Condensed Matter Physics - Free Electron Theory : Sommerfeld Theory of Electrical Conductivity

Sommerfeld provided the theory of electrical conduction on the basis of the Boltzmann Transport Equation and Fermi-Dirac Statistics. When electric field is taken as the perturbing field then there is a systematic drift of electrons in a metallic specimen which causes electrical conduction and hence electrical conductivity. Applying the Fermi-Dirac statistics current density is obtained.Comparing the result with microscopic form of Ohm’s law one can get the expression for electrical conductivity of a metal. It is found that although all electrons take part in the conduction, relaxation times of only those electrons with energy states close to the Fermi level are significant in respect of conductivity.