Anyon braiding and telegraph noise in a graphene interferometer

This study demonstrates the observation of universal anyonic braiding phases in graphene interferometers at fractional quantum Hall states $\nu=1/3$ and $4/3$ by analyzing real-time three-state random telegraph noise, which reveals Aharonov-Bohm oscillations phase-shifted by $2\pi/3$ corresponding to the fractional exchange statistics of anyons.

The Gist

Imagine you are trying to solve a mystery about a very strange, invisible world inside a piece of graphene (a material made of a single layer of carbon atoms). In this world, electricity doesn't flow like water in a pipe; instead, it moves in a special, organized dance called the Quantum Hall Effect.

In this dance, the electrons sometimes split apart to form "ghosts" called Anyons. These aren't normal particles. If you swap two normal particles (like electrons), nothing special happens. But if you swap two Anyons, they leave a magical "fingerprint" on the universe—a change in their quantum state. This is called braiding.

The scientists in this paper wanted to catch these ghosts in the act of braiding. Here is how they did it, explained simply:

1. The Setup: A Tiny Racetrack

Think of the graphene device as a tiny racetrack for electrons.

• The Track: The electrons run along the edge of the graphene, like cars on a highway.
• The Obstacles: The scientists built two tiny "gates" (like speed bumps) on the track. These gates let some cars pass but bounce others back.
• The Goal: They wanted to see what happens when the "ghosts" (Anyons) trapped in the middle of the track swap places with the cars running on the edge.

2. The Problem: The "Static" Noise

In previous experiments, trying to see these ghosts was like trying to hear a whisper in a hurricane. The electrical charges in the material were so messy and "noisy" (due to something called Coulomb interaction) that the delicate quantum signal was drowned out. It was like trying to see a specific color in a room filled with blinding, flashing strobe lights.

3. The Breakthrough: The "Telegraph"

The team used a super-clean graphene device with special graphite gates that acted like noise-canceling headphones. This cleared away the static.

Suddenly, they saw something amazing: The signal started blinking.

Imagine you are listening to a radio station. Usually, the music is smooth. But in this experiment, the volume suddenly jumped between three distinct levels: Low, Medium, and High. Then it jumped back. Then it jumped again.

• This is called Random Telegraph Noise (RTN).
• It's like a telegraph operator tapping out a message, but instead of dots and dashes, they are tapping between three different volumes.

4. The Mystery Solved: The Three-Step Dance

Why did it jump between three levels?

• The scientists realized that the "ghosts" (Anyons) inside the racetrack were moving around randomly.
• Every time a ghost moved, it changed the "phase" (the timing) of the electron wave running on the edge.
• Because these are fractional ghosts (they carry 1/3 of an electron's charge), they have a special rule: You have to swap them three times to get back to where you started.
  • Swap #1: The signal jumps to Level 1.
  • Swap #2: The signal jumps to Level 2.
  • Swap #3: The signal jumps to Level 3.
  • Swap #4: Back to Level 1.

The "blinking" they saw was the real-time evidence of these ghosts swapping places. The three levels corresponded to the three possible "steps" in the dance.

5. The "Magic" Proof

To prove this wasn't just random noise, they did a clever trick. They slowly changed the size of the racetrack (using a voltage knob).

• If it were just random noise, the signal would look messy.
• Instead, they saw three perfect, wavy lines (sine waves) that were perfectly offset from each other.
• It was as if they had taken a single wave and split it into three copies, each shifted by exactly one-third of a cycle. This perfectly matched the math for how these specific "1/3 charge" ghosts should behave.

Why Does This Matter?

This is a huge deal for two reasons:

1. It's a New Way to Look: Instead of waiting for a rare, sudden jump in a signal, they watched the signal "breathe" and fluctuate naturally. This made the evidence much clearer and harder to argue with.
2. The Future of Computers: These "ghosts" (Anyons) are the building blocks for a new type of computer called a Topological Quantum Computer. These computers are supposed to be unbreakable by errors. To build one, we need to understand how to control these ghosts. This experiment showed us that we can actually see them and count them in real-time.

In short: The scientists built a super-clean, quiet racetrack for electrons. They watched the track "blink" in three distinct patterns, proving that invisible, fractional particles were dancing around inside, swapping places and leaving their unique quantum fingerprints behind. It's a major step toward building the super-computers of the future.

Technical Summary

1. Problem Statement

The search for anyons—quasiparticles with fractional charge and exotic exchange statistics—is a central goal in condensed matter physics, particularly for realizing topological quantum computation. While Fractional Quantum Hall (FQH) states are predicted to host these particles, directly observing their braiding phase (the phase acquired when two anyons are exchanged) has been experimentally challenging.

Previous attempts using Fabry-Pérot (FP) interferometers in GaAs-based systems faced significant hurdles:

• Coulomb Coupling: Strong electrostatic coupling between the bulk and the edge states often masks the braiding phase, leading to "Coulomb-dominated" regimes where interference patterns are difficult to interpret.
• Phase Jump Ambiguity: Traditional methods rely on observing discrete phase jumps in interference signals as localized quasiparticles are added/removed. However, distinguishing these jumps from charging events and Coulomb effects requires complex analysis and is often inconclusive.
• Material Limitations: GaAs devices struggle with electrostatic tunability and screening, making it difficult to isolate the Aharonov-Bohm (AB) interference regime.

