pith. sign in

arxiv: 2604.16647 · v1 · submitted 2026-04-17 · ❄️ cond-mat.mes-hall · cond-mat.str-el· cond-mat.supr-con

Nonequilibrium Cooper quartet generation in superconducting devices

Luca Chirolli , Alessandro Braggio , Michele Governale This is my paper

Pith reviewed 2026-05-10 07:14 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.str-elcond-mat.supr-con
keywords Cooper quartetsdouble quantum dotsAndreev currentnonequilibrium transportquartet correlationscurrent noisesuperconducting devices
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The pith

High bias voltage creates a resonance between the vacuum and a four-electron state that generates Cooper quartet correlations.

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

The paper proposes a method to isolate Cooper quartets by driving a double-quantum-dot system out of equilibrium using high bias voltage. This produces a resonance between the empty state and a four-electron state that involves coherent exchange of two Cooper pairs and carries finite quartet correlations. The resulting Andreev current develops a peak whose width scales directly with the strength of the quartet coupling, which the authors show can be tuned by the phase of additional superconducting leads. Current noise measurements reveal equal auto- and cross-correlations, interpreted as evidence of fast coherent oscillations between the dots and leads. A sympathetic reader would care because the setup supplies a concrete, experimentally accessible route to generate and detect four-electron correlated states in solid-state devices.

Core claim

By driving the system out of equilibrium in the high bias voltage regime, a resonance between the vacuum |0⟩ and the four-electron state |4e⟩ emerges, which involves a two-Cooper pair exchange process and is characterized by finite quartet correlations. The transport properties exhibit a peak in the Andreev current at high bias whose width scales with the magnitude of the quartet coupling Γ_4e. This coupling can be tuned by the phase of additional superconducting leads while preserving the transport regime. The current-current correlations and Fano factor establish a regime of equal auto- and cross-correlations that signals fast coherent two-Cooper-pair oscillations.

What carries the argument

The quartet coupling Γ_4e between vacuum and four-electron states, which mediates coherent two-Cooper-pair exchange and is independently tunable by the phase of additional superconducting leads to isolate the resonance in high-bias transport.

If this is right

  • The Andreev current shows a peak at high bias whose width scales directly with the quartet coupling strength.
  • Current-current correlations become equal between auto- and cross-terms under fast coherent two-pair oscillations.
  • Phase tuning of additional leads controls the quartet coupling without exiting the high-bias transport regime.

Where Pith is reading between the lines

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

  • The same nonequilibrium drive could be adapted to generate and detect higher-order multifermion states beyond quartets.
  • Observation of the predicted noise signatures would supply a new experimental handle on correlated electron aggregates in mesoscopic systems.
  • The platform could be extended to study how quartet states interact with external fields or additional degrees of freedom.

Load-bearing premise

The high-bias regime must isolate the quartet resonance without dominant contributions from other processes, while allowing the quartet coupling to be tuned independently by lead phases.

What would settle it

If the width of the high-bias Andreev current peak does not scale with the phase-tunable Γ_4e, or if auto- and cross-correlations remain unequal in that regime, the isolated quartet resonance would not be present.

Figures

Figures reproduced from arXiv: 2604.16647 by Alessandro Braggio, Luca Chirolli, Michele Governale.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Schematics of the system constituted by two quantum dots coupled to a common superconducting lead, [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Simple schematics, at the resonance condition [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Quartet correlator [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Andreev current [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Fano factor [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (a) Schematics of the state [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Josephson currents [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
read the original abstract

Cooper quartets are aggregates of four electrons that generalize the concept of Cooper pairs, and their study can unfold unexplored perspectives in correlated matter and many-body physics. We propose a method to isolate them in a double-quantum-dot system coupled to conventional superconducting and normal leads. By driving the system out of equilibrium, we show that a resonance between the vacuum $|0\rangle$ and the four-electron state $|4e\rangle$ emerges in the high bias voltage regime, which involves a two-Cooper pair exchange process and is characterized by finite quartet correlations. We study the transport properties of the system and show that a peak in the Andreev current at high bias voltage has a width that scales with the magnitude of the quartet coupling $\Gamma_{4e}$, which can be tuned by the phase of additional superconducting leads, yielding distinctive signatures. By further studying the current-current correlations and the Fano factor, we establish a regime characterized by equal auto- and cross-correlations, which we interpret as a definitive signature of fast coherent two-Cooper-pair oscillations between the dots and the superconducting leads. The proposed platform, experimentally accessible in a quantum solid-state laboratory, enables exploration of quartet correlations and multifermion-correlated states of matter.

