Non-quasiconvex dispersion of composite fermions and the fermionic Haffnian state in the first-excited Landau level

TL;DR

This paper investigates how the dispersion of composite fermions influences the nature of fractional quantum Hall states in the first excited Landau level, revealing non-quasiconvex dispersion leads to novel fermionic Haffnian states.

Contribution

It demonstrates that non-quasiconvex composite fermion dispersion causes the fermionic Haffnian state in the 1LL, contrasting with the Laughlin state, and shows how dispersion becomes quasiconvex under certain conditions.

Findings

CF dispersion is non-quasiconvex in 1LL

Fermionic Haffnian wave function describes the ground state in 7/3

Dispersion becomes quasiconvex in wide quantum wells or with four vortices in 11/5

Abstract

It has long been puzzling that fractional quantum Hall states in the first excited Landau level (1LL) often differ significantly from their counterparts in the lowest Landau level. We show that the dispersion of composite fermions (CFs) is a deterministic factor driving the distinction. We find that CFs with two quantized vortices in the 1LL have a non-quasiconvex dispersion. Consequently, in the filling fraction $7/3$, CFs occupy the second $\Lambda$-level instead of the first. The corresponding ground state wave function, based on the CF wave function ansatz, is identified to be the fermionic Haffnian wave function rather than the Laughlin wave function. The conclusion is supported by numerical evidence from exact diagonalizations in both disk and spherical geometries. Furthermore, we show that the dispersion becomes quasiconvex in wide quantum wells or for CFs with four quantized vortices in the filling fraction $11/5$, coinciding with observations that the distinction between the Landau levels disappears under these circumstances.