2. Methodology

The authors utilized a single-layer graphene FP interferometer encapsulated in hexagonal boron nitride (hBN) with graphite gates. This platform offers superior electrostatic control and screening compared to GaAs.

• Device Architecture:
  • A monolayer graphene channel is sandwiched between hBN and graphite gates.
  • The device features a central cavity defined by top graphite gates and two Quantum Point Contacts (QPCs) that allow backscattering of edge channels.
  • Tunability: The device allows independent control of the bulk filling factor ($\nu$), the QPC transmissions, and the cavity area via multiple gate electrodes (plunger gate $V_{PG}$, split gates, and bridge gates).
• Experimental Conditions:
  • Measurements were performed at ultra-low temperatures ($T \approx 20$ mK) and high magnetic fields ($B = 12$ T).
  • The study focused on two specific filling factors: $\nu = 1/3$ and $\nu = 4/3$, both hosting Abelian anyons with charge $e^* = e/3$.
• Measurement Strategy:
  • Instead of sweeping magnetic fields or gate voltages to induce phase jumps, the authors held the device parameters ($B, V_{PG}$) fixed.
  • They monitored the conductance in real-time to observe Random Telegraph Noise (RTN).
  • The RTN arises from the stochastic fluctuation of the number of localized anyons ($n$) trapped within the interferometer cavity.

3. Key Contributions

1. Direct Observation of Three-State RTN: The authors observed a distinct three-level random telegraph noise in the conductance signal. This corresponds to the three possible interference branches arising from braiding around $n \pmod 3$ anyons.
2. Decoupling from Coulomb Effects: By fixing the device parameters and observing the time-dependent fluctuations, the authors demonstrated that the observed phase shifts are purely due to anyon braiding, effectively bypassing the complications of Coulomb-dominated regimes that plagued previous GaAs experiments.
3. Reconstruction of Braiding Phases: By analyzing the statistical distribution of the RTN levels over time, they reconstructed three interwoven sinusoidal oscillations (Aharonov-Bohm signals) shifted by exactly $2\pi/3$. This provides direct evidence of the exchange statistics for $e/3$ anyons.
4. Characterization of Quasiparticle Dynamics: The study provides a detailed analysis of how the RTN switching rates and amplitudes depend on the filling factor (density) and temperature, offering insights into the localization and trapping of anyons.

4. Key Results

• Three-Branch Interference: In both $\nu = 1/3$ and $\nu = 4/3$ states, the conductance fluctuates between three discrete levels. When the plunger gate ($V_{PG}$) is swept, these levels form three sinusoidal curves separated by a phase of $2\pi/3$. This confirms the braiding phase $\theta_a = 2\pi/3$ for $e/3$ anyons.
• Aharonov-Bohm vs. Coulomb Regime:
  • The interference pattern exhibits a negative slope in the $V_{PG}$ vs. $B$ plane, characteristic of the Aharonov-Bohm regime.
  • The magnetic flux super-periodicity was measured as $\Delta \Phi = 3\Phi_0$ (where $\Phi_0 = h/e$), consistent with the interference of $e/3$ quasiparticles.
  • This confirms that the graphite gates successfully screened long-range Coulomb interactions, a critical requirement for observing braiding signatures.
• RTN Dependence on Filling Factor:
  • The switching rate of the RTN is low in the center of the FQH plateau but increases sharply near the edges.
  • The noise spectral density transitions from $1/f^2$ (single timescale) in the plateau center to $1/f$ (multiple timescales) near the edges, suggesting an increase in the number of localized trapping sites near the plateau boundaries.
• Temperature Scaling:
  • Interference visibility decays exponentially with temperature, with a characteristic energy scale $T_0 \approx 110$ mK.
  • The switching rate saturates at low temperatures ($<100$ mK) and follows a variable-range hopping (VRH) model at higher temperatures, indicating thermally activated hopping of anyons between localized states.

5. Significance

• Validation of Anyon Statistics: This work provides one of the most direct and unambiguous experimental demonstrations of Abelian anyon braiding statistics, resolving long-standing ambiguities regarding Coulomb coupling in interferometers.
• Graphene as a Superior Platform: It establishes graphene-based interferometers as a robust platform for topological physics, offering better electrostatic tunability and screening than traditional GaAs heterostructures.
• Pathway to Non-Abelian Anyons: The ability to observe and control anyon fluctuations via RTN paves the way for investigating non-Abelian anyons (e.g., in even-denominator states like $\nu = 5/2$ or bilayer graphene). The techniques developed here can be extended to detect the more complex interference patterns expected from non-Abelian braiding.
• Topological Quantum Computing: Understanding the dynamics of anyon trapping and fluctuations is a prerequisite for building topological qubits. This study demonstrates the feasibility of dynamically controlling and monitoring anyon numbers, a critical step toward fault-tolerant quantum computation.

In summary, the paper introduces a novel measurement paradigm—utilizing real-time telegraph noise in a highly screened graphene interferometer—to directly visualize the braiding phase of anyons, overcoming previous experimental limitations and opening new avenues for topological quantum research.