Observability of counterpropagating modes at fractional-quantum-Hall edges

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When the bulk filling factor is equal to 1 - 1/m with m odd, at least one counterpropagating chiral collective mode occurs simultaneously with magnetoplasmons at the edge of fractional-quantum-Hall samples. Initial experimental searches for an additional mode were unsuccessful. In this paper, we address conditions under which its observation should be expected in experiments where the electronic system is excited and probed by capacitive coupling. We derive realistic expressions for the velocity of the slow counterpropagating mode, starting from a microscopic calculation which is simplified by a Landau-Silin-like separation between long-range Hartree and residual interactions. The microscopic calculation determines the stiffness of the edge to long-wavelength neutral excitations, which fixes the slow-mode velocity, and the effective width of the edge region, which influences the magnetoplasmon dispersion.