ATK in Education: Nanotubes & Graphene

Carbon nanotubes and graphene are ideal systems for demonstrating basic principles of both electronic structure and quantum transport. Their 1D and 2D structures provide foundations for discussions of k-point symmetries etc, and both electronic and transport characteristics can be compared to simple models. Both metallic and semiconducting behavior can be observed and discussed.

The structures are relatively cheap to calculate in ATK by using semi-empirical tight-binding models, and the results can then be compared to more general DFT calculations. Complex geometries, such as Stone-Wales defects or edge roughness in graphene nanoribbons, needs to be optimized first, and this can be done easily and extremely fast by the Brenner potential. See the movie to the right!

Nanotubes of any chirality, and endless variations on graphene nanoribbons can easily be built in VNL; see the figures below, as well as the page on graphene applications with ATK for more inspiration! Why limit yourself to carbon - it's just as easy to set up and calculate a boron-nitride or SiC tube, and for very interesting reasons they have quite different properties.

To get started on this topic in course-work, there are several prepared detailed tutorials on graphene that provide an excellent starting point. and thanks to the ways the GUI can be extended it is easy for a course instructor to provide the students with ready tools to create for specific structures. As an example, there is a plug-in tool which computes an analytic tight-binding band structure of carbon nanotubes. Then, the students can quickly set up the system and calculate the full DFT band structure (or use extended Hückel theory) with just a few mouse clicks and compare it to the simpler models. After that, introduce doping or defects to see how this influences the band structure - or the transport characteristics.

Another interesting exercise is to compute and visualize the Bloch functions in a nanotube or a graphene ribbon, with or without spin polarization, and relate its symmetries to the characteristic of each band (s-type, p-type, px vs pz, etc).