Effects of rotation in the energy spectrum of $C_{60}$

TL;DR

This paper models the effects of rotation on the electronic energy spectrum of $C_{60}$ molecules using an effective Dirac equation with gauge fields, revealing shifts and splittings in energy levels due to rotation.

Contribution

It introduces a continuum model incorporating rotation into the Dirac equation for $C_{60}$, providing analytical solutions and revealing how rotation affects zero modes and energy spectra.

Findings

Rotation causes shifts in zero modes.

Rotation induces Zeeman-like splitting.

Analytical solutions match static case when rotation is zero.

Abstract

In this paper, motivated by the experimental evidence of rapidly rotating $C_{60}$ molecules in fullerite, we study the low-energy electronic states of rotating fullerene within a continuum model. In this model, the low-energy spectrum is obtained from an effective Dirac equation including non-Abelian gauge fields that simulate the pentagonal rings of the molecule. Rotation is incorporated into the model by solving the effective Dirac equation in the rotating referential frame. The exact analytical solution for the eigenfunctions and energy spectrum is obtained, yielding the previously known static results in the no rotation limit. Due to the coupling between rotation and total angular momentum, that appears naturally in the rotating frame, the zero modes of static $C_{60}$ are shifted and also suffer a Zeeman splitting whithout the presence of a magnetic field.