Kinetic simulation of magnetic-field-tuned hydro-dynamic electron transport in a graphene Corbino disk

Kinetic simulation of magnetic-field-tuned hydro-dynamic electron transport in a graphene Corbino disk

Chuang Zhang
1,2
,
Meng Lian
3
,
Hong Liang
4
,
Xiaokang Li
5
,
Zhaoli Guo
6,*
,
Jing-Tao Lü
3,*
*Correspondence to: Zhaoli Guo, Institute of Interdisciplinary Research for Mathematics and Applied Science, Huazhong University of Science and Technol ogy, Wuhan 430074, Hubei, China. E-mail: zlguo@hust.edu.cn
Jing-Tao Lü, School of Physics, Institute for Quantum Science and Engineering and Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China. E-mail: jtlu@hust.edu.cn
Thermo-X. 2026;2:Thermo-X_202613. 10.70401/tx.2026.0028
Received: April 18, 2026Accepted: August 06, 2026Published: August 07, 2026
Tips Icon
This manuscript is made available in its unedited form to allow early access to the reported findings. Further editing will be completed before final publication. As such, the content may include errors, and standard legal disclaimers are applicable.

Abstract

Hydrodynamic electron transport, in which electrical transport in solids resembles fluid hydrodynamics when momentum-conserving electron-electron scattering dominates, has attracted much attention over the past decade. However, its thermal aspects have received considerably less attention. In this paper, we systematically simulate electron transport in a graphene Corbino disk by solving the steady-state Boltzmann transport equation with a dual relaxation-time Callaway model, in which momentum-conserving and momentum-relaxing scatterings are explicitly distinguished. By varying the magnetic field strength and scattering rates, we compare the charge and heat flux responses across the diffusive-to-hydrodynamic crossover under both electric field and temperature-gradient driving. We show that magnetic-field-induced deflection of both fluxes is strongly enhanced in the hydrodynamic regime but nearly suppressed in the diffusive regime. Under electric-field driving, a pronounced temperature rise is observed in the hydrodynamic regime du to reduced dissipation, while the diffusive regime remains nearly isothermal. Under temperature-gradient driving, the deflection exhibits the opposite chirality to that in the electric-field case. These findings establish that thermal transport can provide a sensitive and independent diagnostic of electro hydrodynamics, and identify the magnetic field as an effective discriminator between collective and dissipative conduction.

Keywords

Hydrodynamic electron transport, non-diffusive thermal conduction, boltzmann transport equation, discrete ordinate method, corbino disk geometry

