Quantum Theory of Transverse Magnetoconductivity for Semiconductors

The current correlation formula for the static magneto-conductivity of a electron impurity system is analysed in terms of proper connected diagrams in the extreme quantum limit. By selecting those diagrams appropriate in the region of weak coupling and low impurity concentration an expression for the transverse magnetoconductivity is derived. The method used, incorporates the quasiparticle effect in a self consistent manner and thereby gives a finite value for the resistivity for all realistic potentials. In the limit of high temperatures when the scattering may be regarded elastic this theory is in agreement with the earlier works of Titeica, Adams and Holstein and with the group of Kubo et al. At very low temperatures it predicts a finite conductivity. It is found that the resistivity can be expressed as a power law of the magnetic field in the limit of very high fields. The dependence on temperature and magnetic field is found, to be in general agreement with other theories as well as with experiments.