Fabry–Pérot Quantum Hall Interferometry in Graphene

The fractional quantum Hall (FQH) effect manifests when a large perpendicular magnetic field is applied to a two-dimensional electron system with sufficiently strong electron-electron interactions. The quasiparticle excitations of this highly correlated phase are neither fermions nor bosons; they are anyons possessing anyonic statistics. Braiding of non-Abelian anyons in certain FQH phases was an early proposal for topologically protected quantum computation.

A Fabry–Pérot (FP) interferometer of fractional quantum Hall edge modes may allow direct measurement of anyonic statistics [1] . Experimentally, interferometry in the QHE have been limited only to a few groups having access to high mobility GaAs materials. Recent developments in VdW heterostructures [2,3] have allowed us to cross
the mobility threshold and observe FQH states at moderate magnetic fields. However, since graphene is a gapless semiconductor, quantum point contact attempts have been difficult, slowing progress towards realizing interferometers.

I will present recent developments in our group: graphene-based gate-defined FP interferometers operating in the Quantum Hall effect. Using Landau Level (LL) gaps to direct edge states and create barriers, we demonstrate gate-tunable quantum point contacts (QPCs), which act as beam splitters of edge modes in the integer quantum Hall
(IQH) and FQH regimes. By cascading two QPCs in series, we formed FP interferometers and measure Aharanov-Bohm interference in the IQH regime owing to the unique electrostatic environment offered by our heterostructure. We extract edge mode velocities and phase coherence lengths of the first three electron-doped LLs and compare gate vs. etch defined interferometers.

[1] Nayak, C. et al. Non-Abelian anyons and topological quantum computation. Reviews of Modern Physics 80, 1083–1159 (2008)
[2] Zibrov, A. A. et al. Tunable interacting composite fermion phases in a half-filled bilayer-graphene Landau level. Nature 549,
360–364 (2017).
[3] J. I. A. Li. et al. Even denominator fractional quantum Hall states in bilayer graphene. Science 358, 648-652 (2017).

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