Exchange Coulomb interaction in nanotubes: Dispersion of Langmuir waves

TL;DR

This paper derives the Coulomb exchange interaction for electrons on nanotubes using quantum hydrodynamics, highlighting curvature effects and calculating dispersion relations for electron oscillations.

Contribution

It provides a microscopic derivation of exchange interactions on nanotubes and analyzes curvature effects on electron dynamics.

Findings

Curvature influences exchange interaction strength.

Dispersion relations for Langmuir waves on nanotubes are obtained.

Exchange effects modify electron oscillation characteristics.

Abstract

Microscopic derivation of the Coulomb exchange interaction for electrons located on the nanotubes is presented. Our derivation is based on the many-particle quantum hydrodynamic method. We demonstrate the role of the curvature of the nanocylinders on the force of the exchange interaction. We calculate corresponding dispersion dependencies for electron oscillations on the nanotubes.