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arxiv: 2605.02642 · v1 · submitted 2026-05-04 · ❄️ cond-mat.mes-hall

Floquet-Multiple Andreev Reflections

R\'egis M\'elin , Romain Danneau , Morteza Kayyalha This is my paper

Pith reviewed 2026-05-08 18:34 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords Floquet theoryMultiple Andreev reflectionsJosephson junctionsmultiterminal devicesquantum transportsuperconductivityballistic conductorsnoise spectroscopy
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0 comments X

The pith

Voltage-biased three-terminal Josephson junctions generate Floquet-multiple Andreev reflection resonances through multipair processes.

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

This paper shows that the Josephson relation in voltage-biased multiterminal Josephson junctions causes superconducting phase differences to evolve periodically in time, supplying an intrinsic Floquet drive. In three-terminal devices formed on a ballistic two-dimensional normal conductor, quartet and higher-order multipair tunneling processes then produce distinct resonances in finite-bias conductance and noise, with positions set by the bias voltage and electrochemical potential. A sympathetic reader would care because the setup realizes Floquet physics using only DC voltages, without external periodic driving, and supplies a microscopic route to probe these effects in controllable superconducting systems.

Core claim

In voltage-biased multiterminal Josephson junctions formed on a ballistic two-dimensional normal conductor, the quartet and higher-order multipair processes yield characteristic Floquet-multiple Andreev reflection (Floquet-MAR) finite-bias conductance and noise resonances that are parameterized by the bias voltage and electrochemical potential.

What carries the argument

The intrinsic Floquet drive generated by the time-periodic superconducting phase evolution under the Josephson relation, which couples to multipair processes to produce Floquet-MAR resonances.

If this is right

  • Resonances in conductance and noise occur at bias voltages fixed by the electrochemical potential through the multipair processes.
  • Higher-order multipair contributions become visible as additional resonance features beyond simple Andreev reflections.
  • The resonances remain observable provided the normal region stays ballistic with a dense set of states.
  • Three-terminal geometries allow independent control of bias and potential to map the resonance positions.

Where Pith is reading between the lines

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

  • The same intrinsic drive mechanism could appear in other multiterminal superconducting structures even if the normal region is not strictly two-dimensional.
  • Tuning the electrochemical potential offers a direct experimental knob to shift resonance locations without changing the physical device.
  • Noise measurements at the predicted resonance points would provide an independent signature of the multipair origin separate from conductance data.

Load-bearing premise

The normal conductor is ballistic with a continuum of electronic states and the Josephson relation supplies an intrinsic Floquet drive without significant decoherence or disorder.

What would settle it

Measure differential conductance and noise versus bias voltage in a fabricated three-terminal ballistic Josephson junction and check whether resonances appear or fail to appear at the specific voltage and potential values predicted by the multipair Floquet-MAR conditions.

Figures

Figures reproduced from arXiv: 2605.02642 by Morteza Kayyalha, R\'egis M\'elin, Romain Danneau.

Figure 2
Figure 2. Figure 2: FIG. 2 view at source ↗
Figure 1
Figure 1. Figure 1: FIG. 1 view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 view at source ↗
Figure 1
Figure 1. Figure 1: FIG. 1. The view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The figure shows the emergence of an anomaly at view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The figure shows the absence of an anomaly at view at source ↗
read the original abstract

Floquet theory describes quantum systems governed by time-periodic Hamiltonians, much as Bloch theory describes spatially periodic solids. In voltage-biased multiterminal Josephson junctions, the Josephson relation causes superconducting phase differences to evolve periodically in time, thereby providing an intrinsic Floquet drive. In this Letter, we consider three-terminal Josephson junctions formed on a ballistic two-dimensional normal conductor with a continuum of electronic states. We show that the quartet and higher-order multipair processes yield characteristic Floquet-multiple Andreev reflection (Floquet-MAR) finite-bias conductance and noise resonances that are parameterized by the bias voltage and electrochemical potential. This microscopic picture opens a route toward implementing and probing Floquet-MAR physics in ballistic multiterminal Josephson junctions.

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 paper claims that voltage-biased three-terminal Josephson junctions on a ballistic 2D normal conductor with a continuum of states exhibit Floquet-multiple Andreev reflection (Floquet-MAR) resonances in finite-bias conductance and noise. These arise from quartet and higher-order multipair processes and are parameterized solely by bias voltage and electrochemical potential, with the time-periodic Josephson phase providing an intrinsic Floquet drive.

