where the summation runs over bands with indices n, ⌧ (E) is the scattering time, v(E) is the group velocity, and g(E) is the density of states. The 1/3 factor in ⌃(E) arises from averaging over the three Cartesian directions. The transport coe cients, namely the electrical conductivity , Seebeck coe cient S, electronic thermal conductivity  e and the Lorenz number L, are given by