The Effect of Landau Level-Mixing on the Effective Interaction between Electrons in the fractional quantum Hall regime

TL;DR

This paper investigates how Landau level mixing influences electron interactions in fractional quantum Hall systems, revealing attractive three-body interactions and complex pseudopotential renormalizations, with implications for the =5/2 state.

Contribution

It provides detailed calculations of Landau level mixing effects on two- and three-body pseudopotentials in quantum Hall regimes, highlighting new interaction features.

Findings

Effective three-body interaction is attractive in the lowest angular momentum channel.

Landau level mixing causes notable renormalization of two-body pseudopotentials.

Implications discussed for the =5/2 fractional quantum Hall state.

Abstract

We compute the effect of Landau-level-mixing on the effective two-body and three-body pseudopotentials for electrons in the lowest and second Landau levels. We find that the resulting effective three-body interaction is attractive in the lowest relative angular momentum channel. The renormalization of the two-body pseudopotentials also shows interesting structure. We comment on the implications for the $\nu=5/2$ fractional quantum Hall state.