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Dirac equation & Strain induced graphene. Kyung-Joong KIM Department of Physics, Chungnam National University. Outline. Relativistic quantum mechanical wave equations Hole theory Prediction about antiparticle and the discovery of the positron Chiral tunneling and Klein paradox
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Dirac equation & Strain induced graphene Kyung-Joong KIM Department of Physics, Chungnam National University
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
Relativistic quantum mechanical wave equation 이것이 바로 오늘의 메인!! Dirac had formulated in 1928 결국 무엇이 다른가????? Pauli theory!! Klein-Golden e.q.
Hole theory 디락 방정식은 Negative Energy의 해를 하나 더 갖는다. 그것은 당시 디락에겐 골칫거리였다. • Dirac sea : the Sea of Negative Energy 디락은 이 골칫거리를 해결하기 위해 가설을 세웠고, 그 가설의 주인공은 처음엔 positron이 아닌 proton으로 생각했다.
Prediction aboutantiparticle and the discovery of the positron Carl Anderson CPT symmetry … "Pure cowardice!" Anyway, he shared the Nobel Prize, in 1933.
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
The Dirac equation and graphene Decoupled schrodinger-like eq. in cylindrical problem
Graphene disk with gaussian bump External field [E or G] Landau & Lifshitz ‘Theory of elasticity’
Structure of graphene disk under a central point load Landau & Lifshitz ‘Theory of elasticity’
The Dirac equation (contain the gauge potential) Assumption : In-plane displacement Ux = Uy = 0
Effective magnetic fields Assumption : In-plane displacement Ux = Uy = 0
Effective magnetic fields (point central load) Assumption : In-plane displacement Ux = Uy = 0
