🔬 mesoscale physics

Single anyons and anyon binding in a quantum Hall dot

This study demonstrates the trapping and controlled manipulation of single anyons in a graphene-based quantum Hall dot, revealing complex orbital shell-filling behaviors and experimentally confirming the existence of a significant anyon binding energy that leads to the pairing of fractional charges.

Original authors: Marco Valentini, Will Wang, Amir Shapour Mohammadi, Noah Samuelson, Chengxuan Li, Liam Cohen, Mark Zakharyan, Jiechao Feng, Taige Wang, Takashi Taniguchi, Kenji Watanabe, Michael P. Zaletel, Andrea F.

Published 2026-10-14

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Marco Valentini, Will Wang, Amir Shapour Mohammadi, Noah Samuelson, Chengxuan Li, Liam Cohen, Mark Zakharyan, Jiechao Feng, Taige Wang, Takashi Taniguchi, Kenji Watanabe, Michael P. Zaletel, Andrea F. Young

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the strange world of quantum physics, particles do not always behave like the solid objects we see in daily life. Sometimes, when electrons are trapped in a thin layer of material and cooled to near absolute zero, they organize themselves into a special state of matter known as a fractional quantum Hall fluid. In this fluid, the electrons move in a coordinated dance that creates new, emergent particles. These particles are called anyons. Unlike ordinary electrons, which carry a whole unit of electric charge, anyons carry only a fraction of that charge, such as one-third of an electron's charge. They also possess a unique property called fractional statistics, meaning that if you swap two of them, the quantum state of the system changes in a way that is different from swapping ordinary particles. For decades, scientists have studied these particles in large groups, where many anyons exist together and interact in complex ways. However, to truly understand their nature and potentially use them for future quantum computers, researchers needed to isolate and control a single anyon, holding it alone in a tiny trap to observe its behavior without the noise of its neighbors.

A team of researchers has now succeeded in creating a device that can trap and manipulate a single anyon. Working with a sheet of graphene, a material made of a single layer of carbon atoms, they built a microscopic circuit that acts as a quantum dot, or a tiny cage for electrons. By applying precise voltages to a series of gates surrounding a small hole in the graphene, they were able to squeeze the electron fluid until only a single fractional charge remained inside the trap. This setup functions like a transistor for anyons, allowing the scientists to add or remove these fractional charges one by one and measure the energy required for each step. The device is exceptionally clean and well-controlled, allowing the team to deplete the trap until it holds just one quasiparticle, the name for these fractional excitations, and then add more to see how they arrange themselves.

When the researchers first tested their device at a simpler state where the electrons behave like a normal fluid, they confirmed that they could control the flow of whole electrons. They observed that as they adjusted the voltage, the electrons would get stuck in the trap due to a phenomenon called Coulomb blockade, where the repulsion between like charges prevents new ones from entering until the voltage is high enough to overcome the repulsion. They then moved to the more complex fractional states, where the charge carriers are only one-third of an electron. Here, they found that the energy required to add a new charge was much smaller, consistent with the addition of these tiny fractional particles. By carefully tuning the device, they managed to isolate a single anyon and then add a second, third, and so on, mapping out the energy landscape of the trap.

The results revealed a surprising complexity in how these particles arrange themselves. When the researchers added a small number of anyons, the energy required to add each new one varied in an irregular pattern. This was not random; it reflected the specific way the particles filled up the available energy levels within the tiny trap, similar to how electrons fill orbitals in an atom. The researchers used advanced computer simulations to model this behavior, and the simulations matched their experimental data perfectly, showing that the irregularity came from the competition between the particles trying to stay close to the center of the trap and the energy cost of occupying higher energy states.

As they added more particles, filling the trap with about ten to twenty anyons, a striking pattern emerged. For some types of fractional charges, the energy steps remained regular and predictable. However, for other types, the pattern became highly irregular, with the energy required to add a particle jumping up and down in a way that suggested the particles were attracting each other. The researchers found that by adjusting the confinement of the trap, they could make these particles bind together so tightly that the trap would skip over certain charge states entirely. Instead of adding one particle at a time, the system would jump by adding two particles at once, as if they had formed a molecule. This observation provides strong evidence that anyons can attract one another and form bound pairs, a phenomenon that had been theorized but never directly observed in a controlled setting.

This discovery is significant because it changes our understanding of how these exotic particles interact. It suggests that the rules governing anyons are not just about repulsion, as is common with electrons, but can also include attraction, leading to the formation of composite structures. The ability to trap a single anyon and study its interactions with such precision opens the door to deeper investigations of quantum mechanics. It also brings scientists closer to the goal of building topological quantum computers, which rely on the unique properties of anyons to store and process information in a way that is naturally protected from errors. By demonstrating that these particles can be isolated, counted, and made to bind, the researchers have provided a crucial step toward harnessing the power of the quantum world for future technology.

Technical Summary: Single Anyons and Anyon Binding in a Quantum Hall Dot

Problem Statement
While the theoretical framework for anyons—particles with quantized fractional statistics—was established in the 1980s, experimental verification has largely been confined to mesoscopic structures containing many anyonic excitations that coexist and interact. Previous efforts to probe fractional charge and phase have utilized large dots and interferometers (Fabry-Perot and Mach-Zehnder) in the many-bulk-quasiparticle regime. Furthermore, scanning tunneling microscopy approaches have been limited by the necessity of tunneling whole electrons into the fractional Hall system, preventing direct spectroscopy of a single localized anyon state. The central challenge addressed in this work is the controllability and isolation of a single anyon within a topologically ordered two-dimensional insulator, specifically a fractional quantum Hall (FQH) phase, to serve as a precision probe of strongly correlated physics and a potential element for topologically protected quantum information processing.