Significance. If the microscopic derivation holds, the result supplies a concrete route to realizing and detecting Floquet physics in multiterminal superconducting hybrids, potentially enabling new probes of time-periodic transport without external drives. The emphasis on ballistic continuum states and explicit parameterization by bias and potential distinguishes it from prior MAR literature.

major comments (2)
  1. [Abstract / setup description] The load-bearing assumption that the normal conductor is ballistic with a true continuum of states (allowing clean Floquet drive without mixing of MAR channels) is stated in the abstract but receives no quantitative backing. No estimate is given for the required coherence length, mean-free-path threshold, or disorder tolerance that would preserve the predicted distinct finite-bias resonances.
  2. [Theoretical framework / results section] The central claim that quartet and higher-order processes produce characteristic Floquet-MAR conductance and noise resonances parameterized only by bias voltage and electrochemical potential is asserted without visible derivation. The manuscript must supply the explicit scattering-matrix or Hamiltonian treatment (including how the time-periodic phase enters the Floquet modes) to confirm that the resonances follow directly rather than from unstated approximations.
minor comments (2)
  1. [Abstract] Notation for the electrochemical potential and bias voltage should be defined once at first use and used consistently; the abstract introduces them without symbols.
  2. [Figures] If figures of conductance or noise spectra are present, they should include explicit labels for the predicted resonance positions in terms of the bias and potential parameters.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and for highlighting the potential significance of Floquet-MAR physics in multiterminal Josephson junctions. We address each major comment below.

read point-by-point responses

  1. Referee: [Abstract / setup description] The load-bearing assumption that the normal conductor is ballistic with a true continuum of states (allowing clean Floquet drive without mixing of MAR channels) is stated in the abstract but receives no quantitative backing. No estimate is given for the required coherence length, mean-free-path threshold, or disorder tolerance that would preserve the predicted distinct finite-bias resonances.

    Authors: We agree that the manuscript would benefit from quantitative estimates to support the ballistic continuum assumption. The continuum of states is invoked to ensure that MAR channels remain unmixed by disorder, allowing the intrinsic time-periodic Josephson phase to act as a clean Floquet drive. In the revised version we will add a brief estimate in the setup section: the mean-free path must satisfy l_mfp ≫ L (where L is the junction size) and the disorder scattering rate must be much smaller than the bias energy scale eV, consistent with standard mesoscopic criteria for preserving sharp resonances. This does not change the central results but clarifies the regime of validity. revision: yes

  2. Referee: [Theoretical framework / results section] The central claim that quartet and higher-order processes produce characteristic Floquet-MAR conductance and noise resonances parameterized only by bias voltage and electrochemical potential is asserted without visible derivation. The manuscript must supply the explicit scattering-matrix or Hamiltonian treatment (including how the time-periodic phase enters the Floquet modes) to confirm that the resonances follow directly rather than from unstated approximations.

    Authors: The derivation in the manuscript employs the scattering-matrix formalism for the three-terminal ballistic junction. The time-periodic phases enter via the Josephson relation as a Floquet drive, with quartet and higher-order multipair processes appearing as specific higher-order terms in the expansion that produce resonances when the bias voltage and electrochemical potential satisfy commensurability conditions with the drive frequency. We acknowledge that the key steps of the Floquet-mode construction could be presented more explicitly. In the revision we will expand the theoretical framework section (or add a supplementary note) to include the essential elements of the time-periodic scattering matrix and the resulting conductance expression, making the direct origin of the parameterization by bias and potential transparent. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation is self-contained theoretical analysis from Floquet theory and stated junction assumptions

full rationale

The paper derives Floquet-MAR resonances by applying standard Floquet theory to the time-periodic phase evolution from the Josephson relation in a three-terminal ballistic 2D junction with a continuum of states. The central claims about quartet and higher-order multipair processes producing parameterized conductance and noise resonances follow directly from these inputs and the microscopic picture of multiple Andreev reflections, without any reduction to self-definition, fitted parameters renamed as predictions, or load-bearing self-citations. The ballistic continuum assumption is presented explicitly as a modeling choice rather than derived from the result itself. No equations or steps in the provided derivation chain loop back to the target claims by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The abstract invokes standard Floquet and Josephson physics plus the assumption of a ballistic continuum; no free parameters or new entities are explicitly introduced in the provided text.

axioms (2)
  • domain assumption Josephson relation causes superconducting phase differences to evolve periodically in time
    Stated in the abstract as the source of the intrinsic Floquet drive.
  • domain assumption Ballistic two-dimensional normal conductor with continuum of electronic states
    Required for the microscopic picture of multipair processes.

pith-pipeline@v0.9.0 · 5424 in / 1321 out tokens · 21937 ms · 2026-05-08T18:34:24.748718+00:00 · methodology

discussion (0)

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Reference graph

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    Snake diagram orbits for the Q-quartets In this subsubsection of the SM, we evaluate theδ ˆKR,(Σ),1,1 α,α quartet snake diagram orbits: δ ˆKR,(Σ),1,1 α,α (ω,ω) = ˆΣ1,1 α,a (ω,ω+eV)ˆg R,1,2 a,a (ω+eV,ω+eV) ˆΣ2,2 a,α (ω+eV,ω+2eV)ˆg R,2,2 α,γ (ω+2eV,ω+2eV)×(36) ˆΣ2,2 γ,c (ω+2eV,ω+2eV)ˆg R,2,1 c,c (ω+2eV,ω+2eV) ˆΣ1,1 c,γ (ω+2eV,ω+2eV)ˆg R,1,1 γ,β (ω+2eV,ω+2eV...

