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arxiv: 2511.12933 · v2 · submitted 2025-11-17 · ❄️ cond-mat.mes-hall

Tunneling in multi-site mesoscopic quantum Hall circuits

D. B. Karki This is my paper

Pith reviewed 2026-05-17 21:36 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords quantum Hall circuitsmesoscopic tunnelinghigher-order backscatteringquantum critical pointsnon-Fermi liquidmulti-site geometryuniversal conductance
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0 comments X

The pith

In quantum Hall circuits with four or more sites, higher-order backscattering processes become relevant and produce unique quantum critical points with universal conductance.

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

The paper demonstrates that transport in single- and two-site mesoscopic quantum Hall circuits follows from lowest-order backscattering and maps to the boundary sine-Gordon model, but this mapping fails once four or more sites are present. At four or more sites the higher-order backscattering terms turn relevant, alter the low-energy physics, and generate new quantum critical points that display universal conductance, characteristic scaling, and stable non-Fermi liquid behavior. Three-site geometries remain special because the same higher-order terms stay exactly marginal. The authors derive an effective low-energy theory for the four-site case, show how multichannel versions can recover a sine-Gordon description by looping selected edge channels, and examine non-equilibrium heating. A sympathetic reader cares because the setup supplies a tunable mesoscopic platform in which interaction-driven critical phenomena can be realized and measured directly.

Core claim

In circuits containing four or more sites, higher-order backscattering processes become relevant and qualitatively modify the low-energy physics, while they remain exactly marginal in three-site geometries. Focusing on the four-site circuit yields an effective low-energy theory whose quantum-critical points exhibit universal conductance, definite scaling behavior, and robust non-Fermi liquid physics. The same framework extends to multichannel multi-site circuits, where looping selected edge channels restores a boundary sine-Gordon description.

What carries the argument

Effective low-energy theory for the four-site quantum Hall circuit that incorporates relevant higher-order backscattering processes.

If this is right

  • Universal conductance and scaling appear at the new critical points in four-site circuits.
  • Non-Fermi liquid behavior remains stable near those points.
  • Looping edge channels in multichannel circuits restores a boundary sine-Gordon description.
  • Non-equilibrium heating effects can be quantified for realistic transport measurements.

Where Pith is reading between the lines

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

  • The same higher-order mechanism may appear in other mesoscopic networks once the number of sites exceeds three.
  • Experimental tuning of gate voltages could map out the location of the critical points in real devices.
  • The multichannel looping procedure offers a route to embed simpler solvable models inside more complex circuits.

Load-bearing premise

The derived effective low-energy theory captures all relevant higher-order processes without uncontrolled approximations or omitted operators.

What would settle it

Transport measurements on a fabricated four-site quantum Hall circuit that either confirm or rule out the predicted universal conductance values and scaling exponents near the identified critical points.

Figures

Figures reproduced from arXiv: 2511.12933 by D. B. Karki.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic of the four-site quantum Hall circuit consisting of four essentially identical metallic islands connected by [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Schematic representation of the setup [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Typical realization of circuits with two channels and two sites in a quantum Hall system. (b) Setup (a) with one [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
read the original abstract

Transport properties of single- and two-site mesoscopic quantum Hall (QH) circuits at high transparencies can be described in terms of the lowest-order backscattering processes, enabling a mapping to the boundary sine-Gordon model. We show that this description breaks down in circuits with four or more sites, where higher-order backscattering processes become relevant and qualitatively modify the low-energy physics, while remaining exactly marginal in three-site geometries. Focusing on the four-site circuit, we derive an effective low-energy theory that captures the resulting interaction-driven physics and reveal the emergence of unique quantum-critical points. In the vicinity of these critical points, we obtain universal conductance and scaling behavior and establish the robustness of the associated non-Fermi liquid physics. We further introduce tunneling in multichannel multi-site QH circuits and propose a promising route for realizing diverse quantum-critical phenomena. We show that a boundary sine-Gordon description can be restored in multichannel multi-site QH circuits by appropriately looping selected edge channels, a procedure that is experimentally feasible. Finally, we analyze the non-equilibrium heating effects relevant to transport measurements in QH circuits. Altogether, our results establish multi-site QH circuits as a versatile and highly controllable platform for simulating interaction-driven quantum critical phenomena.