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 proposes isolating Cooper quartets in a double-quantum-dot system coupled to superconducting and normal leads. By driving the system out of equilibrium at high bias, it claims a resonance emerges between the vacuum |0⟩ and four-electron |4e⟩ state via two-Cooper-pair exchange, producing a tunable Andreev current peak whose width scales with quartet coupling Γ_4e (controlled by additional lead phases) and equal auto-/cross-current correlations plus Fano factor signatures of coherent oscillations.

Significance. If the central claims hold, the work provides an experimentally accessible platform for studying higher-order multifermion correlations in mesoscopic superconductors, extending beyond conventional Cooper-pair physics with potential implications for correlated matter. The nonequilibrium driving and phase-tunability approach is a notable strength for controllability.

major comments (2)
  1. [Transport properties section (results on current peak and correlations)] The claim that high bias isolates the |0⟩–|4e⟩ resonance (abstract and transport results) requires that two-Cooper-pair exchange dominates over single-pair tunneling, quasiparticles, and higher-order processes, yet no rate comparison or master-equation solutions with/without those channels are shown to confirm subdominance across the relevant bias window.
  2. [Model and Hamiltonian section (definition of Γ_4e and lead couplings)] The quartet coupling Γ_4e is treated as independently tunable via lead phases while maintaining the described transport regime, but the manuscript does not provide an explicit check (e.g., full parameter scan or comparison of effective rates) that this tuning preserves isolation of the resonance without contamination.
minor comments (2)
  1. [Model section] Clarify the explicit many-body construction of the |4e⟩ state in terms of dot and lead occupations to avoid ambiguity with standard Andreev bound states.
  2. [Figures] In figures showing current vs. bias, label the high-bias regime explicitly and include scaling of peak width with Γ_4e for direct comparison to the claimed behavior.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive report and the positive assessment of the potential significance of our work on nonequilibrium Cooper quartet generation. We address the two major comments point by point below, indicating where revisions will be made to strengthen the manuscript.

read point-by-point responses

  1. Referee: The claim that high bias isolates the |0⟩–|4e⟩ resonance (abstract and transport results) requires that two-Cooper-pair exchange dominates over single-pair tunneling, quasiparticles, and higher-order processes, yet no rate comparison or master-equation solutions with/without those channels are shown to confirm subdominance across the relevant bias window.

    Authors: We agree that an explicit demonstration of the dominance of the two-Cooper-pair channel would strengthen the presentation. In the model, the high-bias condition places the normal-lead chemical potential such that single-pair processes are detuned by the superconducting gap Δ, while quasiparticle contributions are exponentially suppressed. The master equation is solved within the quartet subspace, but to directly address the concern we will add a supplementary analysis comparing the full rate equations to a reduced model excluding single-pair and higher-order terms. This will include numerical checks of the relative rates over the bias window used in the transport results, confirming subdominance. The revised manuscript will incorporate this comparison. revision: yes

  2. Referee: The quartet coupling Γ_4e is treated as independently tunable via lead phases while maintaining the described transport regime, but the manuscript does not provide an explicit check (e.g., full parameter scan or comparison of effective rates) that this tuning preserves isolation of the resonance without contamination.

    Authors: We acknowledge that an explicit verification of the robustness under phase tuning would be valuable. The phase dependence enters through the superconducting-lead couplings in the effective Hamiltonian, allowing Γ_4e to be varied while the high-bias resonance condition is preserved by the detuning from single-pair channels. To provide the requested check, we will add a parameter scan in the revised manuscript (or supplementary material) showing the effective rates and resonance width as functions of the additional lead phases. This will demonstrate that the |0⟩–|4e⟩ isolation remains intact without significant contamination from competing processes across the tunable range. revision: yes