References

  • 1. Varnavides G, Yacoby A, Felser C, Narang P. Charge transport and hydrodynamics in materials. Nat Rev Mater. 2023;8(11):726-741.
    [DOI]
  • 2. Fritz L, Scaffidi T. Hydrodynamic electronic transport. Annu Rev Condens Matter Phys. 2024;15:17-44.
    [DOI]
  • 3. Hui A, Skinner B. Hydrodynamics of the electronic Fermi liquid: A pedagogical overview. J Phys: Condens Matter. 2025;37(36):363001.
    [DOI]
  • 4. Vijayakrishnan S, Berkson-Korenberg Z, Mainville J, Engel LW, Lilly MP, West KW, et al. Two-dimensional hydrodynamic viscous electron flow in annular Corbino rings. Phys Rev Research. 2025;7(2):L022029.
    [DOI]
  • 5. Beardo A, Tur-Prats J, Camacho J, Alvarez FX. Phonon hydrodynamics: Theory and experiments. Thermo-X. 2026. 2(1);202513.
    [DOI]
  • 6. Lian M, Zhang C, Guo Z, Lü JT. Discrete unified gas kinetic scheme for the solution of electron boltzmann transport equation with callaway approximation. Phys Rev E. 2024;109(6-2):065310.
    [DOI] [PubMed]
  • 7. Zhu GL, Lü JT. Out-of-equilibrium ultrafast electron and phonon energy transfer dynamics in metals: The role of non-thermal effect. Thermo-X. 2025. 2(1);202512.
    [DOI]
  • 8. Chandra M, Kataria G, Sahdev D, Sundararaman R. Hydrodynamic and ballistic AC transport in two-dimensional fermi liquids. Phys Rev B. 2019;99(16):165409.
    [DOI]
  • 9. Guo H, Ilseven E, Falkovich G, Levitov LS. Higher-than-ballistic conduction of viscous electron flows. Proc Natl Acad Sci U S A. 2017;114(12):3068-3073.
    [DOI]
  • 10. Sulpizio JA, Ella L, Rozen A, Birkbeck J, Perello DJ, Dutta D, et al. Visualizing poiseuille flow of hydrodynamic electrons. Nature. 2019;576(7785):75-79.
    [DOI]
  • 11. Sano R, Matsuo M. Breaking down the magnonic wiedemann-franz law in the hydrodynamic regime. Phys Rev Lett. 2023;130(16):166201.
    [DOI] [PubMed]
  • 12. Songci L, Andreev AV, Levchenko A. Hydrodynamic electron transport in graphene Hall-bar devices. Phys Rev B. 2022;105(15):155307.
    [DOI]
  • 13. Shavit M, Shytov A, Falkovich G. Freely flowing currents and electric field expulsion in viscous electronics. Phys Rev Lett. 2019;123(2):026801.
    [DOI] [PubMed]
  • 14. Gurzhi RN. Minimum of resistance in impurity-free conductors. Sov Phys JETP. 1963; 44(7), 771-772.
  • 15. Gurzhi RN. Hydrodynamic effects in solids at low temperature. Sov Phys Usp. 1968;11(2):255-270.
    [DOI]
  • 16. Black JE. Contribution of electron-electron normal scattering processes to the electrical resistivity of thin wires. Phys Rev B. 1980;21(8):3279-3286.
    [DOI]
  • 17. de Jong MJ, Molenkamp LW. Hydrodynamic electron flow in high-mobility wires. Phys Rev B. 1995;51(19):13389-13402.
    [DOI]
  • 18. De Gennaro S, Rettori A. The low-temperature electrical resistivity of potassium: Size effects and the role of normal electron-electron scattering. J Phys F: Met Phys. 1984;14(12):L237-L242.
    [DOI]
  • 19. Gurzhi RN, Kalinenko AN, Kopeliovich AI. Electron-electron collisions and a new hydrodynamic effect in two-dimensional electron gas. Phys Rev Lett. 1995;74(19):3872-3875.
    [DOI] [PubMed]
  • 20. Yu ZZ, Haerle M, Zwart JW, Bass J, Pratt WP, Schroeder PA. Negative temperature derivative of resistivity in thin potassium samples: The gurzhi effect? Phys Rev Lett. 1984;52(5):368-371.
    [DOI]
  • 21. Ella L, Rozen A, Birkbeck J, Ben-Shalom M, Perello D, Zultak J, et al. Simultaneous voltage and current density imaging of flowing electrons in two dimensions. Nat Nanotechnol. 2019;14(5):480-487.
