Fractional quantum Hall effect and electron correlations in partially filled first excited Landau level

TL;DR

This paper investigates the unique quantum Hall states in the first excited Landau level, revealing that electron pairing and clustering lead to incompressible states distinct from those in the lowest Landau level.

Contribution

It provides a detailed numerical analysis showing that prominent quantum Hall states in LL1 arise from electron pairing and clustering, differing from traditional Laughlin states.

Findings

Prominent states at 5/2, 7/3, 8/3 are due to electron pairing or clustering.

States at 14/5, 16/7, 11/5, 19/7 are Laughlin correlated and follow Jain's sequence.

The pseudopotential in LL1 is harmonic at short range, influencing state formation.

Abstract

We present a quantitative study of most prominent incompressible quantum Hall states in the partially filled first excited Landau level (LL1) which have been recently studied experimentally by Choi et al. The pseudopotential describing the electron - electron interaction in LL1 is harmonic at short range. It produces a series of incompressible states which is different from its LL0 counterpart. The numerical data indicate that the most prominent states $\nu={5/2}$, 7/3, and 8/3 are not produced by Laughlin correlated electrons, but result from a tendency of electrons to form pairs or larger clusters which eventually become Laughlin correlated. States with smaller gaps at filling factors 14/5, 16/7, 11/5, 19/7 are Laughlin correlated electron or hole states and fit Jain's sequence of filled $\rm{CF}^4$ levels.