# The band calculation and local state analysis for armchair graphene-like nanoribbons with line defects

## TL;DR

This paper introduces an analytical approach based on tight-binding and standing wave assumptions to accurately compute band structures and analyze local states in armchair graphene-like nanoribbons with line defects or strains.

## Contribution

It presents a novel analytical method for calculating band structures and local states in defective armchair nanoribbons, applicable to large systems and semi-infinite models.

## Key findings

- Accurate band structure calculations for large supercell systems.
- Analytical expressions for local states near line defects.
- Criteria for local states in semi-infinite nanoribbons.

## Abstract

In this paper we propose an analytical method to calculate the band structures of graphene-like nanoribbons of the armchair type with arbitrary line defects or uniaxial strains. The model is based on the tight-binding model and the standing wave assumption for the armchair nanoribbons. It gives accurate band results for large supercell systems. Within this method, we analyze different local states near the line defect in the graphene and boron-nitride nanoribbons. We also derive the analytical expression for the local states in a semi-infinite graphene nanoribbon by this method and the transfer matrix technique. The criteria condition for the local states in the semi-infinite nanoribbons is also given.

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Source: https://tomesphere.com/paper/1704.04897