Quantifying defects in graphene via Raman spectroscopy at different excitation energies.

We present a Raman study of Ar(+)-bombarded graphene samples with increasing ion doses. This allows us to have a controlled, increasing, amount of defects. We find that the ratio between the D and G peak intensities, for a given defect density, strongly depends on the laser excitation energy. We quantify this effect and present a simple equation for the determination of the point defect density in graphene via Raman spectroscopy for any visible excitation energy. We note that, for all excitations, the D to G intensity ratio reaches a maximum for an interdefect distance ∼3 nm. Thus, a given ratio could correspond to two different defect densities, above or below the maximum. The analysis of the G peak width and its dispersion with excitation energy solves this ambiguity.

Polarons in carbon nanotubes.

We use ab initio total-energy calculations to predict the existence of polarons in semiconducting carbon nanotubes (CNTs). We find that the CNTs' band edge energies vary linearly and the elastic energy increases quadratically with both radial and with axial distortions, leading to the spontaneous formation of polarons. Using a continuum model parametrized by the ab initio calculations, we estimate electron and hole polaron lengths, energies, and effective masses and analyze their complex dependence on CNT geometry. Implications of polaron effects on recently observed electro- and optomechanical behavior of CNTs are discussed.