Density profile in a weakly modulated two-dimensional system in a magnetic field

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Abstract
The particle density fluctuations generated by a weak unidirectional periodic potential in a two-dimensional interacting electron system, in a strong perpendicular magnetic field, are calculated using a local-density description of the exchange-correlation energy for the lowest Landau level. The correlation effects are discussed with respect to previous results obtained in the Hartree and Hartree-Fock approximations. In the spatial regions where the local filling factor is in the range 0.3–0.7 the correlation corrections cancel the exchange contributions, such that the Hartree picture is shown to be qualitatively correct. In these regions the external potential is strongly screened by the electronic system. In the other spatial regions the density has higher order oscillations with a specific wavelength, which disappear with increasing the temperature or the external potential amplitude. Possible experimental evidence of these oscillations in modulated structures is discussed.