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arxiv: 2308.03089 · v1 · pith:E36NSNKHnew · submitted 2023-08-06 · ❄️ cond-mat.mes-hall · cond-mat.str-el

Quasiparticle Andreev reflection in the Laughlin fractions of the fractional quantum Hall effect

K. Iyer , T. Martin , J. Rech , T. Jonckheere This is my paper

Pith reviewed 2026-05-24 08:09 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.str-el
keywords fractional quantum Hall effectAndreev reflectionquantum point contactscurrent correlationsLaughlin fractionsquasiparticle tunnelingKeldysh formalism
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The pith

The ratio between auto- and cross-correlations of output currents directly manifests quasiparticle Andreev reflection in Laughlin fractional quantum Hall states.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines a double quantum point contact geometry in the fractional quantum Hall effect at Laughlin fractions. Quasiparticles carrying charge e/m that reach the second contact transmit only as full electrons of charge e and reflect holes carrying charge e(1-m)/m. Bosonization combined with Keldysh Green functions yields exact expressions for the current correlations at the outputs, both at zero and finite temperature. The resulting ratio of auto-correlations to cross-correlations serves as the measurable signature of the Andreev process. The temperature dependence of this ratio is extracted and compared with existing experiments.

Core claim

In the two-quantum-point-contact geometry for Laughlin fractions, the Andreev reflection at the second contact produces a fixed ratio between the auto- and cross-correlations of the output currents; this ratio is independent of microscopic details once the fractional charge and the reflection rule are fixed, and it persists at finite temperature according to the Keldysh calculation.

What carries the argument

The ratio of auto- to cross-correlations of the output currents, obtained from the bosonization formalism and out-of-equilibrium Keldysh Green functions.

If this is right

  • The measured ratio directly confirms the occurrence of quasiparticle Andreev reflection and the associated hole charge e(1-m)/m.
  • Temperature dependence of the ratio follows from the same calculation and can be checked against data.
  • The result supplies a concrete diagnostic for the charge of the quasiparticles participating in the tunneling.
  • The same correlation ratio can be used to test the validity of the tunneling model at the quantum point contacts.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same correlation ratio might serve as a diagnostic in related anyonic tunneling experiments that involve different fractional charges.
  • If the ratio remains robust under small changes in bias or temperature, it could be used to calibrate the effective charge in more complex multi-contact geometries.

Load-bearing premise

The bosonization formalism and Keldysh Green function techniques accurately capture the quasiparticle tunneling and reflection processes at the quantum point contacts for Laughlin fractions at the temperatures and biases considered.

What would settle it

An experiment that measures a temperature-independent ratio of auto- to cross-correlations that differs from the value predicted by the Andreev reflection charge rule would falsify the central claim.

Figures

Figures reproduced from arXiv: 2308.03089 by J. Rech, K. Iyer, T. Jonckheere, T. Martin.

Figure 1
Figure 1. Figure 1: The first QPC is tuned to be transparent, and as [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 1
Figure 1. Figure 1: ν = 1/3 fractional quantum Hall bar endowed with two QPCs. QP CL is placed in the weak-backscattering regime, emitting a dilute beam of e/3 quasiparticles on the edge 2. These impinge on QP CR which is placed in the strong-backscattering regime, transmitting only electrons. The arrival of a e/3 quasiparticle on QP CR triggers the emis￾sion of an electron on edge 3, and charge conservation implies that ther… view at source ↗
Figure 2
Figure 2. Figure 2: Auto-correlation noise S exc 33 (full lines) and cross￾correlation noise S23 (dashed lines) plotted as a function of the tunneling current ⟨I3⟩, for different values of the temperature kBθ = 0 (gray), 0.1 (red), 0.5 (green), 1 (blue) (arbitrary energy units), with eV varying from -32 to +32 in the same units. The zero-temperature case (gray lines) correspond to Eqs (28), (32) and (37), while the finite tem… view at source ↗
Figure 3
Figure 3. Figure 3: Ratio of cross-correlations to auto-correlations as a [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
read the original abstract

Andreev reflection occurs in a normal metal-superconductor junction, when an electron on the normal side can only be transmitted as a Cooper pair in the superconductor, with the reflection of a hole on the normal side. A similar phenomenon can occur in strongly correlated systems, in particular in the fractional quantum Hall effect (FQHE), as the system quasiparticles have a charge $e/m$ different from the electron charge. We study theoretically a setup involving two quantum point contacts (QPC) in the FQHE where Andreev reflection occurs, as charges $e/m$ impinging on the second QPC can only be transmitted as charges $e$, with the reflection of holes of charge $e (1-m)/m $. Using the bosonization formalism, and out-of-equilibrium Keldysh Green function techniques, we provide a full analytical calculation of the current correlations at the outputs of the QPC, both at zero and finite temperature. The ratio between the auto- and cross-correlations of the output currents is a direct manifestation of Andreev reflection. Our results agree with recent experimental observations, and give precious information on the temperature dependence of this ratio.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript studies quasiparticle Andreev reflection in Laughlin FQHE states via a two-QPC geometry. Using bosonization and out-of-equilibrium Keldysh Green functions, it derives an analytical expression for the ratio of auto- to cross-correlations of the output currents at zero and finite temperature; this ratio is claimed to be a direct signature of Andreev reflection (with transmitted charge e and reflected hole charge e(1-m)/m) and is stated to match recent experiments while providing the temperature dependence.