    [DOI] [PubMed]
  • 22. Tomadin A, Vignale G, Polini M. Corbino disk viscometer for 2D quantum electron liquids. Phys Rev Lett. 2014;113(23):235901.
    [DOI] [PubMed]
  • 23. Briskot U, Schütt M, Gornyi IV, Titov M, Narozhny BN, Mirlin AD. Collision-dominated nonlinear hydrodynamics in graphene. Phys Rev B. 2015;92(11):115426.
    [DOI]
  • 24. Zeng Y, Li JIA, Dietrich SA, Ghosh OM, Watanabe K, Taniguchi T, et al. High-quality magnetotransport in graphene using the edge-free corbino geometry. Phys Rev Lett. 2019;122(13):137701.
    [DOI] [PubMed]
  • 25. Gabbana A, Polini M, Succi S, Tripiccione R, Pellegrino FMD. Prospects for the detection of electronic preturbulence in graphene. Phys Rev Lett. 2018;121(23):236602.
    [DOI] [PubMed]
  • 26. Kumar C, Birkbeck J, Sulpizio JA, Perello D, Taniguchi T, Watanabe K, et al. Imaging hydrodynamic electrons flowing without landauer-sharvin resistance. Nature. 2022;609(7926):276-281.
    [DOI]
  • 27. Vool U, Hamo A, Varnavides G, Wang Y, Zhou TX, Kumar N, et al. Imaging phonon-mediated hydrodynamic flow in WTe2. Nat Phys. 2021;17(11):1216-1220.
    [DOI]
  • 28. Jaoui A, Fauqué B, Behnia K. Thermal resistivity and hydrodynamics of the degenerate electron fluid in antimony. Nat Commun. 2021;12(1):195.
    [DOI] [PubMed] [PMC]
  • 29. Krebs ZJ, Behn WA, Li S, Smith KJ, Watanabe K, Taniguchi T, et al. Imaging the breaking of electrostatic dams in graphene for ballistic and viscous fluids. Science. 2023;379(6633):671-676.
    [DOI] [PubMed]
  • 30. Ku MJH, Zhou TX, Li Q, Shin YJ, Shi JK, Burch C, et al. Imaging viscous flow of the Dirac fluid in graphene. Nature. 2020;583(7817):537-541.
    [DOI]
  • 31. Stern A, Scaffidi T, Reuven O, Kumar C, Birkbeck J, Ilani S. How electron hydrodynamics can eliminate the Landauer-sharvin resistance. Phys Rev Lett. 2022;129(15):157701.
    [DOI] [PubMed]
  • 32. Bandurin DA, Shytov AV, Levitov LS, Kumar RK, Berdyugin AI, Ben Shalom M, et al. Fluidity onset in graphene. Nat Commun. 2018;9:4533.
    [DOI]
  • 33. Palm ML, Ding C, Huxter WS, Taniguchi T, Watanabe K, Degen CL. Observation of current whirlpools in graphene at room temperature. Science. 2024;384(6694):465-469.
    [DOI] [PubMed]
  • 34. Bandurin DA, Torre I, Kumar RK, Shalom MB, Tomadin A, Principi A, et al. Negative local resistance caused by viscous electron backflow in graphene. Science. 2016;351(6277):1055-1058.
    [DOI] [PubMed]
  • 35. Levin AD, Gusev GM, Levinson EV, Kvon ZD, Bakarov AK. Vorticity-induced negative nonlocal resistance in a viscous two-dimensional electron system. Phys Rev B. 2018;97(24):245308.
    [DOI]
  • 36. Moll PJW, Kushwaha P, Nandi N, Schmidt B, MacKenzie AP. Evidence for hydrodynamic electron flow in PdCoO2. Science. 2016;351(6277):1061-1064.
    [DOI] [PubMed]
  • 37. Aharon-Steinberg A, Völkl T, Kaplan A, Pariari AK, Roy I, Holder T, et al. Direct observation of vortices in an electron fluid. Nature. 2022;607(7917):74-80.
    [DOI]
  • 38. Mayzel J, Steinberg V, Varshney A. Stokes flow analogous to viscous electron current in graphene. Nat Commun. 2019;10(1):937.
    [DOI] [PubMed] [PMC]
  • 39. Berdyugin AI, Xu SG, Pellegrino FMD, Kumar RK, Principi A, Torre I, et al. Measuring Hall viscosity of graphene’s electron fluid. Science. 2019;364(6436):162-165.
    [DOI] [PubMed]
  • 40. Crossno J, Shi JK, Wang K, Liu X, Harzheim A, Lucas A, et al. Observation of the Dirac fluid and the breakdown of the Wiedemann-Franz law in graphene. Science. 2016;351(6277):1058-1061.
