Unconventional Zn parton states at ν=7/3 : Role of finite width

A recent work [Balram, Jain, and Barkeshli, Phys. Rev. Res. 2, 013349 (2020)] has suggested that an unconventional state describing ${\mathbb{Z}}_n$ superconductivity of composite bosons, which supports excitations with charge $1/\left(3n\right)$ 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.