🔬 mesoscale physics

Extracting the anyon charge from shot noise in complex fractional quantum Hall edges

This paper proposes a general framework for extracting the intrinsic anyon charge from shot-noise measurements in complex fractional quantum Hall edges, such as the $\nu=2/3$ state, by deriving a specific combination of auto- and cross-correlations that effectively suppresses confounding contributions from intermode equilibration and heating.

Original authors: Jinhong Park, Christian Sp{\ra}nsl{ätt

Published 2026-10-05

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CC BY 4.0

Original authors: Jinhong Park, Christian Sp{\ra}nsl{ätt

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, super-cold world of quantum physics, electricity does not always flow like a smooth river. Sometimes, it moves in tiny, distinct packets, much like raindrops falling one by one. When these packets of charge are forced to split or scatter, they create a faint, crackling static known as shot noise. Scientists have long used this noise as a listening device to hear the size of the individual charge carriers moving through a material. In the simplest, most orderly quantum states, this listening is straightforward: the noise tells you exactly how much charge is passing through. However, nature is often more complicated than the simplest cases. In certain exotic materials, the edges where electricity flows become crowded with multiple lanes of traffic moving in opposite directions. Here, the lanes interact, heat up, and exchange energy, creating a chaotic background of noise that drowns out the clear signal of the individual charge carriers. For years, this background static made it nearly impossible to measure the true size of the charge particles in these complex environments, leaving a major gap in our understanding of how these quantum materials work.

A team of researchers has now built a new theoretical map to navigate this confusion, specifically focusing on a complex quantum state known as the fractional quantum Hall effect at a specific filling factor. In this state, the edge of the material acts like a two-lane highway: one lane carries electrons downstream, while the other carries fractional charge carriers upstream. As these two lanes travel side by side, they constantly exchange energy and charge, a process called equilibration. This interaction generates its own heat and noise, which mixes with the noise created when the particles are forced to tunnel through a narrow gate, known as a quantum point contact. The researchers realized that previous attempts to measure the charge of the particles had struggled because they could not separate the noise coming from the tunneling gate from the noise generated by the heating lanes. They developed a detailed framework to calculate exactly how voltage and temperature change along these edges and how the resulting noise travels to the measurement points.

The core of their discovery lies in how they analyzed the noise arriving at the two exit points of their experimental setup. They found that the noise generated by the heating of the lanes affects the two exit points in very different ways. When looking at the noise at a single exit point, known as the auto-correlation, the heating contribution is overwhelming and grows larger as the tunneling gate is opened less. This makes it difficult to see the true charge of the particles. However, when they looked at the noise correlation between the two different exit points, known as the cross-correlation, the heating contribution was significantly suppressed. The researchers showed that the heating noise from the lanes cancels out much more effectively in this cross-correlation measurement, leaving a much clearer signal of the tunneling particles.

To solve the problem completely, the team proposed a specific mathematical recipe that combines the measurements from both the single exit and the two exits. By adding the auto-correlation and the cross-correlation together in a precise way, they demonstrated that the dominant heating noise from the outer lanes could be mathematically removed. This new method, which they call a "clean" measurement, allows scientists to isolate the intrinsic noise of the tunneling particles with high precision, even when the tunneling gate is not perfectly closed. Their calculations show that this approach recovers the true charge of the particles much more reliably than previous methods, which often resulted in incorrect values due to the hidden heating effects.

The researchers applied their framework to the specific case of a state where the charge carriers are expected to have a charge of one-third of an electron. They found that without their new method, the measured charge would appear to be larger than it actually is because of the heating noise. By using their combined correlation technique, the measured value converges to the correct one-third fraction. This work does not just fix a measurement for one specific state; it provides a general guide for how to interpret noisy signals in any complex quantum edge where multiple lanes of traffic interact. It offers a systematic way to distinguish between the noise of the journey and the noise of the destination, ensuring that the fundamental properties of these exotic particles can finally be read clearly, even in the presence of significant thermal interference.

Technical Summary: Extracting Anyon Charge from Shot Noise in Complex Fractional Quantum Hall Edges

Problem Statement
Shot-noise measurements using a quantum point contact (QPC) have historically provided direct evidence for fractional quasiparticle charges in Laughlin fractional quantum Hall (FQH) states. However, interpreting these measurements becomes significantly more complex in multichannel FQH edges, such as the hole-conjugate $\nu = 2/3$ state. In these systems, edge modes are counterpropagating, leading to intermode equilibration. Consequently, the measured noise at the drain contacts is a superposition of two distinct sources: the intrinsic partition noise generated by quasiparticle tunneling at the QPC, and noise generated by intermode equilibration and Joule heating along the edge arms. Previous studies have observed anomalous effective charges and finite noise on conductance plateaus in these states, but a microscopic framework distinguishing these contributions has been lacking. Specifically, while recent experiments compared auto- and cross-correlations, the heating contribution was often treated phenomenologically, leaving the mechanism by which equilibration-induced noise enters measured correlations unsettled.

