Composite Fermions and quantum Hall systems: Role of the Coulomb pseudopotential

TL;DR

This paper analyzes how the Coulomb pseudopotential influences the applicability of the composite fermion model in fractional quantum Hall systems, highlighting when it accurately predicts energy spectra and when it fails, especially in higher Landau levels.

Contribution

It clarifies the role of the Coulomb pseudopotential in the composite fermion model and identifies conditions under which the model is valid or invalid in different Landau levels.

Findings

The CF model accurately predicts energy spectra in the lowest Landau level.

In higher Landau levels, the pseudopotential behavior can invalidate the CF picture.

The analysis explains successes and failures of the CF model in various charged fermion systems.

Abstract

The mean field composite Fermion (CF) picture successfully predicts angular momenta of multiplets forming the lowest energy band in fractional quantum Hall (FQH) systems. This success cannot be attributed to a cancellation between Coulomb and Chern-Simons interactions beyond the mean field, because these interactions have totally different energy scales. Rather, it results from the behavior of the Coulomb pseudopotential V(L) (pair energy as a function of pair angular momentum) in the lowest Landau level (LL). The class of short range repulsive pseudopotentials is defined that lead to short range Laughlin like correlations in many body systems and to which the CF model can be applied. These Laughlin correlations are described quantitatively using the formalism of fractional parentage. The discussion is illustrated with an analysis of the energy spectra obtained in numerical diagonalization of up to eleven electrons in the lowest and excited LL's. The qualitative difference in the behavior of V(L) is shown to sometimes invalidate the mean field CF picture when applied to higher LL's. For example, the nu=7/3 state is not a Laughlin nu=1/3 state in the first excited LL. The analysis of the involved pseudopotentials also explains the success or failure of the CF picture when applied to other systems of charged Fermions with Coulomb repulsion, such as the Laughlin quasiparticles in the FQH hierarchy or charged excitons in an electron-hole plasma.