1. Dirac equation & Strain induced graphene Kyung-Joong KIM Department of Physics, Chungnam National University

2. Outline Relativistic quantum mechanical wave equations Hole theory Prediction about antiparticle and the discovery of the positron Chiral tunneling and Klein paradox Graphene and band structure The Dirac equation and graphene Strain induced graphene quatum dot

3. Relativistic quantum mechanical wave equation 결국 무엇이 다른가 ????? 이것이 바로 오늘의 메인 !! Klein-Golden e.q. Pauli theory!! Dirac had formulated in 1928

4. Hole theory Dirac sea : the Sea of Negative Energy 디락 방정식은 Negative Energy 의 해를 하나 더 갖는다. 그것은 당시 디락에겐 골칫거리였다. 디락은 이 골칫거리를 해 결하기 위해 가설을 세웠 고, 그 가설의 주인공은 처음엔 positron 이 아닌 proton 으로 생각했다.

5. Prediction about antiparticle and the discovery of the positron CPT symmetry … "Pure cowardice!" Anyway, he shared the Nobel Prize, in 1933. Carl Anderson

6. Chiral tunneling and Klein paradox Massless Dirac particles cannot be confined by an electrostatic potential : Klein paradox but confinement can be achieved with a magnetic field

7. Graphene and band structure

8. The Dirac equation and graphene Decoupled schrodinger-like eq. in cylindrical problem

9. Graphene disk with gaussian bump External field [E or G] Landau & Lifshitz ‘Theory of elasticity’

10. Structure of graphene disk under a central point load Landau & Lifshitz ‘Theory of elasticity’

11. The Dirac equation (contain the gauge potential) Assumption : In-plane displacement Ux = Uy = 0

12. Effective magnetic fields Assumption : In-plane displacement Ux = Uy = 0

13. Effective magnetic fields (point central load) Assumption : In-plane displacement Ux = Uy = 0

14. Black hole of the electron