Girvin-MacDonald-Platzman Collective Mode at General Filling Factors: Magneto-Roton Minimum at Half-Filled Landau Level

TL;DR

This paper extends the single mode approximation to predict multiple magneto-roton minima in the collective mode spectrum for various fractional quantum Hall states, including at half-filled Landau levels, highlighting new features in excitation spectra.

Contribution

It introduces a generalized application of the single mode approximation to fractional quantum Hall states at various filling factors, revealing multiple magneto-roton minima.

Findings

Predicts n magneto-roton minima at filling factors n/(2n+1)

Identifies a single magneto-roton minimum at half-filled Landau level

Suggests experimental relevance of the predicted minima

Abstract

The single mode approximation has proved useful for the excitation spectrum at $\nu=1/3$. We apply it to general fractions and find that it predicts $n$ magneto-roton minima in the dispersion of the Girvin-MacDonald-Platzman collective mode for the fractional quantum Hall states at $\nu=n/(2n+1)$, and one magneto-roton minimum for both the composite Fermi sea and the paired composite fermion state. Experimental relevance of the results will be considered.