Fractional quantum Hall effect in higher Landau levels

TL;DR

This paper uses numerical methods to explore the fractional quantum Hall effect in higher Landau levels, revealing the presence of an incompressible state at 7/3 and its dependence on finite thickness, while ruling out many other fractions.

Contribution

It provides new numerical evidence for the existence of the FQHE at 7/3 in higher Landau levels and analyzes how finite thickness affects this state.

Findings

Incompressible state at ν=7/3 found in higher Landau level.

FQHE at ν=2+2/5 not observed.

Finite thickness enhances the 7/3 state.

Abstract

We investigate, using finite size numerical calculations, the spin-polarized fractional quantum Hall effect (FQHE) in the first excited Landau level (LL). We find evidence for the existence of an incompressible state at $\nu = \frac{7}{3} = 2+\frac{1}{3}$, but not at $\nu = 2+\frac{2}{5}$. Surprisingly, the 7/3 state is found to be strongest at a finite thickness. The structure of the low- lying excited states is found to be markedly different from that in the lowest LL. This study also rules out FQHE at a large number of odd-denominator fractions in the lowest LL.