Thanks for your questions.
The first one I don't quite understand... A ribbon is straight, the graphene junction is z-shaped. But the junction is of course built from pieces of ribbons.
There are two primary ingredients in a transport calculation, which you must compute accurately to get good results:
- the electronic structure
- the response of the system to the electrostatic environment
For graphene, the Huckel method provides an excellent electronic structure of graphene, as long as you use the Cerda basis set, and don't strain or abuse the structure too much. Hence for the first point, Huckel is fine, and the results agree very well with DFT.
The second point is implemented in more or less the same way in DFT and Huckel in ATK, so there the choice of method is not so important.
For other systems, perhaps with strong polarizations induced by the field, and where the Huckel parameters are not capable of describing the complex chemistry, the Huckel method might not give as good results.
I think the primary reasons why there are still relatively few publications with Huckel in ATK is simply that the method has only been properly available for little over 2 years (ATK-DFT goes back 6-7 years), and it takes time for people to first of all switch to the new version of ATK, and then of course produce the results and publish the articles. I hope in the future, more and more people will discover how well the Huckel method performs, both in terms of calculation speed and quality of the results
Note that in ATK 11.8 you can now also do spin-polarized calculations with Huckel, and also use even simpler methods like nearest-neighbor tight-binding, which also can give quite excellent results for "simple" graphene systems, which don't involve any other atoms than carbon (i.e. if you are just playing with the shape of the graphene). In this case you can run very many atoms, for sure over 10,000, quite easily.
