Cross-Correlation Investigation of Anyon Statistics in the ν=1/3 and 2/5 Fractional Quantum Hall States

Abstract

Recent pioneering works have set the stage for exploring anyon braiding statistics from negative current cross-correlations along two intersecting quasiparticle beams. In such a dual-source-analyzer quantum point contact setup, also referred to as “collider,” the anyon exchange phase of fractional quantum Hall quasiparticles is predicted to be imprinted into the cross-correlations characterized by an effective Fano factorP. In the case of symmetric incoming quasiparticle beams, conventional fermions result in a vanishingP. In marked contrast, we observe signatures of anyon statistics in the negativePfound both for thee/3Laughlin quasiparticles at filling factorν=1/3(P≈−2, corroborating previous findings) and for thee/5quasiparticles in the hierarchical stateν=2/5(P≈−1). Nevertheless, we argue that the quantitative connection between a numerical value ofP≠0and a specific fractional exchange phase is hampered by the influence of the analyzer conductance dependence on the voltages used to generate the quasiparticles. Finally, we address the important challenge how to distinguish atν=1/3between negative cross-correlations induced by a fractional braid phase and those resulting from a different Andreev-like mechanism. Although with symmetric sourcesPdoes not exhibit signatures of a crossover when the analyzer is progressively detuned to favor Andreev processes, we demonstrate that changing the balance between sources provides a means to discriminate between the two mechanisms.

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Plain Language Summary

In the three-dimensional world, particles can be only fermions or bosons. Paradigmatic examples are, respectively, electrons and photons. But when a system is confined to one or two dimensions, other types of quasiparticles called anyons can emerge. Highly pure 2D electron gases immersed in strong magnetic fields offer an outstanding exploration platform for a variety of anyons. The first convincing signatures of anyon statistics have been detected only recently by two different approaches. Here, we build upon one of these approaches, extending it to other types of anyons and establishing the amount of information that it provides on the quasiparticles.

In these 2D gases, electronic quasiparticles can carry a fraction of an electron charge. The recently detected signatures of anyon behavior were specifically for quasiparticles that behave like one-third of an electron. In the approach that we focus on, two beams of quasiparticles are targeted at each other. Signs of anyon statistics—or more specifically, the particular quantum phase that anyons acquire upon the exchange of two indiscernible particles—are imprinted on correlations between current fluctuations along the outgoing quasiparticle beams. In our work, we explore how deeply the nature of quasiparticles can be characterized by cross-correlations, and we expand the investigation to another strange quasiparticle with one-fifth the charge of an electron, whose exotic anyon statistics we at least establish.

Our findings advance the search of unconventional quasiparticles and establish a practicable methodology to demonstrate their anyon character. This opens a path to observe further exotic states, including the non-Abelian anyons envisioned for protected quantum information manipulation.