Spectrum and Franck-Condon factors of interacting suspended single-wall carbon nanotubes

TL;DR

This paper develops a low energy theoretical model for suspended carbon nanotube quantum dots, analyzing how their spectrum and Franck-Condon factors depend on junction geometry and vibronic modes, revealing different electromechanical regimes.

Contribution

It introduces a comprehensive theory linking junction geometry and vibronic modes to the electromechanical properties of suspended carbon nanotube quantum dots.

Findings

Different regimes: short vibron with plasmon-vibron excitations

Long vibron with polaron excitations

Position-dependent Franck-Condon couplings

Abstract

A low energy theory of suspended carbon nanotube quantum dots in weak tunnelling coupling with metallic leads is presented. The focus is put on the dependence of the spectrum and the Franck-Condon factors on the geometry of the junction including several vibronic modes. The relative size and the relative position of the dot and its associated vibrons strongly influence the electromechanical properties of the system. A detailed analysis of the complete parameters space reveals different regimes: in the short vibron regime the tunnelling of an electron into the nanotube generates a plasmon-vibron excitation while in the long vibron regime polaron excitations dominate the scenario. The small, position dependent Franck-Condon couplings of the small vibron regime convert into uniform, large couplings in the long vibron regime. Selection rules for the excitations of the different plasmon-vibron modes via electronic tunnelling events are also derived.