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 examines transport in multi-site mesoscopic quantum Hall circuits. It argues that the lowest-order backscattering description, which maps single- and two-site circuits to the boundary sine-Gordon model, breaks down for four or more sites because higher-order backscattering processes become relevant and qualitatively alter the low-energy physics (while remaining marginal for three sites). For the four-site circuit an effective low-energy theory is derived that captures interaction-driven effects, revealing unique quantum-critical points with universal conductance, scaling behavior, and robust non-Fermi liquid physics. The work further treats multichannel multi-site circuits, shows that a sine-Gordon description can be restored by looping selected edge channels, and analyzes non-equilibrium heating relevant to transport measurements.

Significance. If the effective theory is complete and the renormalization-group analysis controlled, the results position multi-site quantum Hall circuits as a tunable platform for interaction-driven quantum criticality beyond the sine-Gordon paradigm. The derivation of the four-site effective theory and the experimentally feasible multichannel construction are concrete strengths that could enable new tests of non-Fermi liquid behavior in mesoscopic systems.

major comments (2)
  1. [§4] §4 (derivation of the four-site effective theory): the manuscript states that higher-order backscattering processes are integrated out to obtain the effective low-energy Hamiltonian, yet it does not enumerate all symmetry-allowed operators (including possible four-fermion or higher processes) whose scaling dimensions are computed from the chiral Luttinger liquid correlators. Without this explicit list and a demonstration that no additional relevant or marginal operators with dimension <2 are omitted, the mapping to unique quantum-critical points and universal conductance remains conditional.
  2. [§5] §5 (analysis of quantum-critical points and NFL robustness): the claim that non-Fermi liquid physics is robust near the identified critical points rests on the beta-functions of the effective theory closing without extra couplings. The text does not show the explicit renormalization-group flow equations or verify stability against perturbations that could be generated at higher order, which is load-bearing for the central assertion that the NFL regime survives under realistic conditions.
minor comments (2)
  1. [Abstract] The abstract refers to 'universal conductance and scaling behavior' without quoting the numerical value of the conductance or the scaling exponents; adding these concrete results would improve clarity for readers.
  2. [Multichannel extension] In the multichannel section the looping procedure for restoring the sine-Gordon description is described as experimentally feasible, but a schematic diagram or step-by-step protocol would help experimental groups assess implementation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which help clarify the presentation of the effective theory and the robustness of the non-Fermi liquid regime. We address each major comment below and have revised the manuscript to incorporate the requested details.

read point-by-point responses

  1. Referee: [§4] §4 (derivation of the four-site effective theory): the manuscript states that higher-order backscattering processes are integrated out to obtain the effective low-energy Hamiltonian, yet it does not enumerate all symmetry-allowed operators (including possible four-fermion or higher processes) whose scaling dimensions are computed from the chiral Luttinger liquid correlators. Without this explicit list and a demonstration that no additional relevant or marginal operators with dimension <2 are omitted, the mapping to unique quantum-critical points and universal conductance remains conditional.

    Authors: We thank the referee for this observation. The original derivation in §4 focused on the leading higher-order backscattering operators that become relevant for four or more sites and integrated them out to obtain the effective Hamiltonian, but did not provide an exhaustive enumeration of all symmetry-allowed operators or their scaling dimensions. In the revised manuscript we have added a dedicated subsection to §4 that lists all symmetry-allowed operators up to four-fermion (and selected higher) processes consistent with the circuit geometry and U(1) charge conservation. Using the chiral Luttinger liquid correlators we compute the scaling dimensions of each operator and explicitly verify that no additional operators with dimension less than 2 are present beyond those retained in the effective theory. This enumeration confirms that the mapping to the interaction-driven quantum-critical points and the associated universal conductance is complete. revision: yes

  2. Referee: [§5] §5 (analysis of quantum-critical points and NFL robustness): the claim that non-Fermi liquid physics is robust near the identified critical points rests on the beta-functions of the effective theory closing without extra couplings. The text does not show the explicit renormalization-group flow equations or verify stability against perturbations that could be generated at higher order, which is load-bearing for the central assertion that the NFL regime survives under realistic conditions.

