two-photon excitons, the single particle gaps, as well as a subset of the dark excitons. The strong e-e interactions in addition lead to strongly renormalized dispersion relations where the consequences of spin-charge separation can be readily observed.
authors.affiliation: Condensed Matter Physics and Material Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA.
authors.forename: Robert M
authors.initials: RM
authors.lastname: Konik