Unconventional $\mathbb{Z}_{n}$ parton states at $\nu = 7/3$: The role of finite width

TL;DR

This paper investigates how finite width influences the stability of unconventional $ ext{Z}_n$ parton states at filling factor 7/3, predicting a phase transition to the Laughlin state as width increases, with implications for GaAs and bilayer graphene systems.

Contribution

It demonstrates that finite width induces a phase transition from unconventional $ ext{Z}_n$ states to the Laughlin state at $ u=7/3$, clarifying experimental observations.

Findings

Finite width causes a transition from $ ext{Z}_n$ to Laughlin state at ~1.5 magnetic lengths.

Unconventional $ ext{Z}_n$ states are stabilized in bilayer graphene under certain parameters.

Landau level mixing and spin effects are also analyzed.

Abstract

A recent work [Balram, Jain, and Barkeshli, Phys. Rev. Res. ${\bf 2}$, 013349 (2020)] has suggested that an unconventional state describing $\mathbb{Z}_{n}$ superconductivity of composite bosons, which supports excitations with charge $1/(3n)$ of the electron charge, is energetically better than the Laughlin wave function at $\nu=7/3$ in GaAs systems. All experiments to date, however, are consistent with the latter. To address this discrepancy, we study the effect of finite width on the ground state and predict a phase transition from an unconventional $\mathbb{Z}_{n}$ state at small widths to the Laughlin state for widths exceeding $\sim$ 1.5 magnetic lengths. We also determine the parameter region where an unconventional state is stabilized in the one third filled zeroth Landau level in bilayer graphene. The roles of Landau level mixing and spin are also considered.