The continuum gauge field-theory model for low-energy electronic states of icosahedral fullerenes

TL;DR

This paper develops a gauge field-theory model to analyze the low-energy electronic states of icosahedral fullerenes, incorporating geometric and topological effects, and provides exact solutions for eigenfunctions and energy spectra.

Contribution

It introduces a novel continuum gauge field-theory approach that accounts for pentagonal disclinations and spherical geometry in fullerene electronic structure analysis.

Findings

Exact analytical solutions for eigenfunctions.

Explicit energy spectrum calculations.

Effective magnetic monopole representation.

Abstract

The low-energy electronic structure of icosahedral fullerenes is studied within the field-theory model. In the field model, the pentagonal rings in the fullerene are simulated by two kinds of gauge fields. The first one, non-abelian field, follows from so-called K spin rotation invariance for the spinor field while the second one describes the elastic flow due to pentagonal apical disclinations. For fullerene molecule, these fluxes are taken into account by introducing an effective field due to magnetic monopole placed at the center of a sphere. Additionally, the spherical geometry of the fullerene is incorporated via the spin connection term. The exact analytical solution of the problem (both for the eigenfunctions and the energy spectrum) is found.