THEORY OF IMPURITY BANDS IN MAGNETIC FIELDS .I. MAGNETIC SUSCEPTIBILITY

By using the Green function method for the random lattice, the susceptibility of the impurity band in weak magnetic fields is investigated in a simplified model in which the impurity potential is attractive and of short range and the electron-electron correlation can be negligible. Simple analytical expressions for the susceptibility are obtained and are computed numerically as a function of the concentration of impurities c. When c/c00 (c00 is the critical concentration at which the impurity band touches the conduction band) is very small so that the impurity band width is smaller than the binding energy of the impurity potential, the orbital susceptibility in the impurity band region is simply of the type of the atomic diamagnetism, while it is of the type of the ordinary Landau diamagnetism in the conduction band region. The result for the case c/c00≫ 1 explains the observed discrepancy from the existing Landau theory. © 1969, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.