Stabilization mechanism of edge states in graphene

TL;DR

This paper investigates how next nearest-neighbor hopping affects the energy of edge states in graphene ribbons, showing it lowers their energy and aligns with experimental observations.

Contribution

It introduces an analytical and numerical analysis of the energy shift of edge states due to next nearest-neighbor hopping in graphene.

Findings

Next nearest-neighbor hopping decreases edge state energy.

The model aligns with recent scanning tunneling spectroscopy data.

Analytical and numerical methods confirm the energy shift.

Abstract

It has been known that edge states of a graphite ribbon are zero-energy, localized eigen-states. We show that next nearest-neighbor hopping process decreases the energy of the edge states at zigzag edge with respect to the Fermi energy. The energy reduction of the edge states is calculated analytically by first-order perturbation theory and numerically. The resultant model is consistent with the peak of recent scanning tunneling spectroscopy measurements.