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

TL;DR

This study reveals new fractional quantum Hall states in bilayer graphene, providing insights into their topological orders and the competition between different correlated states, with implications for fault-tolerant quantum computing.

Contribution

It reports the observation of quarter- and half-filled quantum Hall states and their daughter states, constraining their topological order and revealing a universal pattern in bilayer graphene.

Findings

Observed four quarter-filled states and their daughter states.

Detected states at v=-3/2 and v=1/2 with non-Abelian order indications.

Identified several 'next-generation' quantum Hall states requiring strong interactions.

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.