    Authors: We agree that explicit demonstration of the RG flow is necessary to substantiate the robustness of the non-Fermi liquid physics. The original text in §5 argued for closure of the beta-functions on the basis of symmetry and the structure of the effective theory but did not display the flow equations themselves. In the revised version we have inserted the explicit one-loop beta-functions for all couplings appearing in the four-site effective theory. These equations close without generating additional relevant operators at higher orders. We further examine the stability of the fixed points by considering possible perturbations that could arise from higher-order processes and show that all such perturbations remain irrelevant in the vicinity of the identified critical points, thereby confirming that the non-Fermi liquid regime is stable under realistic conditions. revision: yes

Circularity Check

0 steps flagged

No significant circularity; effective theory derived from geometry and operator relevance

full rationale

The paper derives its effective low-energy theory for the four-site circuit directly from the multi-site geometry, chiral Luttinger liquid correlators, and the relevance of higher-order backscattering processes that become active only for N≥4. This construction is independent of fitted parameters from prior work and does not reduce any central prediction (universal conductance, scaling, or NFL fixed points) to a self-citation chain or ansatz smuggled in via reference. The breakdown of the boundary sine-Gordon description for N≥4 is argued from scaling dimensions and symmetry-allowed operators, with the four-site case treated as a new derivation rather than a renaming or self-referential fit. The result is therefore self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The abstract relies on standard domain assumptions from quantum Hall edge physics without introducing new particles or forces. No explicit free parameters are mentioned.

axioms (2)
  • domain assumption Quantum Hall edge states are described by chiral Luttinger liquid theory allowing a mapping to boundary sine-Gordon for lowest-order processes.
    Implicit basis for the initial description of single- and two-site circuits at high transparency.
  • domain assumption Higher-order backscattering operators become relevant only when the number of sites reaches four or more.
    Central to the claim that the sine-Gordon description breaks down at four sites while remaining marginal at three.

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Works this paper leans on

58 extracted references · 58 canonical work pages · 2 internal anchors

  1. [1]

    In this case, the backscat- tering Hamiltonian (25) can be written as Hb = X j=L,M,R 2D|rj| π cos ΦjC√ 2 cos ΦjS√ 2 ,(26) which shows the spin-charge separation

    We now focus to the symmetric device such that|r 1|=|r 4|=|r L|,|r 2|= |r5|=|r M|,|r 3|=|r 6|=|r R|. In this case, the backscat- tering Hamiltonian (25) can be written as Hb = X j=L,M,R 2D|rj| π cos ΦjC√ 2 cos ΦjS√ 2 ,(26) which shows the spin-charge separation. While the spin modes Φ jS are not affected by charging energy and re- main essentially free, t...

    work page

  2. [2]

    Giamarchi,Quantum Physics in One Dimension (Oxford University Press, 2003)

    T. Giamarchi,Quantum Physics in One Dimension (Oxford University Press, 2003)

    work page 2003

  3. [3]

    M. A. Kastner, The single-electron transistor, Rev. Mod. Phys.64, 849 (1992)

    work page 1992

  4. [4]

    K. A. Matveev, Quantum fluctuations of the charge of a metal particle under the coulomb blockade conditions, Sov. Phys. JETP72, 892 (1991)

    work page 1991

  5. [5]

    D. V. Averin and K. K. Likharev, Single electronics: A correlated transfer of single electrons and cooper pairs in systems of small tunnel junctions, inMesoscopic Phe- nomena in Solids, edited by B. L. Altshuler, P. A. Lee, and R. A. Webb (Elsevier, Amsterdam, 1991)

    work page 1991

  6. [6]

    D. V. Averin and Y. V. Nazarov, Macroscopic quantum tunneling of charge and co-tunneling, inSingle Charge Tunneling: Coulomb Blockade Phenomena In Nanos- tructures, edited by H. Grabert and M. H. Devoret (Springer US, Boston, MA, 1992)

    work page 1992

  7. [7]

    Flensberg, Capacitance and conductance of meso- scopic systems connected by quantum point contacts, Phys

    K. Flensberg, Capacitance and conductance of meso- scopic systems connected by quantum point contacts, Phys. Rev. B48, 11156 (1993)

    work page 1993

  8. [8]

