Optical selection rules of graphene nanoribbons

TL;DR

This paper analytically investigates the optical selection rules in graphene nanoribbons, revealing how edge structures influence electronic transitions and enabling predictions of transition energies for experimental validation.

Contribution

It provides a theoretical explanation of optical selection rules based on the tight-binding model, highlighting differences between armchair and zigzag nanoribbons.

Findings

Armchair nanoribbons have J=0 selection rule.

Zigzag nanoribbons follow |J|=odd rule.

Transition energies can be predicted and measured experimentally.

Abstract

Optical selection rules for one-dimensional graphene nanoribbons are analytically studied and clarified based on the tight-binding model. A theoretical explanation, through analyzing the velocity matrix elements and the features of wavefunctions, can account for the selection rules, which depend on the edge structure of nanoribbon, namely armchair or zigzag edges. The selection rule of armchair nanoribbons is \Delta J=0, and the optical transitions occur from the conduction to valence subbands of the same index. Such a selection rule originates in the relationships between two sublattices and between conduction and valence subbands. On the other hand, zigzag nanoribbons exhibit the selection rule |\Delta J|=odd, which results from the alternatively changing symmetry property as the subband index increases. An efficiently theoretical prediction on transition energies is obtained with the application of selection rules. Furthermore, the energies of band edge states become experimentally attainable via optical measurements.