Connecting bright and dark states through accidental degeneracy caused by lack of symmetry

TL;DR

This paper investigates how accidental degeneracy in excitonic ring structures, caused by missing symmetry elements, links bright and dark states, revealing unique optical properties in specific ring sizes.

Contribution

It identifies the cause of accidental degeneracy in excitonic rings and derives a complete selection rule explaining this phenomenon based on symmetry analysis.

Findings

Degeneracy occurs only in rings with size N=4l+2.

Lack of certain symmetry elements causes the degeneracy.

Selection rules are derived for excitation manifolds.

Abstract

Coupled excitonic structures are found in natural and artificial light harvesting systems where optical transitions link different excitation manifolds. In systems with symmetry, some optical transitions are allowed, while others are forbidden. Here we examine an excitonic ring structure and identify an accidental degeneracy between two categories of double-excitation eigenstates with distinct symmetries and optical transition properties. To understand the accidental degeneracy, a complete selection rule between two arbitrary excitation manifolds is derived with a physically motivated proof. Remarkably, symmetry analysis shows the lack of certain symmetry elements in the Hamiltonian is responsible for this degeneracy, which is unique to rings with size N=4l+2 (l being an integer).