Electron Wave Function in Armchair Graphene Nanoribbons

TL;DR

This paper analytically investigates the electron wave functions in armchair graphene nanoribbons, revealing standing wave formation, boundary effects, and implications for experimental observations like STM and Raman spectroscopy.

Contribution

It provides an analytical solution for electron wave functions in armchair nanoribbons, clarifying boundary effects and their impact on observable phenomena.

Findings

Wave functions form standing waves due to intervalley scattering

Strong boundary potentials are inconsistent with STM observations

Analytical solutions explain Raman G band selection rules

Abstract

By using analytical solution of a tight-binding model for armchair nanoribbons, it is confirmed that the solution represents the standing wave formed by intervalley scattering and that pseudospin is invariant under the scattering. The phase space of armchair nanoribbon which includes a single Dirac singularity is specified. By examining the effects of boundary perturbations on the wave function, we suggest that the existance of a strong boundary potential is inconsistent with the observation in a recent scanning tunneling microscopy. Some of the possible electron-density superstructure patterns near a step armchair edge located on top of graphite are presented. It is demonstrated that a selection rule for the G band in Raman spectroscopy can be most easily reproduced with the analytical solution.