# Gap engineering and wave function symmetry in C and BN armchair nanoribbons

## TL;DR

This study uses density functional theory to explore how stress, electric fields, and edge functionalization differently affect the band gaps of armchair graphene and boron nitride nanoribbons, linking responses to wave function symmetries.

## Contribution

It reveals the opposite responses of graphene and BN nanoribbons to stimuli, connecting these behaviors to wave function symmetries through a tight-binding model.

## Key findings

- Graphene and BN nanoribbons respond oppositely to stimuli.
- Wave function symmetry explains the different responses.
- Strategies for gap engineering should be material-specific.

## Abstract

Many are the ways of engineering the band gap of nanoribbons including application of stress, electric field and functionalization of the edges. In this article, we investigate separately the effects of these methods on armchair graphene and boron nitride nanoribbons. By means of density functional theory calculations, we show that, despite their similar structure, the two materials respond in opposite ways to these stimuli. By treating them as perturbations of a heteroatomic ladder model based on the tight-binding formalism, we connect the two behaviours to the different symmetries of the top valence and bottom conduction wave functions. These results indicate that opposite and complementary strategies are preferable to engineer the gapwidth of armchair graphene and boron nitride nanoribbons.