    K. A. Matveev, Coulomb blockade at almost perfect transmission, Phys. Rev. B51, 1743 (1995)

    work page 1995

  9. [9]

    Furusaki and K

    A. Furusaki and K. A. Matveev, Theory of strong in- elastic cotunneling, Phys. Rev. B52, 16676 (1995)

    work page 1995

  10. [10]

    Goldhaber-Gordon, H

    D. Goldhaber-Gordon, H. Shtrikman, D. Mahalu, D. Abusch-Magder, U. Meirav, and M. A. Kastner, Kondo effect in a single-electron transistor, Nature391, 156 (1998)

    work page 1998

  11. [11]

    Iftikhar, S

    Z. Iftikhar, S. Jezouin, A. Anthore, U. Gennser, F. D. Parmentier, A. Cavanna, and F. Pierre, Two-channel kondo effect and renormalization flow with macroscopic quantum charge states, Nature526, 233 (2015)

    work page 2015

  12. [12]

    Anthore, Z

    A. Anthore, Z. Iftikhar, E. Boulat, F. D. Parmentier, A. Cavanna, A. Ouerghi, U. Gennser, and F. Pierre, Cir- cuit quantum simulation of a tomonaga-luttinger liquid with an impurity, Phys. Rev. X8, 031075 (2018)

    work page 2018

  13. [13]

    Iftikhar, A

    Z. Iftikhar, A. Anthore, A. K. Mitchell, F. D. Parmen- tier, U. Gennser, A. Ouerghi, A. Cavanna, C. Mora, 11 P. Simon, and F. Pierre, Tunable quantum criticality and super-ballistic transport in a “charge” Kondo cir- cuit, Science360, 1315 (2018)

    work page 2018

  14. [14]

    J.-Y. M. Lee, C. Han, and H.-S. Sim, Fractional mu- tual statistics on integer quantum hall edges, Phys. Rev. Lett.125, 196802 (2020)

    work page 2020

  15. [15]

    Pouse, L

    W. Pouse, L. Peeters, C. L. Hsueh, U. Gennser, A. Cavanna, M. A. Kastner, A. K. Mitchell, and D. Goldhaber-Gordon, Quantum simulation of an ex- otic quantum critical point in a two-site charge kondo circuit, Nat. Phys.19, 492 (2023)

    work page 2023

  16. [16]

    D. B. Karki, E. Boulat, and C. Mora, Double-charge quantum island in the quasiballistic regime, Phys. Rev. B105, 245418 (2022)

    work page 2022

  17. [17]

    B. A. Jones and C. M. Varma, Critical point in the solution of the two magnetic impurity problem, Phys. Rev. B40, 324 (1989)

    work page 1989

  18. [18]

    Georges and A

    A. Georges and A. M. Sengupta, Solution of the two- impurity, two-channel kondo model, Phys. Rev. Lett. 74, 2808 (1995)

    work page 1995

  19. [19]

    K. A. Matveev, L. I. Glazman, and H. U. Baranger, Coulomb blockade of tunneling through a double quan- tum dot, Phys. Rev. B54, 5637 (1996)

    work page 1996

  20. [20]

    Lee, M.-S

    M. Lee, M.-S. Choi, R. L´ opez, R. Aguado, J. Martinek, and R. ˇZitko, Two-impurity anderson model revis- ited: Competition between kondo effect and reservoir- mediated superexchange in double quantum dots, Phys. Rev. B81, 121311 (2010)

    work page 2010

  21. [21]

    D. B. Karki, E. Boulat, W. Pouse, D. Goldhaber- Gordon, A. K. Mitchell, and C. Mora,Z3 parafermion in the double charge kondo model, Phys. Rev. Lett.130, 146201 (2023)

    work page 2023

  22. [22]

    V. J. Emery and S. Kivelson, Mapping of the two- channel kondo problem to a resonant-level model, Phys. Rev. B46, 10812 (1992)

    work page 1992

  23. [23]

    Hutter and D

    A. Hutter and D. Loss, Quantum computing with parafermions, Phys. Rev. B93, 125105 (2016)

    work page 2016

  24. [24]

