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Abstract
We employ multichannel quantum scattering theory to treat the magnetoconductance of finite-size two-dimensional samples using a non-perturbative treatment of sample impurities and the magnetic field. First we study the Aharonov-Bohm effect in a cylindrical geometry with flux along the axis of the cylinder. The periodicity of the average conductance as a function of the flux changes from hc/2e to hc/e as the impurity potential is weakened. Then we consider the conductance of a rectangular sample with impurities subject to transverse magnetic field. First we have studied an impurity-free sample and found σxx(B) decreases monotonically with magnetic field without any oscillation with period of the quantum flux. Second, for weak impurity scattering, ⟨σxx(B)⟩ is smaller (larger) than the impurity-free sample conductivity for small (large) B values.