Abstract
The longitudinal (ρ xx ) and Hall (ρ xy ) resistivities are calculated for a strongly modulated two-dimensional electron gas. This modulation is simulated by a square array of 6-potential scatterers. It is shown that when the strength of the potential is sufficiently strong ρ xy can be negative and quenched and ρ xx has commensurate oscillations. Similar features have been observed experimentally for a square array of antidots. The quenching of the Hall resistivity is shown to be due to the collimated states from resonant scattering of the electrons by a lattice potential in a magnetic field when the magnetic and lattice Brillouin zones become commensurate. Impurities do not qualitatively change ρ xy but they quantitatively change ρ xx
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