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arXiv · 2405.19405

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

Ravi Kumar·André Haug·Jehyun Kim·Misha Yutushui·Konstantin Khudiakov·Vishal Bhardwaj·Alexey Ilin·Kenji Watanabe·Takashi Taniguchi·David F. Mross·Yuval Ronen
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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.

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Ravi Kumar, André Haug, Jehyun Kim, Misha Yutushui, Konstantin Khudiakov, Vishal Bhardwaj, Alexey Ilin, Kenji Watanabe, Takashi Taniguchi, David F. Mross, Yuval Ronen. 2024-05-29. Quarter- and half-filled quantum Hall states and their topological orders revealed by daughter states in bilayer graphene. https://doi.org/10.1038/s41467-025-62650-9

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