Theory of optical transitions in graphene nanoribbons

TL;DR

This paper analytically investigates optical transitions in graphene nanoribbons, revealing how electron-light interactions depend on edge structure, polarization, and Fermi energy, and explaining characteristic absorption peaks.

Contribution

It provides an analytical framework for understanding optical selection rules and absorption features in graphene nanoribbons based on tight-binding models.

Findings

Indirect transitions induce characteristic absorption peaks.

Absorption is sensitive to Fermi energy and edge irregularities.

Depolarization effects influence the absorption spectrum.

Abstract

Matrix elements of electron-light interactions for armchair and zigzag graphene nanoribbons are constructed analytically using a tight-binding model. The changes in wavenumber ($\Delta n$) and pseudospin are the necessary elements if we are to understand the optical selection rule. It is shown that an incident light with a specific polarization and energy, induces an indirect transition ($\Delta n=\pm1$), which results in a characteristic peak in absorption spectra. Such a peak provides evidence that the electron standing wave is formed by multiple reflections at both edges of a ribbon. It is also suggested that the absorption of low-energy light is sensitive to the position of the Fermi energy, direction of light polarization, and irregularities in the edge. The effect of depolarization on the absorption peak is briefly discussed.