Aharonov–Bohm interference in even-denominator fractional quantum Hall states

Position exchange of non-Abelian anyons affects the quantum state of their system in a topologically protected way¹. Their expected manifestations in even-denominator fractional quantum Hall (FQH) systems offer the opportunity to directly study their unique statistical properties in interference experiments². Here we present the observation of coherent Aharonov-Bohm interference at two even-denominator states in high-mobility bilayer-graphene-based van der Waals (vdW) heterostructures by using the Fabry-Pérot interferometry technique. Operating the interferometer at a constant filling factor, we observe an oscillation period corresponding to two flux quanta inside the interference loop, ΔΦ = 2Φ₀, at which the interference does not carry signatures of non-Abelian statistics. The absence of the expected periodicity of ΔΦ = 4Φ₀ may indicate that the interfering quasiparticles carry the charge <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow> <mml:mrow><mml:mo>*</mml:mo></mml:mrow> </mml:msup> <mml:mo>=</mml:mo> <mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:mfrac> <mml:mi>e</mml:mi></mml:mrow> </mml:math> or that interference of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow> <mml:mrow><mml:mo>*</mml:mo></mml:mrow> </mml:msup> <mml:mo>=</mml:mo> <mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow> <mml:mrow><mml:mn>4</mml:mn></mml:mrow> </mml:mfrac> <mml:mi>e</mml:mi></mml:mrow> </mml:math> quasiparticles is thermally smeared. Notably, at two hole-conjugate states, we also observe oscillation periods of half the expected value, indicating interference of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow> <mml:mrow><mml:mo>*</mml:mo></mml:mrow> </mml:msup> <mml:mo>=</mml:mo> <mml:mfrac><mml:mrow><mml:mn>2</mml:mn></mml:mrow> <mml:mrow><mml:mn>3</mml:mn></mml:mrow> </mml:mfrac> <mml:mi>e</mml:mi></mml:mrow> </mml:math> quasiparticles instead of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow> <mml:mrow><mml:mo>*</mml:mo></mml:mrow> </mml:msup> <mml:mo>=</mml:mo> <mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow> <mml:mrow><mml:mn>3</mml:mn></mml:mrow> </mml:mfrac> <mml:mi>e</mml:mi></mml:mrow> </mml:math> . To investigate statistical phase contributions, we operated the Fabry-Pérot interferometer (FPI) with controlled deviations of the filling factor, thereby introducing fractional quasiparticles inside the interference loop. The resulting changes to the interference patterns at both half-filled states indicate that the extra bulk quasiparticles carry the fundamental charge <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow> <mml:mrow><mml:mo>*</mml:mo></mml:mrow> </mml:msup> <mml:mo>=</mml:mo> <mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow> <mml:mrow><mml:mn>4</mml:mn></mml:mrow> </mml:mfrac> <mml:mi>e</mml:mi></mml:mrow> </mml:math> , as expected for non-Abelian anyons.