Electron orbits in an impure metal in the presence of a strong magnetic field

A detailed analysis of the classical motion of an electron in a strong magnetic field and in the presence of a random potential is presented. A map of the possible projections of the orbits on the plane perpendicular to the field is extracted. The implications of different orbit shapes to measurable quantities are discussed. It is suggested that, under strong magnetic fields, a three-dimensional system may be an insulator, be a conductor, show a quantized Hall effect, or demonstrate edge conductivity, depending on the orbit corresponding to the Fermi energy.