Shape of the magnetoroton at $\nu=1/3$ and $\nu=7/3$ in real samples

TL;DR

This paper investigates the collective excitation modes in the fractional quantum Hall effect at filling factors 1/3 and 7/3, considering finite thickness effects and Landau level mixing, revealing differences in mode behavior between the lowest and second Landau levels.

Contribution

It provides a detailed analysis of the magnetoroton mode in real samples, including finite thickness and Landau level mixing effects, using exact diagonalizations in the torus geometry.

Findings

In the lowest Landau level, the magnetoroton merges into the continuum at long wavelengths.

In the second Landau level, the mode is well-defined only below a critical wavevector.

The dispersion shape persists under Landau level mixing perturbations.

Abstract

We revisit the theory of the collective neutral excitation mode in the fractional quantum Hall effect at Landau level filling fractions $\nu=1/3$ and $\nu=7/3$. We include the effect of finite thickness of the two-dimensional electron gas and use extensive exact diagonalizations in the torus geometry. In the lowest Landau level the collective gapped mode i.e. the magnetoroton always merges in the continuum in the long-wavelength limit. In the second Landau level the mode is well-defined only for wavevectors smaller than a critical value and disappears in the continuum beyond this point. Its curvature near zero momentum is opposite to that of the LLL. It is well separated from the continuum even at zero momentum and the gap of the continuum of higher-lying states is twice the collective mode gap at $k=0$. The shape of the dispersion relation survives a perturbative treatment of Landau level mixing.