Band gap engineering in finite elongated graphene nanoribbon heterojunctions: Tight-binding model

TL;DR

This paper presents a tight-binding model for finite elongated graphene nanoribbon heterojunctions, demonstrating how to tune the band gap by varying the middle segment's length, with results validated against DFT calculations.

Contribution

The study introduces a simple divide and conquer tight-binding approach to analyze and engineer band gaps in GNR heterojunctions, validated by DFT comparisons.

Findings

Band gap can be continuously tuned by changing the middle segment length.

The tight-binding model agrees well with DFT calculations.

Finite size effects significantly influence electronic properties.

Abstract

A simple model based on the divide and conquer rule and tight-binding (TB) approximation is employed for studying the role of finite size effect on the electronic properties of elongated graphene nanoribbon (GNR) heterojunctions. In our model, the GNR heterojunction is divided into three parts: a left (L) part, middle (M) part, and right (R) part. The left part is a GNR of width $W_{L}$, the middle part is a GNR of width $W_{M}$, and the right part is a GNR of width $W_{R}$. We assume that the left and right parts of the GNR heterojunction interact with the middle part only. Under this approximation, the Hamiltonian of the system can be expressed as a block tridiagonal matrix. The matrix elements of the tridiagonal matrix are computed using real space nearest neighbor orthogonal TB approximation. The electronic structure of the GNR heterojunction is analyzed by computing the density of states. We demonstrate that for heterojunctions for which $W_{L} = W_{R}$, the band gap of the system can be tuned continuously by varying the length of the middle part, thus providing a new approach to band gap engineering in GNRs. Our TB results were compared with calculations employing divide and conquer rule in combination with density functional theory (DFT) and were found to agree nicely.