Energy band of graphene ribbons under the tensile force

TL;DR

This paper analyzes how tensile force affects the electronic energy bands of graphene ribbons with zigzag and armchair edges, revealing that tensile force can open and increase energy gaps at the K point.

Contribution

It provides analytic relations between tensile force and energy bands of graphene ribbons considering only nearest-neighbor interactions.

Findings

Tensile force opens an energy gap at the K point for ZGR and AGR.

Force perpendicular to zigzag edges more easily opens an energy gap.

Energy gaps increase with increasing tensile force.

Abstract

According to the tight-binding approximation, we investigate the electronic structures of graphene ribbons with zigzag shaped edges (ZGRs) and armchair shaped edges (AGRs) drawn by the tensile force, and obtain the analytic relations between the energy bands of pi-electrons in ZGR, AGR and the tensile force based on only considering the nearest-neighbor interaction and the hydrogen-like atomic wave function is considered as pi-electron wave function. Importantly, we find the tensile force can open an energy gap at the K point for ZGR and AGR, and the force perpendicular to the zigzag edges can open energy gap more easily besides the gap values of ZGR and AGR at the K point both increase as the tensile force increases.