1D RELATIVISTIC UNCONFINED COULOMB PROBLEM FOR DIRAC EQUATION (Z < 137)
Abstract
Single-particle 1D Dirac matrix Hamiltonian can be expressed by the following equation,
where, - Fermi velocity;
For carbon nanotubes or graphene nanoribbons: ;
- band gap;
- momentum operator acts along the axis of the effectively 1D system.
References
- Valeri N. Kotov, Bruno Uchoa, Vitor M. Pereira, F. Guinea, and A. H. Castro Neto, Rev. Mod.Phys. 84, 1067, (2012).
- V. M. Pereira, J. Nilsson, and A. H. Castro Neto,Phys. Rev. Lett. 99, 166802 (2007).
- A. V. Shytov, M. I. Katsnelson, and L. S. Levitov,Phys. Rev. Lett.99, 246802 (2007).
- O. V. Gamayun, E. V. Gorbar, and V. P. Gusynin,Phys. Rev. B 80, 165429 (2009).
- D. Klöpfer, A. De Martino, and R. Egger, Crystals 3, 14 (2013). [6] Y. Wang, V.W. Brar, A. V. Shytov, Q. Wu, W. Regan, H.-Z. Tsai, A. Zettl, L. S. Levitov, and M. F. Crommie,Nat. Phys. 8, 653 (2012).