Magnetoroton instabilities and static susceptibilities in higher Landau levels

We present analytical results concerning the magnetoroton instability in higher Landau levels (LL's) 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 q(0)(n)similar to1/root2n+1, as expected from Hartree-Fock predictions. We thus obtain a unified description of the leading charge instabilities in all LL's.