Dielectric constant of a two-dimensional electron gas with a partially occupied Landau level

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Abstract
We calculate the response to an external static sinusoidal potential from the partially occupied Landau level of a two-dimensional electron gas in a strong magnetic field, by taking into account the interaction between the electrons in the random-phase approximation (RPA). A complete orthonormal set of eigenfunctions is found which diagonalizes the perturbation. The perturbed energy spectrum and the induced one-electron potential are calculated self-consistently, as functions of the temperature and the partial-filling factor of the level. The dielectric constant diverges as the reciprocal of the absolute temperature, and it is shown that a charge-density wave is unstable in RPA, whatever the value of the temperature.