Electron-plasmon interaction in a cylindrical mesoscopic system: important similarities with Kaluza-Klein theories

TL;DR

This paper explores the analogy between electron-plasmon interactions in cylindrical mesoscopic systems and Kaluza-Klein theories, revealing long-range interactions and their implications for electromagnetic and transport properties in quantum wires.

Contribution

It introduces a novel analogy between mesoscopic electron-plasmon interactions and Kaluza-Klein theories, providing new insights into long-range interactions and their effects on quantum wire properties.

Findings

Electron and plasmon states with non-zero angular momentum exhibit strong long-range interactions.

Solutions to nonlinear Maxwell equations confirm the interaction mechanisms.

Density-dependent spin polarization can be explained by electron energy level splitting.

Abstract

Similarities between nonlinear electron-plasmon interactions in a cylindrical mesoscopic system and Kaluza-Klein theories, which stem from the analogy between the angular coordinate of a nanocylinder with the compactified coordinates of the Kaluza-Klein theories, have been considered. These similarities indicate that electron and plasmon states with non-zero angular momenta exhibit strong long-range interaction with each other via exchange of plasmons with zero angular momentum. This insight has been confirmed by finding correspondent solutions of the nonlinear Maxwell equations for interacting plasmons. Such solutions have important consequences for description of electromagnetic and transport properties of mesoscopic metallic wires, holes and rings, such as recent observation of density-dependent spin polarization in quantum wires. Numerical estimates indicate that the latter effect can be explained by the electron energy level splitting in the gyration field induced due to the magneto-optical effect by the current flowing through the quantum wire.