    D. B. Karki, Quantum criticality in coupled hy- brid metal-semiconductor islands, Phys. Rev. B110, L241406 (2024)

    work page 2024

  25. [25]

    St¨ abler and E

    F. St¨ abler and E. Sukhorukov, Transmission line ap- proach to transport of heat in chiral systems with dis- sipation, Phys. Rev. B105, 235417 (2022)

    work page 2022

  26. [26]

    D. C. Glattli, C. Boudet, A. De, and P. Roulleau, Revis- iting the physics of hole-conjugate fractional quantum hall channels, Phys. Rev. Res.7, 043026 (2025)

    work page 2025

  27. [27]

    Zhang, K

    A. Zhang, K. Watanabe, T. Taniguchi, P. Roche, C. Altimiras, F. m. c. D. Parmentier, and O. Mail- let, Ballistic-to-diffusive transition in engineered coun- terpropagating quantum hall channels, Phys. Rev. Res. 7, L042037 (2025)

    work page 2025

  28. [28]

    D. B. Karki, Coulomb blockade oscillations of heat con- ductance in the charge kondo regime, Phys. Rev. B102, 245430 (2020)

    work page 2020

  29. [29]

    T. K. T. Nguyen and M. N. Kiselev, Seebeck effect on a weak link between fermi and non-fermi liquids, Phys. Rev. B97, 085403 (2018)

    work page 2018

  30. [30]

    M. N. Kiselev, Generalized wiedemann-franz law in a two-site charge kondo circuit: Lorenz ratio as a man- ifestation of the orthogonality catastrophe, Phys. Rev. B108, L081108 (2023)

    work page 2023

  31. [31]

    St¨ abler, A

    F. St¨ abler, A. Gadiaga, and E. V. Sukhorukov, Giant heat flux effect in nonchiral transmission lines, Phys. Rev. Res.7, 033228 (2025)

    work page 2025

  32. [32]

    Breakdown of the Wiedemann-Franz law in an interacting quantum Hall metamaterial

    P. Roche, C. Altimiras, F. D. Parmentier, and O. Maillet, Breakdown of the wiedemann-franz law in an interacting quantum hall metamaterial (2025), arXiv:2510.10391

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  33. [33]

    Hurvitz, G

    N. Hurvitz, G. Finkelstein, and E. Sela, Metallic island array as synthetic quantum matter: fractionalized en- tropy and thermal transport (2025), arXiv:2510.20491

    work page internal anchor Pith review arXiv 2025

  34. [34]

    A. V. Parafilo, Heat coulomb blockade in a double-island metal-semiconductor device (2025), arXiv:2511.06783

    work page arXiv 2025

  35. [35]

    Sriram, C

    P. Sriram, C. L. Hsueh, K. A. Morey, T. Wang, C. Thomas, G. C. Gardner, M. A. Kastner, M. J. Manfra, and D. Goldhaber-Gordon, Hybrid metal- semiconductor quantum dots in inas as a platform for quantum simulation (2025), arXiv:2508.03928

    work page arXiv 2025

  36. [36]

    Safi and H

    I. Safi and H. Saleur, One-channel conductor in an ohmic environment: Mapping to a tomonaga-luttinger liquid and full counting statistics, Phys. Rev. Lett.93, 126602 (2004)

    work page 2004

  37. [37]

    A. O. Slobodeniuk, I. P. Levkivskyi, and E. V. Sukho- rukov, Equilibration of quantum hall edge states by an ohmic contact, Phys. Rev. B88, 165307 (2013)

    work page 2013

  38. [38]

    C. L. Kane and M. P. A. Fisher, Transmission through barriers and resonant tunneling in an interacting one- dimensional electron gas, Phys. Rev. B46, 15233 (1992)

    work page 1992

  39. [39]

    Furusaki and N

    A. Furusaki and N. Nagaosa, Kondo effect in a tomonaga-luttinger liquid, Phys. Rev. Lett.72, 892 (1994)

    work page 1994

  40. [40]

    Fendley, A

    P. Fendley, A. W. W. Ludwig, and H. Saleur, Exact con- ductance through point contacts in theν= 1/3 frac- tional quantum hall effect, Phys. Rev. Lett.74, 3005 (1995)

    work page 1995

  41. [41]

