1. Tight Binding Method for Calculating Band Structure Of Carbon Nanostructures

2. Team work Majed AbdELSalam Nashaat,
Department Of Physics – Cairo University
Abbas Hussein Abbas,
Department Of Physics – Cairo University
Loay Elalfy AbdelHafiz,
Center Of Nanotechnology – Nile University

3. Supervisor
V.L. Katkov
Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Russia.

4. Aim Of Practice
Calculate band structure for different carbon Nanostructure and investigate their characteristics ( metallic – semiconductor )
Using tight binding method and Dresselhause method
For
Graphene – bilayer ( A-A & A-B)
Carbon nanotube – graphene Nano ribbon
The effect of electric field on Gb ( A-A & A-B)

5. Outlines Tight – binding method Graphene band structure
Bilayer graphene
Carbon nanotube
Graphene Nano ribbon
infinite thermal conductivity :meaning that no temperature differential can exist between two superfluids or two parts of the same superfluid.

6. Carbon Graphene C - Hexagonal lattice; 1 pz orbital at each site
4 valence electrons
1 pz orbital
3 sp2 orbitals

7. Tight – binding method
Step 1: Bloch sum (discrete Fourier Transform) of each localized wave function.
Step 2: Write wave function as linear combination of Bloch sums.
Step 3: Expand the Hamiltonian in terms of the Bloch sums.
Eg. For two atoms per unit cell

8. Interaction Range 2NN 3NN NN Tight-binding Models
Nearest neighbors only
Nearest + Distant neighbors
Tight-binding Models
2NN NN
Interaction
sub-matrices
3NN

9. Band structure calculation
Tight binding method
Dresselhause method
1- Eigen value equ. In matrix form:
2- Non trivial sol. is given by:
3- Solving the Det w.r.t 𝜀 we get the band structure

10. Graphene Band Structure of Graphene Two identical atoms in unit cell:
A B
Band Structure of Graphene
Tight-binding model: P. R. Wallace, (1947) (nearest neighbor overlap = γ0)

11. Graphene & Graphite

12. Bilayer graphene

13. For A-A bilayer

14. For A-B bilayer

15. A tunable graphene bandgap opens the way to nanoelectronics and nanophotonics
Wang: Department of Physics at the University of California at Berkeley
Generate a bandgap in bilayer graphene that can be precisely controlled from 0 to 250 milli-electron volts (250 meV, or .25 eV).
For A-A bilayer
For A-B bilayer

16. Carbon nanotube

17. Band structure for carbon nanotube
Dresselhause method
Tight binding method

18. Band structure for armchair carbon nanotube
1st brillouin zone
2ndzone 1st bril zone 2ndzone
For 5 - 5
1st brillouin zone
2ndzone 1st bril zone 2ndzone

19. Band structure for zigzag carbon nanotube
F0R 9-0
F0R 10-0
F0R 11-0

20. Graphene Nanoribbon a) Nz: no zigzag chains (Nz-zGNR)
Narrow rectangle made from graphene sheet , Has width in order of nm up to tens of nm.
Considered as quasi-1D nanomaterials.
Has metallic or semiconducting character.
a) Nz: no zigzag chains (Nz-zGNR)
b) Na :no of armchair chains (Na-aGNR)
width of the GNRs can be expressed in terms of the no of lateral chains
The red lines are the zigzag or armchair chains that are used to determine Nz or Na respectively.

21. For A-A bilayer ribbon with ү1 = 0
For A-A bilayer ribbon with ү1 = .4 eV

22. For A-A bilayer ribbon with doped Hydrogen atom
Eg=0.3 eV

23. Conclusions

24. Refrences
Tight binding approach to incorporate accurate bandstructure in nanoscale device simulation (Anisur Rahman and Mark Lundstrom School of Electrical and Computer Engineering Purdue University, West Lafayette)
Carbon Nanotube and Graphene Device Physics, H.-S. P H I L I P WONG