Inelastic electron tunneling spectroscopy at local defects in graphene

TL;DR

This paper investigates how vibrational impurities affect the local electronic structure of graphene, revealing inelastic scattering features, Friedel oscillations, and the formation of a negative U-center that destroys the Dirac cone at strong coupling.

Contribution

It provides a detailed analysis of the evolution from weak to strong coupling in inelastic electron scattering at local defects in graphene, including the formation of negative U-centers.

Findings

Detectable inelastic scattering peaks in $d^2I/dV^2$ spectra.

Inelastic Friedel oscillations distort the local density of states.

Strong coupling destroys the Dirac cone, leaving only impurity resonances.

Abstract

We address local inelastic scattering from vibrational impurity adsorbed onto graphene and the evolution of the local density of electron states near the impurity from weak to strong coupling regime. For weak coupling the local electronic structure is distorted by inelastic scattering developing peaks/dips and steps. These features should be detectable in the inelastic electron tunneling spectroscopy, $d^2I/dV^2$, using local probing techniques. Inelastic Friedel oscillations distort the spectral density at energies close to the inelastic mode. In the strong coupling limit, a local negative $U$-center forms in the atoms surrounding the impurity site. For those atoms, the Dirac cone structure is fully destroyed, that is, the linear energy dispersion as well as the V-shaped local density of electron states is completely destroyed. We further consider the effects of the negative $U$ formation and its evolution from weak to strong coupling. The negative $U$-site effectively acts as local impurity such that sharp resonances appear in the local electronic structure. The main resonances are caused by elastic scattering off the impurity site, and the features are dressed by the presence of vibrationally activated side resonances. Going from weak to strong coupling, changes the local electronic structure from being Dirac cone like including midgap states, to a fully destroyed Dirac cone with only the impurity resonances remaining.