Theory of Quantum Transport in a Two-Dimensional Electron System under Magnetic Fields. III. Many-Site Approximation

Effects of simultaneous scattering from many scatterers on the level broadening of each Landau level are investigated by assuming short-ranged scatterers. The double-site approximation, which is the direct extension of the single-site approximation, does not give physically reasonable solution of the self-consistency equation which determines the Green's function. Such singular behavior is a result of the incorrect analyticity of the self-energy part and is shown to exist in still higher approximations. At high concentrations of scatterers, an approximate infinite summation of the many-site series gives a reasonable density of states, which has low- and high-energy tails and whose width is effectively smaller than that in the lowest approximation.