Dirac equation & Strain induced graphene
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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
Dirac equation & Strain induced graphene
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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