Methodology
The authors utilize high-quality graphene-based van der Waals heterostructures to construct a tunable quantum dot embedded within a quantum point contact (QPC). The device consists of a monolayer graphene active layer encapsulated between hexagonal boron nitride (hBN) dielectrics, controlled by a multi-layer gate architecture:

Global Control: A graphite bottom gate tunes the global filling factor.
QPC Definition: A top graphite gate, patterned via atomic force lithography, defines a QPC geometry with a central 90 nm diameter hole.
Dot and Edge Tuning: Three aluminum finger gates are aligned over the hole (dot gate, $V_{dot}$ ) and the adjacent trenches (edge gates, $V_{edge}$ ) to independently control the dot occupation and the tunnel coupling between the dot and the chiral Luttinger liquid (CLL) edge states.

Transport is measured via the induced DC current ( $I$ ) and voltage ( $V$ ) in response to a bias ( $V_{DC}$ ). The system operates in a regime where the dot mediates weak backscattering between the top and bottom CLL edge modes. By tuning the edge filling factor ( $\nu_{edge}$ ) relative to the bulk ( $\nu_{bulk}$ ), the authors control the tunneling of fractional charges ( $e^*$ ) from the delocalized edge to the localized dot. The experimental data is benchmarked against Density Matrix Renormalization Group (DMRG) simulations on a Haldane sphere, which model the dot as a finite sphere with a gate-defined potential, accounting for screened Coulomb interactions and orbital shell-filling effects.

Key Results

Benchmarking at Integer Filling ( $\nu = 1$ ):
- The device demonstrates backscattering between Fermi liquid edge states mediated by whole-electron Coulomb blockade.
- The dot can be depleted to the last quasihole. The authors observe robust spin blockade for transitions to the opposite-spin Landau level. When the dot is populated with quasiparticles (electrons in the opposite spin level), tunneling is suppressed at low bias due to spin conservation.
- At finite bias ( $|V_{DC}| \gtrsim 1$ mV), conductance dips reappear due to inelastic tunneling accompanied by magnon absorption, overcoming the Zeeman energy gap ( $E_Z \approx 0.58$ meV).
- The system exhibits well-separated excited states ( $\Delta \approx 0.3 - 0.8$ meV) and low-frequency charge noise ( $\sim 10^{-3} e/\sqrt{\text{Hz}}$ at 10 mHz), indicating a high-quality dielectric environment suitable for qubit applications.
Single Anyon Transistor at Fractional Filling ( $\nu = 1/3, 2/3$ ):
- At fractional fillings, the authors observe backscattering resonances with a frequency three times that of the integer case, consistent with the resonant transmission of $e/3$ charges.
- Controlled depletion to the last quasiparticle forms a "single anyon quantum dot."
- Irregular Addition Energies: For a small number of quasiparticles ( $N_{qp} = 1-5$ ), the charge addition spectrum is highly irregular. DMRG modeling attributes this to a complex orbital shell-filling behavior, where there is a competition between spatially extended states (minimizing higher-energy $\Lambda$ -level occupation) and compact states (minimizing confinement energy). This results in an "even-odd" effect in the stability of the first few quasiparticle states.
Evidence for Anyon Binding:
- At higher quasiparticle numbers ( $|N_{qp}| \approx 10\text{--}20$ ), a striking asymmetry emerges. Quasiholes at $\nu = 1/3$ (and quasiparticles at $\nu = 2/3$ ) exhibit a regular addition spectrum. Conversely, quasiparticles at $\nu = 1/3$ (and quasiholes at $\nu = 2/3$ ) display irregular spectra.
- By experimentally tuning the confining energy (via the top gate voltage $V_T$ ), the authors observe the complete suppression of alternating charge sectors. In this regime, the dot charges in increments of twice the fundamental charge ( $2e/3$ ).
- This phenomenon indicates the emergence of an attractive component in the inter-anyon interaction. The binding energy ( $E_B$ ) is at least as large as the charging energy ( $E_C$ ), leading to the formation of "anyon molecules."
- The authors note that while their DMRG calculations predict no binding for isolated $e/3$ anyons in a uniform system at $\nu=1/3$ , binding is predicted at $\nu=2/5$ . They suggest the observed binding in the dot may arise from the dot localizing a puddle of $\nu=2/5$ or forming a $\nu=2/3$ droplet within the $\nu=1/3$ bulk.

Significance and Claims
The paper claims to demonstrate the trapping of a single anyon in a device capable of quantitative metrology of inter-anyon interactions. The primary significance lies in:

Precision Physics: Moving beyond many-body ensembles to isolate single anyons, allowing for the study of fundamental properties like spin blockade and orbital shell filling in the fractional regime.
Anyon Chemistry: Providing experimental evidence for "anyon binding," where attractive interactions lead to the formation of composite particles (molecules) with charges larger than the elementary fractional charge. This observation suggests that intrinsic pairing may account for anomalous charges observed in previous transport and shot noise experiments in FQH systems.
Technological Relevance: The exceptional charge stability and low noise achieved in this graphene geometry support the feasibility of topological qubits. The authors posit that the same techniques could be adapted to confine single non-Abelian anyons and create fractional charge pumps for metrology-grade measurements.

The authors maintain a modest stance regarding the mechanism of binding, acknowledging that while the dot exhibits binding, it does not definitively prove intrinsic binding in a uniform $\nu=1/3$ state, but rather highlights the complex energetics of "anyon chemistry" that must be accounted for in large anyon-number experiments.

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