Counting the number of excited states in organic semiconductor systems using topology

TL;DR

This paper introduces a topological approach using winding numbers and intersection theory to count excited states in organic semiconductor systems modeled as quasi-one-dimensional structures.

Contribution

It presents a novel method linking topological invariants to the enumeration of excited electronic states in molecular materials.

Findings

Topological invariant (winding number) characterizes scattering centers.

Application of intersection theory to quantum state counting.

Provides a new framework for analyzing excitations in organic semiconductors.

Abstract

Exciton Scattering (ES) theory attributes excited electronic states to standing waves in quasi-one-dimensional molecular materials by assuming a quasi-particle picture of optical excitations. The quasi-particle properties at branching centers are described by the corresponding scattering matrices. Here we identify the topological invariant of scattering center, referred to as its winding number, and apply topological intersection theory to count the number of quantum states in a quasi-one-dimensional system.