Significance. If the central derivation holds, the work supplies a parameter-free analytical prediction for a measurable correlation ratio in a strongly correlated anyonic system, together with its full temperature dependence. This is a concrete strength: the calculation is performed from the model rather than fitted post hoc, and the explicit finite-T result is potentially useful for experimental analysis of edge-state tunneling.

major comments (2)
  1. [bosonization and Keldysh techniques section] The central claim that the auto/cross-correlation ratio is a direct manifestation of Andreev reflection rests on the leading-order single-quasiparticle tunneling operators at both QPCs producing the ratio without contamination. The Keldysh expansion (described in the bosonization and Keldysh techniques section) does not contain an explicit demonstration or bound showing that higher-order multi-tunneling processes or finite-temperature occupation factors in the edge Green functions remain parametrically small or cancel in the ratio across the full bias/temperature range; this assumption is load-bearing for the claim.
  2. [setup and results sections] The abstract and setup state that the ratio equals a fixed value set by the fractional charges. However, no section provides a concrete check (e.g., an expansion to next order in the tunneling amplitude or a numerical estimate of thermal corrections) that multi-quasiparticle exchanges do not alter the ratio; without this, the identification of the ratio as Andreev-specific is not fully secured.
minor comments (2)
  1. [introduction] Notation for the charge of the reflected hole (e(1-m)/m) should be introduced with an explicit equation number on first use for clarity.
  2. Figure captions for the correlation plots should state the precise bias and temperature values used in the curves to allow direct comparison with the analytic expressions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive evaluation of the work's significance and for the constructive comments on the robustness of the leading-order result. We address each major comment below and outline revisions that will be incorporated.

read point-by-point responses

  1. Referee: [bosonization and Keldysh techniques section] The central claim that the auto/cross-correlation ratio is a direct manifestation of Andreev reflection rests on the leading-order single-quasiparticle tunneling operators at both QPCs producing the ratio without contamination. The Keldysh expansion (described in the bosonization and Keldysh techniques section) does not contain an explicit demonstration or bound showing that higher-order multi-tunneling processes or finite-temperature occupation factors in the edge Green functions remain parametrically small or cancel in the ratio across the full bias/temperature range; this assumption is load-bearing for the claim.

    Authors: We agree that an explicit bound would strengthen the presentation. The calculation is performed in the weak-tunneling regime, where each QPC tunneling amplitude is a small parameter; multi-tunneling processes therefore enter at higher order in this parameter and are parametrically suppressed. Finite-temperature occupation factors are already included through the full Keldysh edge Green functions. In the revised manuscript we will add a scaling argument in the bosonization and Keldysh techniques section that quantifies the suppression of corrections to the ratio, together with the relevant range of bias and temperature where the leading-order result holds. revision: partial

  2. Referee: [setup and results sections] The abstract and setup state that the ratio equals a fixed value set by the fractional charges. However, no section provides a concrete check (e.g., an expansion to next order in the tunneling amplitude or a numerical estimate of thermal corrections) that multi-quasiparticle exchanges do not alter the ratio; without this, the identification of the ratio as Andreev-specific is not fully secured.

    Authors: The fixed value quoted in the abstract is the leading-order result in the weak-tunneling limit. To supply the requested concrete check we will add, in the revised results section, a brief next-order expansion in the tunneling amplitude demonstrating that the ratio remains unchanged at this order. The temperature dependence is already contained in the closed-form integrals; the added expansion will also indicate the size of thermal corrections within the perturbative regime. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper computes the auto/cross-correlation ratio analytically from the bosonized Keldysh expansion applied to the defined two-QPC geometry and tunneling operators. This is a forward derivation from the model rather than a fit, self-definition, or reduction to prior self-citations. No steps reduce by construction to the target ratio or to author-specific uniqueness theorems. The result is presented as a testable prediction matching external data.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The calculation assumes the standard chiral Luttinger liquid description of FQHE edges at Laughlin fractions and the validity of the Keldysh formalism for out-of-equilibrium tunneling; no new free parameters or invented entities are introduced beyond the model geometry.

axioms (2)
  • domain assumption Bosonization accurately describes the edge states and quasiparticle operators at Laughlin fractions.
    Invoked to model the fractional charges and their tunneling at the QPCs.
  • domain assumption Keldysh Green function techniques capture the non-equilibrium current correlations.
    Used for the full analytical calculation at finite temperature.

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