Resistivity of a highly correlated gas

In the presence of impurities we think the resistivity should be calculated by taking the current carriers into account, and each impurity should give a cross-sectional area for them of order a2. Thus the mean free path l is 1/N0a2, where N0 is the concentration of impurities. The conductivity is given by 

The effective cross-section is enhanced by a factor iy2/3. McWhan et al (1973a) pointed out that in V203, dilute solutions of Cr203 give a cross-section greater than a2 per Cr atom, which tends to confirm our analysis. 

Interacting Electrons in Non-Crystalline Systems. Impurity Bands and Metal-Insulator Transitions in Doped Semiconductors 

Interaction of electrons with phonons, and the fact that the presence of a trapped electron can deform the surrounding material, allows the radius of an empty localized state to change when the state is occupied. Also, in a condensed electron gas phonons lead to a mass enhancement near the Fermi energy, or in some circumstances to polaron formation. For the development of the theory, and comparison with experiment, it is therefore desirable to begin by choosing a system where these effects are unimportant. The study of doped semiconductors provides such a system. This is because the radius aH of a donor is given, apart from central cell corrections, by the hydrogen-like formula 

Impurity conduction can also be studied in compensated semiconductors, i.e. materials containing acceptors as well as donors, the majority carriers (or the other way round). For such materials, even at low concentrations, activated hopping conduction can occur (Chapter 1, Section 15), some of the donors being unoccupied so that an electron can move from an occupied to an empty centre. Here too a metal-insulator transition can be observed, which is certainly of Anderson type, the insulating state being essentially a result of disorder. 

---