Methodology
The authors develop a general theoretical framework to address this issue, using the $\nu = 2/3$ FQH edge as a paradigmatic example of a complex multichannel edge. The model consists of two primary components:

Equilibrating Line Junction: A single edge segment containing a downstream integer $\nu=1$ channel and an upstream fractional $\nu=1/3$ channel. The authors model charge and thermal equilibration using a discrete network of cells that transitions to a continuum limit. They derive coupled differential equations for the spatial profiles of local voltages ( $V_1, V_3$ ) and temperatures ( $T_1, T_3$ ), accounting for distinct charge ( $\ell_{ch}$ ) and thermal ( $\ell_{th}$ ) equilibration lengths. The model assumes strong charge equilibration ( $\ell_{ch} \ll L$ ) while allowing for general thermal equilibration regimes.
Four-Terminal QPC Geometry: The authors construct a four-terminal setup where four such edge segments (Upper-Left, Upper-Right, Down-Left, Down-Right) are connected by a single QPC. The QPC is treated as a scattering element where the integer channel passes through unchanged, while the fractional channel is partially transmitted with probability $\mathcal{T}$ .

The framework calculates the low-frequency current fluctuations by solving for voltage and temperature profiles under specific boundary conditions (bias voltage $V_0$ applied to the Upper-Left contact, Down-Right grounded, and floating conditions at the drains). The authors explicitly separate the noise sources into:

Intrinsic Arm Noise: Generated by equilibration links along the arms, characterized by "noise-generating spots" near the contacts.
QPC Partition Noise: Generated by the tunneling process at the QPC.
Equilibrium Noise: Johnson-Nyquist noise injected from the reservoirs.

Key Contributions and Results
The paper derives analytical expressions for the drain auto-correlations ( $S_{UR,UR}, S_{DL,DL}$ ) and cross-correlations ( $S_{UR,DL}$ ) in the four-terminal geometry. The central findings are:

Parametric Difference in Heating Effects: The authors demonstrate that equilibration-induced heating affects auto- and cross-correlations in parametrically different ways. In the strong charge-equilibration and weak-transmission regime ( $\mathcal{T} \ll 1$ ):
- The auto-correlation contains a heating contribution proportional to the temperature rise at the "outer-arm" noise-generating spots. This contribution scales as $\mathcal{T}^{-1/2}$ , meaning the heating effect grows as transmission decreases, potentially dominating the intrinsic signal.
- The cross-correlation contains a heating contribution from the same outer-arm spots that is suppressed by an additional factor of $\mathcal{T}$ , scaling as $\mathcal{T}^{1/2}$ . Consequently, the cross-correlation is significantly less sensitive to edge heating than the auto-correlation.
Renormalization of QPC Transmission: Due to the chirality of the edge and the feedback loop created by equilibration, the effective transmission probability of the QPC is renormalized from the bare transmission $\mathcal{T}$ to an effective transmission $\mathcal{T}_{eff} \approx \mathcal{T}/(1+\mathcal{T})$ . This self-consistent determination of the local voltage drop across the QPC is crucial for accurate noise calculation.
The "Clean" Fano Factor ( $F_{clean}$ ): Recognizing that even the cross-correlation retains a finite heating correction at non-zero transmission, the authors propose a specific linear combination of the measured excess auto- and cross-correlations. By noting that $\Delta S_{auto} + \Delta S_{cross}$ isolates the excess noise from the outer-arm heating spots, they construct a new Fano factor:
$F_{clean} \equiv \frac{-\Delta S_{cross} + \mathcal{T}_{eff}(2-\mathcal{T}_{eff})(\Delta S_{auto} + \Delta S_{cross})/2}{2e|I_T|(1-\mathcal{T}_{eff})^2}$
This quantity exactly cancels the dominant outer-arm heating contribution. The remaining heating correction in $F_{clean}$ scales as $\mathcal{T}^{3/2}$ , which vanishes much faster than the corrections in standard auto- or cross-correlation Fano factors as $\mathcal{T} \to 0$ .
Extraction of Anyon Charge: The authors show that $F_{clean}$ allows for a more reliable extraction of the tunneling quasiparticle charge $e^*$ (where $F \approx e^*/e$ ) in the presence of upstream modes and edge heating. Numerical results confirm that $F_{clean}$ remains close to the ideal value $e^*/e$ over a wider range of bias voltages and transmissions compared to $F_{auto}$ and $F_{cross}$ .

Significance and Claims
The paper claims to provide a systematic framework for interpreting shot-noise measurements in complex FQH edges where intermode equilibration and heating are non-negligible. By distinguishing between noise generated at the QPC and noise generated by edge equilibration, the authors resolve the ambiguity in extracting quasiparticle charges from multichannel edges.

The significance of the work lies in:

Microscopic Understanding: It moves beyond phenomenological descriptions of heating (e.g., single effective temperatures) by explicitly modeling the spatial dependence of voltage and temperature profiles and their specific contributions to different noise correlations.
Experimental Utility: It offers a concrete, experimentally accessible protocol (the $F_{clean}$ factor) to isolate the intrinsic quasiparticle charge from the confounding effects of edge heating, which is critical for characterizing complex states like the $\nu = 2/3$ edge and potentially non-Abelian states like $\nu = 5/2$ .
Generalizability: The authors state that the framework is not restricted to $\nu = 2/3$ but can be extended to more general counterpropagating edge structures, including those with multiple modes and non-Abelian candidates, by grouping co-propagating modes into effective sectors and applying the same decomposition of noise sources.

Technical Summary: Extracting Anyon Charge from Shot Noise in Complex Fractional Quantum Hall Edges

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