Trapping $e/4$ quasiparticles in bilayer graphene

Abstract

Measuring the charge of the quasiparticles hosted by even-denominator fractional quantum Hall (FQH) states is essential to identify the topology of their ground state. Here, we use a gate-defined antidot in bilayer graphene, with an additional gate to control only the antidot potential, to measure the charge of the quasiparticles trapped around it in even-denominator FQH states. We observe a localized charge of $e/4$ at $ν=-5/2$, $-1/2$, and $3/2$, consistent with the minimal excitation expected for leading candidate even-denominator ground states, and $e/3$ at the hole-conjugate state $ν=2/3$. We further show that increasing the coupling between the antidot-bound states and extended edge states drives a crossover between two regimes, characterized by the minimal-excitation gate-voltage period and approximately twice that period, respectively. We discuss two possible explanations for this crossover: quasiparticle bunching and a crossover between distinct antidot transport regimes. Our results, together with previous observations of the daughter states, show that the even-denominator FQH states in bilayer graphene are compatible with a non-Abelian ground state, and that their quasiparticles can be localized around a quantum Hall antidot, a necessary ingredient for topological quantum computation.