Slow Quasiparticle Dynamics and Anyonic Statistics in a Fractional Quantum Hall Fabry-Pérot Interferometer

Anyons are two-dimensional particles with fractional exchange statistics that emerge as elementary excitations of fractional quantum Hall phases. Experimentally, their exchange statistics can be measured in the edge-state Fabry-Pérot interferometer, wherein the presence of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>N</a:mi> <a:mrow> <a:mi>q</a:mi> <a:mi>p</a:mi> </a:mrow> </a:msub> </a:math> localized anyons contributes a phase <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msub> <c:mi>N</c:mi> <c:mrow> <c:mi>q</c:mi> <c:mi>p</c:mi> </c:mrow> </c:msub> <c:msub> <c:mi>θ</c:mi> <c:mi>a</c:mi> </c:msub> </c:math> to the interference pattern where <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msub> <e:mi>θ</e:mi> <e:mi>a</e:mi> </e:msub> </e:math> is twice the exchange phase. Here we report the observation of large, hysteretic phase jumps in a monolayer graphene Fabry-Pérot interferometer at <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>ν</g:mi> <g:mo>=</g:mo> <g:mn>1</g:mn> <g:mo>/</g:mo> <g:mn>3</g:mn> </g:math> . When the filling factor is increased from <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>ν</i:mi> <i:mo>&lt;</i:mo> <i:mn>1</i:mn> <i:mo>/</i:mo> <i:mn>3</i:mn> </i:math> toward the center of the plateau, we observe phase slips with magnitude <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi mathvariant="normal">Δ</k:mi> <k:mi>θ</k:mi> <k:mo>≈</k:mo> <k:mn>2</k:mn> <k:mi>π</k:mi> <k:mo>/</k:mo> <k:mn>3</k:mn> </k:math> , consistent with the addition of individual quasiparticles to the interferometer bulk. These phase slips occur as instantaneous jumps in the interference signal, with intervals between the jumps indicating quasiparticle equilibration times exceeding 20 min. We use this long timescale to investigate the effect of changes in interferometer area <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:msub> <n:mi>A</n:mi> <n:mi>I</n:mi> </n:msub> </n:math> and <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:mrow> <p:msub> <p:mrow> <p:mi>N</p:mi> </p:mrow> <p:mrow> <p:mi>q</p:mi> <p:mi>p</p:mi> </p:mrow> </p:msub> </p:mrow> </p:math> independently at fixed magnetic field, revealing a striking memory effect in the phase slip magnitude. In particular, as the <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:mi>ν</r:mi> <r:mo>=</r:mo> <r:mn>1</r:mn> <r:mo>/</r:mo> <r:mn>3</r:mn> </r:math> plateau is approached from higher filling, we observed phase slips with <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"> <t:mi mathvariant="normal">Δ</t:mi> <t:mi>θ</t:mi> </t:math> significantly larger than <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mn>2</w:mn> <w:mi>π</w:mi> <w:mo>/</w:mo> <w:mn>3</w:mn> </w:math> over the same range of gate voltage where quantized jumps are seen for increasing <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:mi>ν</y:mi> </y:math> . We discuss this asymmetry in terms of bulk-edge coupling of quasiparticles localized near the edge or in the bulk, and argue that this effect can be qualitatively reconciled with theoretical expectations for strongly interacting quasiparticles in the presence of weak disorder and strongly nonequilibrium charge dynamics. Besides providing a replication of interferometric measurements sensitive to <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:msub> <ab:mi>θ</ab:mi> <ab:mi>a</ab:mi> </ab:msub> </ab:math> , our results highlight the key role played by charge dynamics on signatures of the anyon phase, and demonstrate that fractional quasiparticles can be indefinitely localized in nonequilibrium configurations.