Choice of the unit cell, selection rules, and optical matrix elements: a tight-binding study of graphene nanoribbons

TL;DR

This paper emphasizes the importance of selecting the correct unit cell in tight-binding calculations of graphene nanoribbons to accurately compute optical matrix elements and preserve selection rules.

Contribution

It demonstrates that proper symmetry considerations in unit cell choice are crucial for correct optical property calculations in tight-binding models.

Findings

Band structure is insensitive to unit cell choice.

Incorrect unit cell leads to violation of selection rules.

Symmetry-aware unit cell selection yields correct optical matrix elements.

Abstract

In this work we argue that it is important to make a proper choice of the unit cell within tight-binding theory if one aims to compute the optical matrix elements. By considering zigzag graphene nanoribbons, we demonstrate that the band structure is insensitive to the choice of the unit cell. However, if the chosen unit cell does not incorporate the symmetries of the system, wrong values of optical matrix elements are obtained, leading to the violation of well-known selection rules. This result holds irrespective of the formalism utilized for calculating the optical matrix elements.