1. Roberto Fuentes Badilla University of Arizona Acknowledgements: Dr. Sumit Mazumdar Dr. Zhendong Wang U.S. N.S.F.

2.  Introduction to SWCNT  Semiconductor vs. metallic conductor  Exciton  PPP Model  Semiconductor exciton  Metallic exciton  Conclusions

3. Metallic -if (n-m) is a multiple of 3 -all armchair Semiconducting -all other combinations of (n,m)‏

4. Classification of band structure a) Insulator b) Semiconductor c) Metal (partially filled band) ‏ Semiconductor

5. Bound state of electron-hole pair

6. Incident light parallel to tube Incident light perpendicular to tube Polarization of carbon nanotube optical excitations

7.  Take into account only π-electrons  The Pariser-Parr-Pople (PPP) model Hamiltonian Atomic units π-electrons

8. Rewrite using second quantization Creates a π-electron with spin σ on the i th carbon atom Number of π-electrons with spin σ on atom i Total number of π-electrons on the atom One-electron hopping integrals Repulsion between two π -electrons Occupying same atom Intersite Coulomb interactions

9. Coulomb InteractionU=8.0 eV Dielectric Screening Hopping IntegraleV Semi-empirical parameters

10. Black dashed curves – experiment; blue curves - PPP model, t1 = 2.0 eV Zhendong Wang,Hongbo Zhao & Sumit Mazumdar PRB 115431 (2007)‏ Prediction vs. Experiment

11.  No excitons in conventional metals because no optical gap/excitation  Multiple pairs of valence and conduction bands  nonzero band gap in M-SWCNTs except between the lowest pair  Trigonal warping effect E k E 11 E 22 E k Nonarmchair Armchair

12. Overall shift in energy Excitonic energy Change the dielectric constant

13. Prediction  Diamter size ~1nm

14.  Parameterization of the π-electron Hamiltonian  Parallel and Transverse excitons in semiconducting carbon nanotube  Change in dielectric constant in metallic carbon nanotube  No transverse exciton predicted for metallic carbon nanotube