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 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 <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ν</mi> <mo>=</mo> <mo>-</mo> <mfrac><mrow><mn>3</mn></mrow> <mrow><mn>2</mn></mrow> </mfrac> </math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ν</mi> <mo>=</mo> <mfrac><mrow><mn>1</mn></mrow> <mrow><mn>2</mn></mrow> </mfrac> </math> 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.