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 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 Z(n) state at small widths to the Laughlin state for widths exceeding similar to 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.