Exciton absorption in narrow armchair graphene nanoribbons

TL;DR

This paper presents an analytical method to study exciton optical absorption in narrow armchair graphene nanoribbons, revealing how exciton peaks shift and broaden with ribbon width and providing results consistent with numerical methods.

Contribution

The authors develop an analytical framework for exciton absorption in narrow AGNRs, incorporating size quantization and electron-hole interactions, which aligns well with numerical approaches.

Findings

Exciton peaks are blue-shifted and broadened as the ribbon narrows.

At subband edges, excitons convert singularities into finite absorption.

Analytical results agree with numerical and experimental estimates.

Abstract

We develop an analytical approach to the exciton optical absorption for narrow gap armchair graphene nanoribbons (AGNR). We focus on the regime of dominant size quantization in combination with the attractive electron-hole interaction. An adiabatic separation of slow and fast motions leads via the two-body Dirac equation to the isolated and coupled subband approximations. Discrete and continuous exciton states are in general coupled and form quasi Rydberg series of purely discrete and resonance type character. Corresponding oscillator strengths and widths are derived. We show that the exciton peaks are blue-shifted, become broader and increase in magnitude upon narrowing the ribbon. At the edge of a subband the singularity related to the 1D density of states is transformed into finite absorption via the presence of the exciton. Our analytical results are in good agreement with those obtained by other methods including numerical approaches. Estimates of the expected experimental values are provided for realistic AGNRs.