Circularity Check

0 steps flagged

No significant circularity; model assumptions and transport calculations are independent of target observables

full rationale

The paper constructs a driven double-quantum-dot Hamiltonian, applies a high-bias master-equation treatment, and computes Andreev current, Fano factor, and current correlations as functions of the externally tunable quartet coupling Γ_4e and lead phases. These quantities are obtained by direct solution of the rate equations under stated assumptions (high-bias isolation of |0⟩–|4e⟩ subspace, phase control of Γ_4e). No parameter is fitted to the resonance signature itself, no prediction is renamed as an input, and no self-citation supplies a uniqueness theorem or ansatz that closes the derivation. The central claims therefore remain falsifiable against independent measurements of the same transport observables.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The central claim rests on standard models of superconducting leads and quantum-dot tunneling together with the assumption that a tunable quartet coupling term can be introduced without additional uncontrolled processes.

free parameters (1)
  • quartet coupling Γ_4e
    Magnitude of the four-electron interaction that sets the width of the current peak; tuned by lead phase but treated as a free parameter in the model.
axioms (1)
  • standard math Standard BCS theory for superconducting leads and sequential tunneling for quantum dots
    Invoked to define the leads and the transport processes in the nonequilibrium regime.
invented entities (1)
  • Cooper quartet state |4e> no independent evidence
    purpose: Four-electron aggregate that generalizes Cooper pairs and participates in the resonance
    Postulated as the target state in the resonance; no independent falsifiable evidence supplied in the abstract.

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Reference graph

Works this paper leans on

132 extracted references · 2 canonical work pages

  1. [1]

    Effective Hamiltonian atϵ=ϵ Q Our goal is to obtain an effective Hamiltonian for the quartet subspace. Here, we provide the procedure for the most general case with the three-superconducting termi- nal configuration and to this end we relabel asϕ i the phase of the superconducting leadS i, withi= 0,1,2. This way, in the Hamiltonian Eq. (4), the LAR-induce...

  2. [2]

    We make use of the expressions Eqs

    Quartet correlator in the reduced model Here, we provide details of the calculation of the quar- tet correlator in the framework of the reduced model. We make use of the expressions Eqs. (B9),(B10) for the states| ¯0⟩and| ¯4e⟩, and the expressions for the eigenstates in the quartet sector|±⟩ 4e =±u 4e,∓|¯0⟩+e −iθ4e u4e,±| ¯4e⟩. We then find 4e⟨±|d1↓d1↑d2↓...

  3. [3]

    The matrixW(χ) can be written in the form W(χ) =W diag + X j W in j e−iχj +W out j eiχj ,(E4) where the matricesW in/out j are purely off-diagonal in the sequential tunneling regime we are considering and the detW= 0 condition is enforced by the matrix diagonal matrixW diag, whose entries are the negative sum of the columns of theW in j andW out j . Intro...

  4. [4]

    Wu, Phys

    C. Wu, Phys. Rev. Lett.95, 266404 (2005)

    2005

  5. [5]

    Lecheminant, E

    P. Lecheminant, E. Boulat, and P. Azaria, Phys. Rev. Lett.95, 240402 (2005)

    2005

  6. [6]

    Capponi, G

    S. Capponi, G. Roux, P. Azaria, E. Boulat, and P. Le- cheminant, Phys. Rev. B75, 100503 (2007)

    2007

  7. [7]

    Capponi, G

    S. Capponi, G. Roux, P. Lecheminant, P. Azaria, E. Boulat, and S. R. White, Phys. Rev. A77, 013624 (2008)

    2008

  8. [8]

    M. O. Soldini, M. H. Fischer, and T. Neupert, Phys. Rev. B109, 214509 (2024)

    2024

  9. [9]

    X. W. Guan, M. T. Batchelor, C. Lee, and J. Y. Lee, Europhysics Letters86, 50003 (2009)

    2009

  10. [10]

    Kuklov, N

    A. Kuklov, N. Prokof’ev, and B. Svistunov, Phys. Rev. Lett.92, 030403 (2004)

    2004

  11. [11]

    Kuklov, N

    A. Kuklov, N. Prokof’ev, and B. Svistunov, Phys. Rev. Lett.92, 050402 (2004)

    2004

  12. [12]

    Dou¸ cot and J

    B. Dou¸ cot and J. Vidal, Phys. Rev. Lett.88, 227005 (2002)

    2002

  13. [13]

    Vidal, R

    J. Vidal, R. Mosseri, and B. Dou¸ cot, Phys. Rev. Lett. 81, 5888 (1998)

    1998

  14. [14]

    Rizzi, V

    M. Rizzi, V. Cataudella, and R. Fazio, Phys. Rev. B 73, 100502 (2006)

    2006

  15. [15]

