Formation of Subgap States in Carbon Nanotubes Due to a Local Transverse Electric Field

TL;DR

This paper models how a localized transverse electric field can induce subgap states in semiconducting carbon nanotubes, revealing threshold and resonant behaviors affecting the binding energies of these states.

Contribution

It introduces simple models to analyze the formation and properties of localized subgap states caused by local electric fields in carbon nanotubes.

Findings

Weak fields create localized states inside the band gap.

Binding energy exhibits threshold and rapid increase behaviors.

Resonant maximum in binding energy as potential range varies.

Abstract

We introduce two simple models to study the effect of a spatially localized transverse electric field on the low-energy electronic structure of semiconducting carbon nanotubes. Starting from the Dirac Hamiltonian for the low energy states of a carbon nanotube, we use scattering theory to show that an arbitrarily weak field leads to the formation of localized electronic states inside the free nanotube band gap. We study the binding energy of these subgap states as a function of the range and strength of the electrostatic potential. When the range of the potential is held constant and the strength is varied, the binding energy shows crossover behavior: the states lie close to the free nanotube band edge until the potential exceeds a threshold value, after which the binding energy increases rapidly. When the potential strength is held constant and the range is varied, we find resonant behavior: the binding energy passes through a maximum as the range of the potential is increased. Large electric fields confined to a small region of the nanotube are required to create localized states far from the band edge.