CHARGE-DENSITY EXCITATIONS IN THE FRACTIONAL QUANTIZED HALL-EFFECT IN SUPERLATTICES

We have studied collective excitations in the fractional quantized Hall effect, using the single-mode approximation for a semi-infinite superlattice. Dispersion relations are derived for the bulk and surface collective modes corresponding to 1/3 and 1/5 filling fractions of the lowest Landau level. The model consists of a periodic array of two-dimensional electron layers in strong magnetic field embedded in a material of dielectric constant epsilon-s terminating at the interface with a homogeneous medium of dielectric constant epsilon-0. The bulk modes form a continuum; and the surface mode, which exists only for wavelengths shorter than a critical value, can occur either above or below the bulk continuum, depending on the ratio epsilon-s/epsilon-0.