    Rizzi, V

    M. Rizzi, V. Cataudella, and R. Fazio, Phys. Rev. B 73, 144511 (2006)

    2006

  16. [16]

    Cartwright, G

    C. Cartwright, G. De Chiara, and M. Rizzi, Phys. Rev. B98, 184508 (2018)

    2018

  17. [17]

    T. Chen, C. Huang, I. Velkovsky, T. Ozawa, H. Price, J. P. Covey, and B. Gadway, Nature Physics21, 221 (2025)

    2025

  18. [18]

    Babaev, A

    E. Babaev, A. Sudbø, and N. W. Ashcroft, Nature431, 666 (2004)

    2004

  19. [19]

    Radzihovsky and A

    L. Radzihovsky and A. Vishwanath, Phys. Rev. Lett. 103, 010404 (2009)

    2009

  20. [20]

    E. Berg, E. Fradkin, and S. A. Kivelson, Nature Physics 5, 830 (2009)

    2009

  21. [21]

    Radzihovsky, Phys

    L. Radzihovsky, Phys. Rev. A84, 023611 (2011)

    2011

  22. [22]

    Wu and Y

    Y.-M. Wu and Y. Wang, npj Quantum Materials9, 66 (2024)

    2024

  23. [23]

    R. M. Fernandes and L. Fu, Phys. Rev. Lett.127, 047001 (2021)

    2021

  24. [24]

    S.-K. Jian, Y. Huang, and H. Yao, Phys. Rev. Lett. 127, 227001 (2021)

    2021

  25. [25]

    Y.-B. Liu, J. Zhou, C. Wu, and F. Yang, Nature Com- munications14, 7926 (2023)

    2023

  26. [26]

    Maccari and E

    I. Maccari and E. Babaev, Phys. Rev. B105, 214520 (2022)

    2022

  27. [27]

    Maccari, J

    I. Maccari, J. Carlstr¨ om, and E. Babaev, Phys. Rev. B 107, 064501 (2023)

    2023

  28. [28]

    Babaev, Phys

    E. Babaev, Phys. Rev. Res.6, L032034 (2024)

    2024

  29. [29]

    Grinenko, D

    V. Grinenko, D. Weston, F. Caglieris, C. Wuttke, C. Hess, T. Gottschall, I. Maccari, D. Gorbunov, S. Zherlitsyn, J. Wosnitza, A. Rydh, K. Kihou, C.-H. Lee, R. Sarkar, S. Dengre, J. Garaud, A. Charnukha, R. H¨ uhne, K. Nielsch, B. B¨ uchner, H.-H. Klauss, and E. Babaev, Nature Physics17, 1254 (2021)

    2021

  30. [30]

    G. E. Volovik, JETP Letters119, 330 (2024)

    2024

  31. [31]

    Mizel and D

    A. Mizel and D. A. Lidar, Phys. Rev. Lett.92, 077903 (2004)

    2004

  32. [32]

    X. Peng, J. Zhang, J. Du, and D. Suter, Phys. Rev. Lett.103, 140501 (2009)

    2009

  33. [33]

    H.-N. Dai, B. Yang, A. Reingruber, H. Sun, X.-F. Xu, Y.-A. Chen, Z.-S. Yuan, and J.-W. Pan, Nature Physics 13, 1195 (2017)

    2017

  34. [34]

    Kumar, H

    S. Kumar, H. Zhang, and Y.-P. Huang, Communica- tions Physics3, 108 (2020)

    2020

  35. [35]

    Zhang, H

    K. Zhang, H. Li, P. Zhang, J. Yuan, J. Chen, W. Ren, Z. Wang, C. Song, D.-W. Wang, H. Wang, S. Zhu, G. S. Agarwal, and M. O. Scully, Phys. Rev. Lett.128, 190502 (2022)

    2022

  36. [36]

    Blatter, V

    G. Blatter, V. B. Geshkenbein, and L. B. Ioffe, Phys. Rev. B63, 174511 (2001)

    2001

  37. [37]

    L. B. Ioffe, M. V. Feigel’man, A. Ioselevich, D. Ivanov, M. Troyer, and G. Blatter, Nature415, 503 (2002)

    2002

  38. [38]

    L. B. Ioffe and M. V. Feigel’man, Phys. Rev. B66, 224503 (2002)

    2002

  39. [39]

