Conductors with small Fermi energies and small gap energies

If the Fermi energy is of the order of meV's, the usual treatment of the density of free electrons is not valid, but use can be made of an averaged density of states that depends weakly on temperature, so that the temperature variation of the conductivity can be expressed by the equation: σ congruent CT(1-s) 1n{[(exp(βEf) + 1)/2][exp(-β(Eg - Ef)) + 1)]} in which Ef is the Fermi energy, Eg is the top of the energy gap for thermal activation, s is the exponent of the temperature-dependent scattering. This equation serves to define a class of solids consisting of a microcomposite with a narrow conduction band for which Ef of the order of ceV's or less and a thermal activated conduction for which Eg is of the order of ceV's. It describes quantitatively the conductivity, σ(T;Δ, for YBa2Cu3O7-Δ and σ(T;p) as the hydrostatic pressure p is varied for κ-(BEDT-TTF)2CuN(CN)2Br