Fullerenic solitons

TL;DR

This paper investigates solutions to a modified non-linear Schrödinger equation on a sphere, modeling electron-phonon interactions in fullerenes, revealing new solution branches and their relation to planar cases.

Contribution

It introduces a study of non-linear Schrödinger solutions on a sphere with finite radius, connecting spherical and planar solutions, relevant for fullerene electron-phonon interactions.

Findings

Existence of non-spinning and spinning solutions characterized by wave function nodes.

Discovery of specific solution branches for small sphere radius R.

Some solutions persist as R approaches infinity, matching planar solutions.

Abstract

We study a modified non-linear Schroedinger equation on a 2 dimensional sphere with radius R aiming to describe electron-phonon interactions on fullerenes and fullerides. These electron-phonon interactions are known to be important for the explanation of the high transition temperature of superconducting fullerides. Like in the $R\to \infty$ limit, we are able to construct non-spinning as well as spinning solutions which are characterised by the number of nodes of the wave function. These solutions are closely related to the spherical harmonic functions. For small R, we discover specific branches of the solutions. Some of the branches survive in the $R\to\infty$ limit and the solutions obtained on the plane ($R=\infty$) are recovered.