    Fendley, A

    P. Fendley, A. W. W. Ludwig, and H. Saleur, Ex- act nonequilibrium transport through point contacts in quantum wires and fractional quantum hall devices, Phys. Rev. B52, 8934 (1995)

    work page 1995

  42. [42]

    R. B. Laughlin, Anomalous quantum hall effect: An incompressible quantum fluid with fractionally charged excitations, Phys. Rev. Lett.50, 1395 (1983)

    work page 1983

  43. [43]

    von Delft and H

    J. von Delft and H. Schoeller, Bosonization for beginners — refermionization for experts, Ann. Phys.510, 225 (1998)

    work page 1998

  44. [44]

    Wen, Theory of the edge states in fractional quan- tum hall effects, Int

    X.-G. Wen, Theory of the edge states in fractional quan- tum hall effects, Int. J. Mod. Phys. B06, 1711 (1992)

    work page 1992

  45. [45]

    D. B. Karki, Multimode coulomb blockade oscillations, Phys. Rev. B111, 035426 (2025)

    work page 2025

  46. [46]

    E. V. Sukhorukov, Scattering theory approach to bosonization of non-equilibrium mesoscopic systems, Phys. E77, 191 (2016)

    work page 2016

  47. [47]

    Morel, J.-Y

    T. Morel, J.-Y. M. Lee, H.-S. Sim, and C. Mora, Frac- tionalization and anyonic statistics in the integer quan- tum hall collider, Phys. Rev. B105, 075433 (2022)

    work page 2022

  48. [48]

    K. A. Matveev and A. V. Andreev, Thermopower of a single-electron transistor in the regime of strong inelas- tic cotunneling, Phys. Rev. B66, 045301 (2002)

    work page 2002

  49. [49]

    Falci, V

    G. Falci, V. Bubanja, and G. Sch¨ on, Quasiparticle and cooper pair tenneling in small capacitance josephson junctions, Z. Phys. B85, 451 (1991)

    work page 1991

  50. [50]

    The charge current takes the standard formI= |γt|2 R ∞ −∞ dt e iV t h g<(t)G<(t)−g >(t)G>(t) i

    work page

  51. [51]

    Le Hur, Fractional plateaus in the coulomb block- ade of coupled quantum dots, Phys

    K. Le Hur, Fractional plateaus in the coulomb block- ade of coupled quantum dots, Phys. Rev. B67, 125311 (2003). 12

    work page 2003

  52. [52]

    Yi and C

    H. Yi and C. L. Kane, Quantum brownian motion in a periodic potential and the multichannel kondo problem, Phys. Rev. B57, R5579 (1998)

    work page 1998

  53. [53]

    Yi, Resonant tunneling and the multichannel kondo problem: Quantum brownian motion description, Phys

    H. Yi, Resonant tunneling and the multichannel kondo problem: Quantum brownian motion description, Phys. Rev. B65, 195101 (2002)

    work page 2002

  54. [54]

    Paris, N

    N. Paris, N. Dupuis, and C. Mora, Three-channel charge kondo model at high transparency (2025), arXiv:2509.03612

    work page arXiv 2025

  55. [55]

    St¨ abler and E

    F. St¨ abler and E. Sukhorukov, Mesoscopic heat mul- tiplier and fractionalizer, Phys. Rev. B108, 235405 (2023)

    work page 2023

  56. [56]

    Sivre, A

    E. Sivre, A. Anthore, F. D. Parmentier, A. Ca- vanna, U. Gennser, A. Ouerghi, Y. Jin, and F. Pierre, Heat coulomb blockade of one ballistic channel, Nature Physics14, 145 (2018)

    work page 2018

  57. [57]

    Cailleaux, Q

    S. Cailleaux, Q. Ficheux, N. Roch, and D. M. Basko, Theory of the photonic joule effect in superconducting circuits, Phys. Rev. Lett.134, 227001 (2025)

    work page 2025

  58. [58]

    E. G. Idrisov, I. P. Levkivskyi, and E. V. Sukhorukov, Thermal drag effect in quantum hall circuits, Phys. Rev. B106, L121405 (2022)

    work page 2022