Electron-phonon coupling: a tutorial - …

Electron-phonon coupling : a tutorialW. H bner, C. D. Dong, and G. LefkidisUniversity of Kaiserslautern and Research Center OPTIMAS, Box 3049, 67653 Kaiserslautern, GermanyTargoviste, 29 August 2011 Outline1. The harmonic oscillator real space energy basis2. 1D lattice vibrations one atom per primitive cell two atoms per primitive cells3. electron phonon interactions localized electrons small polaron theory phonons in metals4. Superconductivity5. A numerical example: CO6. LiteratureOutline1. The harmonic oscillator real space energy basis2. 1D lattice vibrations one atom per primitive cell two atoms per primitive cells3. electron phonon interactions localized electrons small polaron theory phonons in metals4. Superconductivity5. A numerical example: CO6. Literature1) The harmonic oscillatorquantization of the oscillator in real spaceEigenvalues ofProjection of eigenvalue equation to X basis(Substitution by differential operators) leads to222221()22dmxEmdx 1) The harmonic oscillatorquantization of the oscillator in real space1) Dimensionless variablesxby 12bm 22mEbE ''2(2) 0y ''20y 22224222220dmEbmbydy leads toand22myAy e with solutionsince22''222222

Electron-phonon coupling: a tutorial W. Hübner, C. D. Dong, and G. Lefkidis University of Kaiserslautern and Research Center OPTIMAS,

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  Tutorials, Coupling, Electron, A tutorial, Electron phonon coupling, Phonon

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