HOPPING CONDUCTION IN DISORDERED-SYSTEMS IN THE PRESENCE OF A MAGNETIC-FIELD - LINEARIZED RATE-EQUATION AND MAGNETORESISTANCE

Rate equations are derived, in the linear approximation with respect to the electric field, for hopping transport in disordered systems in the presence of a magnetic field H. The resulting system of linear equations is in general not equivalent to a random resistor network. By means of an effective-medium approximation, an analytical expression for the magnetoresistance Delta sigma(H) has been obtained for R hopping. In the case of strong coupling with phonons, Delta sigma(H) is independent of the temperature T and it is proportional to H-2 in the region of weak magnetic fields. For weak coupling with phonons, we find that Delta sigma(H)similar to H-2/T. Delta sigma(H) shows a monotonic behavior in a wide range of magnitude of the magnetic field. It does not exhibit an oscillating contribution. The sign of Delta sigma(H) depends on the character of the conductivity (electronlike or holelike). Delta sigma(H) approaches zero at some point if one varies the chemical potential.