Analytical Study of Electronic Structure in Armchair Graphene Nanoribbons

TL;DR

This paper provides an analytical solution for the electronic structure of armchair graphene nanoribbons, confirming numerical and first-principles results, and highlights the presence of energy gaps due to edge deformation.

Contribution

It offers an analytical approach to determine wavefunctions and energy dispersion in armchair GNRs, aligning with numerical and first-principles findings.

Findings

Analytical solutions match tight-binding numerical results.

Wavevector discretization due to boundary conditions.

Edge deformation induces energy gaps in all armchair GNRs.

Abstract

We present the analytical solution of the wavefunction and energy dispersion of armchair graphene nanoribbons (GNRs) based on the tight-binding approximation. By imposing hard-wall boundary condition, we find that the wavevector in the confined direction is discretized. This discrete wavevector serves as the index of different subbands. Our analytical solutions of wavefunction and associated energy dispersion reproduce the numerical tight-binding results and the solutions based on the k*p approximation. In addition, we also find that all armchair GNRs with edge deformation have energy gaps, which agrees with recently reported first-principles calculations.