Non-Abelian quantized Hall states of electrons at filling factors 12/5 and 13/5 in the first excited Landau level

TL;DR

This paper uses numerical calculations to investigate the ground state of electrons in the first excited Landau level at filling factors 12/5 and 13/5, supporting the existence of a non-Abelian k=3 liquid phase relevant to experiments.

Contribution

It provides numerical evidence for the non-Abelian k=3 liquid phase at specific filling factors in the first excited Landau level, including effects of finite thickness.

Findings

Support for non-Abelian k=3 phase at 12/5 and 13/5

Energy spectrum consistent with trial states

Overlap results favor non-Abelian liquid hypothesis

Abstract

We present results of extensive numerical calculations on the ground state of electrons in the first excited (n=1) Landau level with Coulomb interactions, and including non-zero thickness effects, for filling factors 12/5 and 13/5 in the torus geometry. In a region that includes these experimentally-relevant values, we find that the energy spectrum and the overlaps with the trial states support the previous hypothesis that the system is in the non-Abelian k = 3 liquid phase we introduced in a previous paper.