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    Calculation of the Q-quartet current susceptibility withµ N ̸=0and V̸=0 In this subsubsection of the SM, we evaluate theQ-quartet current susceptibility, which demonstrates Eq. (3) in the main text. We obtain the following expression for the quartet current: I(Q)(ω) = (ΣL)2(ΣR)2(ΣB)4 2W8(kF Rα,γ )(kF Rγ,β ) ×cosΨ Q ×(42) [nF (ω−µ N)−n F (ω+µ N) +n F (ω+2e...

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  60. [60]

    Performing the integral over energy In this subsubsection of the SM, we proceed further by integrating Eq. (48) over the energyω, which leads to the following expression for the corresponding contribution to the current susceptibilityI (A) Q = R I (A) Q (ω)dω: ∂I (A) Q ∂ µN = (ΣL)2 (ΣR)2 (ΣB)4 W 8 × 1 (kF Rα,γ )(kF Rγ,β ) exp[i(2ϕ B −ϕ L −ϕ R)]×(49) cos (...

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  61. [61]

    The expression forI (B) Q (ω) = n ˆΣa,α ˆG2,2 α,a o+,− is deduced fromI (A) Q (ω)in Eq

    Taking into account the other component of the spectral supercurrent In this subsubsection of the SM, we present the final step in the evaluation of the quartet current susceptibility. The expression forI (B) Q (ω) = n ˆΣa,α ˆG2,2 α,a o+,− is deduced fromI (A) Q (ω)in Eq. (45) by exchanging the electron and the hole Nambu labels. 9 As a result, the superc...

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  62. [62]

    Expression for one of the components of the O-octet spectral supercurrent In this subsubsection of the SM, we present the expression of theO-octet spectral supercurrent. Similarly to the above calculations, we expandI (A) O (ω) = n ˆΣa,α ˆG1,1 α,a o+,− according to I (A) O (ω) = n ˆΣ1,1 a,α (ω,ω−eV)ˆg 1,1 α,ε (ω−eV,ω−eV) ˆΣ1,1 ε,e (ω−eV,ω−eV)ˆg 1,2 e,e (ω...

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  63. [63]

    Specifically, integrating Eq

    Performing the integral over energy In this subsubsection of the SM, we proceed further by evaluating the energy-integral of theO-octet spectral supercurrent. Specifically, integrating Eq. (53) over the energyωleads to ∂I (A) O ∂ µN = Z ∂I (A) O (ω) ∂ µN dω= (ΣL)4 (ΣR)4 (ΣB)8 8W16 ×exp(−iΨ O)×(54) 1 (kF Rα,ε )(kF Rβ,ε )(kF Rβ,δ )(kF Rα,γ ) ×[A 1 +A 2 +A 3...

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  64. [64]

    Final expression for thecosΨ O-component of the O-octet supercurrent In this subsubsection of the SM, we conclude the calculation of theO-octet supercurrent. Taking all components of the supercurrent into account leads to the following final form of the partial derivative of theO-octet supercurrent with respect to the electrochemical potentialµ N: ∂I O ∂ ...

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  65. [65]

    Expression for one of the components of the Q ′-quartet spectral supercurrent In this subsubsection of the SM, we present the first steps in the calculation of theQ′-quartet supercurrent. Similarly as above, we find the following expression forI (A) Q′ (ω) = n ˆΣa,α ˆG1,1 α,a o+,− : I (A) Q′ (ω) = n ˆΣ1,1 α,a (ω,ω+eV)ˆg 1,2 a,a(ω+eV,ω+eV) ˆΣ2,2 a,α (ω+eV,...

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  66. [66]

    Performing the integral over energy In this subsubsection of the SM, we present the result of integrating theQ ′-quartet supercurrent over the energyω. Similarly as above, we find the following forI Q′ = R IQ′(ω)dω: ∂I Q′ ∂ µN = (ΣL)4 (ΣR)4 (ΣB)8 8W16 ×exp(−iΨ Q)× 1 (kF Rα,δ )(kF Rδ,ε )(kF Rβ,ε )(kF Rγ,β ) ×(62) [B1 +B 2 +B 3 +B 4 +B 5 +B 6 +B 7 +B 8], wh...

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  67. [67]

    1” and the “2

    Final expression for thecosΨ Q-component of the Q ′-quartet supercurrent In this subsubsection of the SM, we conclude the calculation of theQ ′-quartet supercurrent. The derivative of theQ ′-quartet supercurrent with respect to the electrochemical potentialµ N is the following: ∂I Q′ ∂ µN = (ΣL)4 (ΣR)4 (ΣB)8 2W16 ×cos(Ψ Q)× 1 (kF Rα,δ )(kF Rδ,ε )(kF Rβ,ε ...

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