Even-denominator fractional quantum Hall states are promising candidates for fault-tolerant quantum computing due to their underlying non-Abelian topological order. 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 <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41467_2025_62650_Article_IEq1.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="54" /> </InlineMediaObject> <EquationSource Format="TEX">$\nu=-\frac{3}{2}$</EquationSource> <EquationSource Format="MATHML"><math> <mi>ν</mi> <mo>=</mo> <mo>−</mo> <mfrac> <mrow> <mn>3</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41467_2025_62650_Article_IEq2.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">$\nu=\frac{1}{2}$</EquationSource> <EquationSource Format="MATHML"><math> <mi>ν</mi> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </math></EquationSource> </InlineEquation> 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.

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

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2025年8月6日

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Ravi Kumar,
André Haug,
Jehyun Kim,
Misha Yutushui,
Konstantin Khudiakov,
Vishal Bhardwaj,
Alexey Ilin,
K. Watanabe,
T. Taniguchi,
David F. Mross,
Yuval Ronen

摘要

Even-denominator fractional quantum Hall states are promising candidates for fault-tolerant quantum computing due to their underlying non-Abelian topological order. 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 $\nu=-\frac{3}{2}$ $ν = - \frac{3}{2}$ and $\nu=\frac{1}{2}$ $ν = \frac{1}{2}$ 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.