Exciton Hierarchies in Gapped Carbon Nanotubes

TL;DR

This paper investigates how strong electron-electron interactions in gapped carbon nanotubes create a hierarchy of excitons, revealing detailed gap ratios and dispersion relations through a field theoretic and numerical renormalization approach.

Contribution

It introduces a novel field theoretic reduction and numerical analysis to precisely determine exciton hierarchies and gap ratios in gapped carbon nanotubes under strong interactions.

Findings

Determined gap ratios of one-photon excitons as a function of interaction strength.

Calculated gaps of two-photon and dark excitons within the same subband.

Observed strongly renormalized dispersion relations indicating spin-charge separation.

Abstract

We present evidence that the strong electron-electron 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 electron-electron 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 electron-electron interactions in addition lead to strongly renormalized dispersion relations where the consequences of spin-charge separation can be readily observed.