Pseudospin for Raman D Band in Armchair Graphene Nanoribbons

TL;DR

This paper analytically investigates the Raman D band in armchair graphene nanoribbons, revealing how pseudospin and momentum conservation influence its components, intensity, and phonon behavior, with implications for experimental observations.

Contribution

It introduces an analytical framework linking pseudospin and momentum conservation to the D band features in armchair graphene nanoribbons, highlighting boundary condition effects.

Findings

D band has two components due to pseudospin and momentum conservation

Raman intensity is maximized with parallel polarization to the edge

D band behavior is correlated with G band through Kohn anomaly

Abstract

By analytically constructing the matrix elements of an electron-phonon interaction for the $D$ band in the Raman spectra of armchair graphene nanoribbons, we show that pseudospin and momentum conservation result in (i) a $D$ band consisting of two components, (ii) a $D$ band Raman intensity that is enhanced only when the polarizations of the incident and scattered light are parallel to the armchair edge, and (iii) the $D$ band softening/hardening behavior caused by the Kohn anomaly effect is correlated with that of the $G$ band. Several experiments are mentioned that are relevant to these results. It is also suggested that pseudospin is independent of the boundary condition for the phonon mode, while momentum conservation depends on it.