    Dou¸ cot, M

    B. Dou¸ cot, M. V. Feigel’man, and L. B. Ioffe, Phys. Rev. Lett.90, 107003 (2003)

    2003

  40. [40]

    Dou¸ cot, M

    B. Dou¸ cot, M. V. Feigel’man, L. B. Ioffe, and A. S. Ioselevich, Phys. Rev. B71, 024505 (2005)

    2005

  41. [41]

    Protected qubit based on a superconducting current mirror

    A. Kitaev, (2006), arXiv:cond-mat/0609441

    work page Pith review arXiv 2006

  42. [42]

    Dou¸ cot and L

    B. Dou¸ cot and L. B. Ioffe, Reports on Progress in Physics75, 072001 (2012)

    2012

  43. [43]

    Gladchenko, D

    S. Gladchenko, D. Olaya, E. Dupont-Ferrier, B. Dou¸ cot, L. B. Ioffe, and M. E. Gershenson, Nature Physics5, 48 (2009)

    2009

  44. [44]

    M. T. Bell, J. Paramanandam, L. B. Ioffe, and M. E. Gershenson, Phys. Rev. Lett.112, 167001 (2014)

    2014

  45. [45]

    J. D. Bondar, L. Banszerus, W. Marshall, T. Linde- mann, T. Zhang, M. J. Manfra, C. M. Marcus, and S. Vaitiek˙ enas, (2025), arXiv:2510.07412

    work page arXiv 2025

  46. [46]

    T. W. Larsen, M. E. Gershenson, L. Casparis, A. Kringhøj, N. J. Pearson, R. P. G. McNeil, F. Kuem- meth, P. Krogstrup, K. D. Petersson, and C. M. Mar- cus, Phys. Rev. Lett.125, 056801 (2020)

    2020

  47. [47]

    Messelot, N

    S. Messelot, N. Aparicio, E. de Seze, E. Eyraud, J. Coraux, K. Watanabe, T. Taniguchi, and J. Renard, Phys. Rev. Lett.133, 106001 (2024)

    2024

  48. [48]

    E. G. Arnault, J. Chiles, T. F. Q. Larson, C.-C. Chen, L. Zhao, K. Watanabe, T. Taniguchi, F. m. c. Amet, and G. Finkelstein, Phys. Rev. Lett.134, 067001 (2025)

    2025

  49. [49]

    Leblanc, C

    A. Leblanc, C. Tangchingchai, Z. Sadre Momtaz, E. Kiyooka, J.-M. Hartmann, F. Gustavo, J.-L. Thomassin, B. Brun, V. Schmitt, S. Zihlmann, R. Mau- rand, ´E. Dumur, S. De Franceschi, and F. Lefloch, Na- ture Communications16, 1010 (2025)

    2025

  50. [50]

    Banszerus, W

    L. Banszerus, W. Marshall, C. W. Andersson, T. Linde- mann, M. J. Manfra, C. M. Marcus, and S. Vaitiek˙ enas, Phys. Rev. Lett.133, 186303 (2024)

    2024

  51. [51]

    Ciaccia, R

    C. Ciaccia, R. Haller, A. C. C. Drachmann, T. Lindemann, M. J. Manfra, C. Schrade, and C. Sch¨ onenberger, Communications Physics7, 41 (2024)

    2024

  52. [52]

    Banszerus, C

    L. Banszerus, C. W. Andersson, W. Marshall, T. Linde- mann, M. J. Manfra, C. M. Marcus, and S. Vaitiek˙ enas, Phys. Rev. X15, 011021 (2025)

    2025

  53. [53]

    J. C. Cuevas and H. Pothier, Phys. Rev. B75, 174513 (2007)

    2007

  54. [54]

    Freyn, B

    A. Freyn, B. Dou¸ cot, D. Feinberg, and R. M´ elin, Phys. Rev. Lett.106, 257005 (2011)

    2011

  55. [55]

    Jonckheere, J

    T. Jonckheere, J. Rech, T. Martin, B. Dou¸ cot, D. Fein- berg, and R. M´ elin, Phys. Rev. B87, 214501 (2013)

    2013

  56. [56]

    A. H. Pfeffer, J. E. Duvauchelle, H. Courtois, R. M´ elin, 21 D. Feinberg, and F. Lefloch, Phys. Rev. B90, 075401 (2014)

    2014

  57. [57]

