Sci. Technol. Adv. Mater. 11 (2010) 054504 and J. Appl. Phys. 111, 074318 (2012) provide a derivation for the spectrum of graphene nanoribbons on a tight binding basis. I have been trying to understand the edge state based on these articles but hit a bit of a road block.
When plotting the band structure as derived in the articles (see attached image) the bulk states (blue) come out very nicely, but the edge state (red) invariably ends up being a mess and nowhere near what it should be.
Does anyone know other good resources for a derivation of the flat band or can explain it to me based on the articles above?
http://cnl.ut.ac.ir/PDF/J26.pdf
http://iopscience.iop.org/1468-6996/11/5/054504/pdf/1468-6996_11_5_054504.pdf
Hi there,
The Wakabayashi work IS a good reference (I am not as familiar with the work by the authors of the other paper you listed). I was about to point to you Ref 15 (Fujita 1996) of that paper and other early works by those authors, when I realized the Wakabayashi paper you listed covers the old stuff.
I think your difficulty is in the numerical implementation.
Hope my comment is of a bit if help.
You can reproduce numerically the band structure of zig-zag nanoribbons relatively easy as follows. First you have to build the Hamiltonian of each unit cell say H0 being a single linear chain for the zig-zag nanoribbon. Then you can build the Hamiltonian representing connections between the unit cells say, H01. After that you have to diagonalize H0+H01*exp(ik)+H10*exp(-ik) (Bloch's theorem) and plot the eigenvalues for every k. If everything is done correctly you should be able to reproduce the flat bands along with the rest of the band structure. Hope this helps, although it's not the analytical derivation you are seeking.
I have reproduced it numerically with my prog,but i dont know how to do in case of if T is function of Energy as well as applied bias,so please if any one has idea about how to determine T(E,V),I shall be highly thankful.
regards
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Materials Science
- Materials
- Carbon Materials
- Graphite
- Graphene