On the Collective Mode Spectrum for Composite Fermions at 1/3 Filling Factor

TL;DR

This paper analyzes the collective mode spectrum of the composite fermion state at 1/3 filling, revealing a threshold indicating potential instability and confirming the Kohn theorem, with implications for understanding quantum Hall states.

Contribution

It provides a detailed evaluation of the collective mode spectrum at 1/3 filling, highlighting unexpected results and raising questions about mean field approximation limitations.

Findings

Collective mode matches cyclotron energy at zero momentum.

No magneto roton minimum observed, replaced by a threshold.

Indicates possible instability towards crystalline structures.

Abstract

The collective mode spectrum of the composite fermion state 1/3 filling factor is evaluated. At zero momentum, the result coincides with the cyclotron energy at the external magnetic field value, and not at the effective magnetic field, in spite of the fact that only the former enters in the equations, thus, the Kohn theorem is satisfied. Unexpectedly, in place of a magneto roton minimum, the collective mode gets a treshold indicating the instability of the mean field composite fermion state under the formation of crystalline structures. However, the question about if if this outcome only appears within the mean field approximation should be further considered.