Magnetoroton instabilities and static susceptibilities in higher Landau levels

TL;DR

This paper analytically investigates magnetoroton instabilities and static susceptibilities in higher Landau levels, revealing consistent behaviors with numerical and Hartree-Fock predictions, and providing a unified understanding of charge instabilities across all levels.

Contribution

It offers an analytical framework for magnetoroton instabilities in higher Landau levels, aligning with numerical and Hartree-Fock results, and unifies the description of charge instabilities.

Findings

Roton gap appears at a finite wave vector nearly independent of Landau level index

Large maximum in static susceptibility indicates charge density modulation

Wave vectors for charge modulation scale as 1/√(2n+1)

Abstract

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 $q_0(n)\sim 1/\sqrt{2n+1}$, as expected from Hartree-Fock predictions. We thus obtain a unified description of the leading charge instabilities in all LLs.