Interplay between edge states and simple bulk defects in graphene nanoribbons

TL;DR

This study investigates how a single impurity affects edge states in zigzag graphene nanoribbons, revealing hybridization, energy shifts, and LDOS oscillations that depend on system size and impurity position.

Contribution

It provides a detailed analysis of impurity-edge interactions in graphene nanoribbons using tight-binding and DFT methods, highlighting new hybridization effects and LDOS modifications.

Findings

Half of the eigenstates hybridize with the impurity

Impurity causes energy shifts proportional to impurity potential

LDOS oscillations depend on system size and impurity distance

Abstract

We study the interplay between the edge states and a single impurity in a zigzag graphene nanoribbon. We use tight-binding exact diagonalization techniques, as well as density functional theory calculations to obtain the eigenvalue spectrum, the eigenfunctions, as well the dependence of the local density of states (LDOS) on energy and position. We note that roughly half of the unperturbed eigenstates in the spectrum of the finite-size ribbon hybridize with the impurity state, and the corresponding eigenvalues are shifted with respect to their unperturbed values. The maximum shift and hybridization occur for a state whose energy is inverse proportional to the impurity potential; this energy is that of the impurity peak in the DOS spectrum. We find that the interference between the impurity and the edge gives rise to peculiar modifications of the LDOS of the nanoribbon, in particular to oscillations of the edge LDOS. These effects depend on the size of the system, and decay with the distance between the edge and the impurity.