Transport properties - Boltzmann equation goal: calculation of - PowerPoint PPT Presentation

1 Transport properties - Boltzmann equation goal: calculation of conductivity Boltzmann transport theory: number of particles in infinitesimal distribution function ( ~ phase space volume around r ) k, ~ evolution from Boltzmann equation collision integral for static potential

2 Transport properties - Boltzmann equation relaxation time approximation relaxation equilibrium distribution time small deviations electrons in oscillating electric field linearized

3 Transport properties - Boltzmann equation current density _ concentrated at conductivity tensor

4 Transport properties - Drude form isotropic uniform dc-conductivity ac-conductivity limit f-sum rule Lorentzian Drude peak

5 Electron-phonon interaction screened real space Coulomb potential electron density ion lattice density fluctuation k -space phonon operators

6 Electron-phonon interaction matrix elements of scattering processes collision integral spontaneous emission e-p-coupling

7 Electron-phonon interaction (1) (2) (3) (4) (4) (1) (2) (3)

8 Electron-phonon interaction approximation: static potential limit (Born-Oppenheimer) real space view potential due to quasi-static deformation science photo library