Theory of electrical conductivity

Abstract

The quantum dynamics of electrons has been investigated with the help of double time thermodynamic electron-Green's functions. The model Hamiltonian for the problem consists of the state of a real crystal containing phonon system (harmonic and anharmonic), electron system, localized impurities and interactions thereof. The disorder effects include the mass and force constant changes at the impurity sites. The life times for various scattering process have been evaluated in the new frame work. The expression for the electrical conductivity has been derived with the help of Kubo formalism. It is found that the electrical conductivity is not simply a function of electron energy, but, it depends on a large number of scattering events and other factors depending on crystal characteristics and temperature. It has been investigated that the electron-phonon coupling and defects play prominent role in the electron-transport theory and heralds the temperature dependence of electrical conductivity.