Unconventional <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="double-struck">Z</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:math> parton states at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>ν</mml:mi><mml:mo>=</mml:mo><mml:mn>7</mml:mn><mml:mo>/</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:math>: Role of finite width
W. N. Faugno, Tongzhou Zhao, Ajit C. Balram, Th. Jolicœur, J. K. Jain
Abstract
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 $1/(3n)$ of the electron charge, is energetically better than the Laughlin wave function at $\ensuremath{\nu}=7/3$ 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 $\ensuremath{\sim}1.5$ 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.