Quarter- and half-filled quantum Hall states and their topological orders revealed by daughter states in bilayer graphene

Abstract

Even-denominator fractional quantum Hall states are promising candidates for fault-tolerant quantum computing due to their underlying non-Abelian topological orders. However, the topological order of these states remains hotly debated. Here, we report transport measurements on ultra-clean bilayer graphene heterostructures, where we observed four quarter-filled states and their corresponding Levin-Halperin daughter states, constraining their topological order. Moreover, we complete the sequence of half-filled plateaus by detecting states at v=-3/2 and v=1/2 whose daughters suggest an alternating sequence of non-Abelian orders. This pattern suggests a universal origin supporting their use in identifying topological order at even-denominator fillings, though further confirmation is needed via direct measurements. The observed quarter- and half-filled states appear in N=0 and N=1 Landau levels, respectively, and thus highlight a competition between interactions favoring paired states of either four- or two-flux composite fermions. Additionally, we observe several 'next-generation' quantum Hall states that require strong interactions between composite fermions.

17 pages, 4 figures

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• Paired fermions in strong magnetic fields and daughters of even-denominator Hall plateaus
• Tunable even- and odd-denominator fractional quantum Hall states in trilayer graphene

Cited by in corpus (8)

• Aharonov-Bohm Interference in Even-Denominator Fractional Quantum Hall States
• Fractional quantum Hall state at $\nu =1/2$ with energy gap up to 6 K, and possible transition from one- to two-component state
• Nematic Enhancement of Superconductivity in Multilayer Graphene via Quantum Geometry
• Interaction-driven quantum phase transitions between topological and crystalline orders of electrons
• Anomalous Transport Gaps of Fractional Quantum Hall Phases in Graphene Landau Levels are Induced by Spin-Valley Entangled Ground States
• Interlayer exciton condensates between second Landau level orbitals in double bilayer graphene
• Even-denominator fractional quantum Hall states in the zeroth Landau level of ABA trilayer graphene
• Repulsive-Interaction-Driven Topological Superconductivity in a Landau Level Coupled to an $s$-Wave Superconductor