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

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 $\nu =7/3$ 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.

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• A non-Abelian parton state for the $\nu =2+3/8$ fractional quantum Hall effect
• Transitions from Abelian composite fermion to non-Abelian parton fractional quantum Hall states in the zeroth Landau level of bilayer graphene
• Abelian parton state for the $\nu =4/11$ fractional quantum Hall effect
• Real-space entanglement spectra of parton states in fractional quantum Hall systems
• Analytic exposition of the graviton modes in fractional quantum Hall effects and its physical implications
• Parton wave function for the fractional quantum Hall effect at $\nu =6/17$
• Nature of the anomalous $4/13$ fractional quantum Hall effect in graphene
• Competition between fractional quantum Hall liquid and electron solid phases in the Landau levels of multilayer graphene
• Prediction of non-Abelian fractional quantum Hall effect at $\nu =2+\frac{4}{11}$
• Fractional quantum Hall effect of partons and the nature of the 8/17 state in the zeroth Landau level of bilayer graphene
• Fractional Quantum Hall States of the $\mathcal{A}$ phase in the Second Landau Level
• Conformal field theory approach to parton fractional quantum Hall trial wave functions
• Unlocking new regimes in fractional quantum Hall effect with quaternions
• Possible continuous transition from fractional quantum Hall to stripe phase at ${\nu }_e=7/3$
• From frustration-free parent Hamiltonians to off-diagonal long-range order: Moore-Read and related states in second quantization
• Very high-energy collective states of partons in fractional quantum Hall liquids
• Dispersion of neutral collective modes in partonic fractional quantum Hall states and its applications to paired states of composite fermions
• Numerical demonstration of Abelian fractional statistics of composite fermions in the spherical geometry
• Linking infinite bond-dimension matrix product states with frustration-free Hamiltonians
• Adiabatic Path from Fractional Chern Insulators to the Tao-Thouless State