Recursion and Path-Integral Approaches to the Analytic Study of the Electronic Properties of $C_{60}$

TL;DR

This paper analytically investigates the electronic structure of C60 molecules using recursion and path-integral methods, providing explicit formulas for energy levels and local densities of states.

Contribution

It introduces a novel analytical approach combining recursion and path-integral techniques to study C60's electronic properties.

Findings

Closed-form expressions for eigenvalues and eigenfunctions

Analytic local densities of states around ring clusters

Consistent energy spectrum results from both methods

Abstract

The recursion and path-integral methods are applied to analytically study the electronic structure of a neutral $C_{60}$ molecule. We employ a tight-binding Hamiltonian which considers both the $s$ and $p$ valence electrons of carbon. From the recursion method, we obtain closed-form {\it analytic} expressions for the $\pi$ and $\sigma$ eigenvalues and eigenfunctions, including the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) states, and the Green's functions. We also present the local densities of states around several ring clusters, which can be probed experimentally by using, for instance, a scanning tunneling microscope. {}From a path-integral method, identical results for the energy spectrum are also derived. In addition, the local density of states on one carbon atom is obtained; from this we can derive the degree of degeneracy of the energy levels.