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

Transport properties - Boltzmann equation

goal: calculation of conductivity Boltzmann transport theory:

distribution function

number of particles in infinitesimal phase space volume around

evolution from Boltzmann equation collision integral for static potential

(~ k,~ r)

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Transport properties - Boltzmann equation

relaxation time approximation

equilibrium distribution relaxation time electrons in oscillating electric field small deviations linearized

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Transport properties - Boltzmann equation

current density conductivity tensor

concentrated at _

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Transport properties - Drude form

isotropic uniform dc-conductivity ac-conductivity

Lorentzian

Drude peak

f-sum rule

limit

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k-space

phonon operators

Electron-phonon interaction

ion lattice density fluctuation electron density screened Coulomb potential

real space 5

matrix elements of scattering processes

collision integral

spontaneous emission e-p-coupling

Electron-phonon interaction

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Electron-phonon interaction

(2) (2) (1) (1) (4) (3) (4) (3)

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Electron-phonon interaction

approximation: static potential limit (Born-Oppenheimer) real space view potential due to quasi-static deformation

science photo library

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