QUENCHING OF THE HALL-EFFECT IN STRONGLY MODULATED 2-DIMENSIONAL ELECTRONIC SYSTEMS

The longitudinal (rho(xx)) and Hall (rho(xy)) resistivities are calculated for a strongly modulated two-dimensional electron gas. This modulation is simulated by a square array of delta-potential scatterers. It is shown that when the strength of the potential is sufficiently strong rho(xy) can be negative and quenched and rho(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 rho(xy) but they quantitatively change rho(xx). Numerical results are presented to show how the lattice, impurity scattering, and the electron density affect the quenching of the Hall effect and the commensurate oscillations.