Conduction electron diamagnetism in alloys and magnetic-field-dependent dielectric constant of a Fermi gas

Abstract
The diamagnetism of free electrons in the presence of charged impurity centres which are sufficiently dilute to be non-interacting is calculated to first order in the strength of the potential of the impurity centre. This is done by combining the density-matrix treatment of Landau diamagnetism with the impurity-screening theory o f March & Murray. The susceptibility involves the integrated value of the impurity potential through the crystal, and its first derivative with respect to the magnetic field, B. If the impurity potential is assumed to have a value appropriate to B — 0, then the result for the change in diamagnetic susceptibility on alloying agrees with that of Kohn & Luming (1963). It is shown, however, that the impurity potential is modified in the presence of the magnetic field, and in particular it has angular dependence. The correction to the dia­magnetic susceptibility due to this self-consistency is shown to be significant (25% ). The relevance of the theory to experimental results on dilute alloys is briefly discussed. Finally, as a by-product of the investigation, we have obtained interesting results about the form of the field-dependent dielectric constant.