Spectral footprints of impurity scattering in graphene nanoribbons

TL;DR

This paper investigates how impurity scattering affects the local density of states in graphene nanoribbons, revealing spectral signatures linked to size quantization and impurity effects through analytical and numerical methods.

Contribution

It provides a combined analytical and numerical analysis of impurity effects on the spectral properties of graphene nanoribbons, including effects of trigonal warping.

Findings

Impurity scattering causes non-decaying oscillations in the local density of states.

Spectral signatures relate to transverse modes and impurity superposition effects.

Analytic and atomistic approaches show consistent impurity-induced features.

Abstract

We report a detailed investigation of the interplay between size quantization and local scattering centers in graphene nanoribbons, as seen in the local density of states. The spectral signatures, obtained after Fourier transformation of the local density of states, include characteristic peaks that can be related to the transverse modes of the nanoribbon. In armchair ribbons, the Fourier transformed density of states of one of the two inequivalent sublattices takes a form similar to that of a quantum channel in a two-dimensional electron gas, modified according to the differences in bandstructure. After addition of the second sublattice contribution, a characteristic modulation of the pattern due to superposition is obtained, similar to what has been obtained in spectra due to single impurity scattering in large-area graphene. We present analytic results for the electron propagator in armchair nanoribbons in the Dirac approximation, including a single scattering center within a T-matrix formulation. For comparison, we have extended the investigation with numerics obtained with an atomistic recursive Green's function approach. The spectral signatures of the atomistic approach include the effects of trigonal warping. The impurity induced oscillations in the local density of states are not decaying at large distance in few-mode nanoribbons.