Magnetoroton instabilities and static susceptibilities in higher Landau levels

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We present analytical results concerning the magneto-roton instability in higher Landau levels evaluated in the single mode approximation. The roton gap appears at a finite wave vector, which is approximately independent of the LL index n, in agreement with numerical calculations in the composite-fermion picture. However, a large maximum in the static susceptibility indicates a charge density modulation with wave vectors q₀(n) 1/√2n+1, as expected from Hartree-Fock predictions. We thus obtain a unified description of the leading charge instabilities in all LLs.