    Cohen, Y

    Y. Cohen, Y. Ronen, J.-H. Kang, M. Heiblum, D. Fein- berg, R. M´ elin, and H. Shtrikman, Proceedings of the National Academy of Sciences115, 6991 (2018)

    2018

  58. [58]

    Huang, Y

    K.-F. Huang, Y. Ronen, R. M´ elin, D. Feinberg, K. Watanabe, T. Taniguchi, and P. Kim, Nature Com- munications13, 3032 (2022)

    2022

  59. [59]

    Chirolli, A

    L. Chirolli, A. Braggio, and F. Giazotto, Phys. Rev. Res.6, 033171 (2024)

    2024

  60. [60]

    Moser, J

    J. Moser, J. G¨ uttinger, A. Eichler, M. J. Esplandiu, D. E. Liu, M. I. Dykman, and A. Bachtold, Nature Nanotechnology8, 493 (2013)

    2013

  61. [61]

    M. R. Delbecq, L. E. Bruhat, J. J. Viennot, S. Datta, A. Cottet, and T. Kontos, Nature Communications4, 1400 (2013)

    2013

  62. [62]

    A. Hamo, A. Benyamini, I. Shapir, I. Khivrich, J. Waiss- man, K. Kaasbjerg, Y. Oreg, F. von Oppen, and S. Ilani, Nature535, 395 (2016)

    2016

  63. [63]

    Bhattacharya, T

    U. Bhattacharya, T. Grass, A. Bachtold, M. Lewenstein, and F. Pistolesi, Nano Letters21, 9661 (2021)

    2021

  64. [64]

    Vigneau, J

    F. Vigneau, J. Monsel, J. Tabanera, K. Aggarwal, L. Bresque, F. Fedele, F. Cerisola, G. A. D. Briggs, J. Anders, J. M. R. Parrondo, A. Auff` eves, and N. Ares, Phys. Rev. Res.4, 043168 (2022)

    2022

  65. [65]

    Ishizaka, J

    S. Ishizaka, J. Sone, and T. Ando, Phys. Rev. B52, 8358 (1995)

    1995

  66. [66]

    Fazio and R

    R. Fazio and R. Raimondi, Phys. Rev. Lett.80, 2913 (1998)

    1998

  67. [67]

    Fazio and R

    R. Fazio and R. Raimondi, Phys. Rev. Lett.82, 4950 (1999)

    1999

  68. [68]

    A. A. Clerk and V. Ambegaokar, Phys. Rev. B61, 9109 (2000)

    2000

  69. [69]

    A. A. Clerk, V. Ambegaokar, and S. Hershfield, Phys. Rev. B61, 3555 (2000)

    2000

  70. [70]

    Recher, E

    P. Recher, E. V. Sukhorukov, and D. Loss, Phys. Rev. B63, 165314 (2001)

    2001

  71. [71]

    Recher and D

    P. Recher and D. Loss, Phys. Rev. Lett.91, 267003 (2003)

    2003

  72. [72]

    M. G. Pala, M. Governale, and J. K¨ onig, New Journal of Physics9, 278 (2007)

    2007

  73. [73]

    Governale, M

    M. Governale, M. G. Pala, and J. K¨ onig, Phys. Rev. B 77, 134513 (2008)

    2008

  74. [74]

    Hussein and S

    R. Hussein and S. Kohler, Phys. Rev. B89, 205424 (2014)

    2014

  75. [75]

    Sothmann, S

    B. Sothmann, S. Weiss, M. Governale, and J. K¨ onig, Phys. Rev. B90, 220501 (2014)

    2014

  76. [76]

    Sauret, D

    O. Sauret, D. Feinberg, and T. Martin, Phys. Rev. B 70, 245313 (2004)

    2004

  77. [77]

    Chevallier, J

    D. Chevallier, J. Rech, T. Jonckheere, and T. Martin, Phys. Rev. B83, 125421 (2011)

    2011

  78. [78]

    Burset, W

    P. Burset, W. J. Herrera, and A. L. Yeyati, Phys. Rev. B84, 115448 (2011)

    2011

  79. [79]

    Hussein, L

    R. Hussein, L. Jaurigue, M. Governale, and A. Braggio, Phys. Rev. B94, 235134 (2016)

    2016

  80. [80]

    Brange, K

    F. Brange, K. Prech, and C. Flindt, Phys. Rev. Lett. 127, 237701 (2021)

    2021

Showing first 80 references.