Predicting excitonic gaps of semiconducting single-walled carbon nanotubes from a field theoretic analysis

We demonstrate that a nonperturbative framework for the treatment of the excitations of single-walled carbon nanotubes based upon a field theoretic reduction is able to accurately describe experiment observations of the absolute values of excitonic energies. This theoretical framework yields a simple scaling function from which the excitonic energies can be read off. This scaling function is primarily determined by a single parameter, the charge Luttinger parameter of the tube, which is in turn a function of the tube chirality, dielectric environment, and the tube's dimensions, thus expressing disparate influences on the excitonic energies in a unified fashion. We test this theory explicitly on the data reported by Dukovic et al. [Nano Lett. 5, 2314 (2005)] and Sfeir et al. [Phys. Rev. B 82, 195424 (2010)] and so demonstrate the method works over a wide range of reported excitonic spectra.