Á. Rusznyák

Catastrophe optics of caustics in single and bilayer graphene: Fine structure of caustics

We theoretically study the scattering of a plane wave of a ballistic electron on a circular n-p junction in single and bilayer graphene. We compare the exact wave function inside the junction to that obtained from a semiclassical formula developed in catastrophe optics. In the semiclassical picture short-wavelength electrons are treated as rays of particles that can get reflected and refracted at the n-p junction according to Snells law with negative refraction index. We show that for short wavelength and close to caustics this semiclassical approximation gives good agreement with the exact results in the case of single-layer graphene. We also verify the universal scaling laws that govern the shrinking rate and intensity divergence of caustics in the semiclassical limit. It is straightforward to generalize our semiclassical method to more complex geometries, offering a way to efficiently design and model graphene-based electron-optical systems.

Linear carbon chain in the interior of a single walled carbon nanotube

The physical properties of several kinds of single walled carbon nanotubes containing a single carbon chain in their interior are investigated with density functional theory, using the Vienna ab initio Simulation Package (VASP). The optimized geometry and the electronic band structure are both examined, and compared to the results of the isolated subsystems: the isolated carbon chain and the isolated nanotube. We find bondlength alternation in the optimized geometry of the isolated chain, as well as a gap in the band structure, clear signs of Peierls distortion. In the combined systems, hybridization and charge transfer are found between the tube and the chain, resulting in a partial or complete breakdown of the Peierls distortion of the carbon chain. The combined systems are always predicted to be metallic, even if both subsystems are semiconductors, and even if the chain still exhibits some bond length alternation.