    [DOI] [PubMed]
  • 41. Kumar RK, Bandurin DA, Pellegrino FMD, Cao Y, Principi A, Guo H, et al. Superballistic flow of viscous electron fluid through graphene constrictions. Nature Phys. 2017;13(12):1182-1185.
    [DOI]
  • 42. Estrada-Álvarez J, Domínguez-Adame F, Díaz E. Alternative routes to electron hydrodynamics. Commun Phys. 2024;7:138.
    [DOI]
  • 43. Scaffidi T, Nandi N, Schmidt B, MacKenzie AP, Moore JE. Hydrodynamic electron flow and hall viscosity. Phys Rev Lett. 2017;118(22):226601.
    [DOI] [PubMed]
  • 44. Levitov L, Falkovich G. Electron viscosity, current vortices and negative nonlocal resistance in graphene. Nature Phys. 2016;12(7):672-676.
    [DOI]
  • 45. Lucas A. Stokes paradox in electronic Fermi liquids. Phys Rev B. 2017;95(11):115425.
    [DOI]
  • 46. Torre I, Tomadin A, Geim AK, Polini M. Nonlocal transport and the hydrodynamic shear viscosity in graphene. Phys Rev B. 2015;92(16):165433.
    [DOI]
  • 47. Falkovich G, Levitov L. Linking spatial distributions of potential and current in viscous electronics. Phys Rev Lett. 2017;119(6):066601.
    [DOI] [PubMed]
  • 48. Keser AC, Wang DQ, Klochan O, Ho DYH, Tkachenko OA, Tkachenko VA, et al. Geometric control of universal hydrodynamic flow in a two-dimensional electron fluid. Phys Rev X. 2021;11(3):031030.
    [DOI]
  • 49. Talanov A, Waissman J, Hui A, Skinner B, Watanabe K, Taniguchi T, et al. Observation of electronic viscous dissipation in graphene magneto-thermal transport. arXiv [Preprint]. 2024
    [DOI]
  • 50. Gall V, Narozhny BN, Gornyi IV. Corbino magnetoresistance in neutral graphene. Phys Rev B. 2023;107(23):235401.
    [DOI]
  • 51. Vijayakrishnan S, Poitevin F, Yu O, Berkson-Korenberg Z, Petrescu M, Lilly MP, et al. Anomalous electronic transport in high-mobility Corbino rings. Nat Commun. 2023;14(1):3906.
    [DOI] [PubMed] [PMC]
  • 52. Li S, Levchenko A, Andreev AV. Hydrodynamic thermoelectric transport in Corbino geometry. Phys Rev B. 2022;105(12):125302.
    [DOI]
  • 53. Gall V, Narozhny BN, Gornyi IV. Electronic viscosity and energy relaxation in neutral graphene. Phys Rev B. 2023;107(4):045413.
    [DOI]
  • 54. Estrada-Álvarez J, Domínguez-Adame F, Díaz E. Anisotropic signatures of electron hydrodynamics. Phys Rev Research. 2025;7:013087.
    [DOI]
  • 55. Narozhny BN, Gornyi IV, Mirlin AD, Schmalian J. Hydrodynamic approach to electronic transport in graphene. Ann Der Phys. 2017;529(11):1700043.
    [DOI]
  • 56. Narozhny BN. Electronic hydrodynamics in graphene. Ann Phys. 2019;411:167979.
    [DOI]
  • 57. Gooth J, Menges F, Kumar N, Süβ V, Shekhar C, Sun Y, et al. Thermal and electrical signatures of a hydrodynamic electron fluid in tungsten diphosphide. Nat Commun. 2018;9:4093.
  • 58. Li S, Levchenko A. Nonlocal thermoelectric resistance in vortical viscous transport. Phys Rev B. 2022;105(24):L241405.
    [DOI]
  • 59. Quan Y, Liao B. Coupled electron-phonon hydrodynamics in two-dimensional semiconductors. Phys Rev Lett. 2025;134(22):226301.
    [DOI]
  • 60. Lucas A, Das Sarma S. Electronic hydrodynamics and the breakdown of the Wiedemann-Franz and Mott laws in interacting metals. Phys Rev B. 2018;97(24):245128.
    [DOI]
  • 61. Kaviany M. Heat transfer physics. Cambridge: Cambridge University Press; 2008.
    [DOI]
  • 62. Dembo RS, Eisenstat SC, Steihaug T. Inexact Newton methods. SIAM J Numer Anal. 1982;19(2):400-408.
    [DOI]
  • 63. Van Leer B. Towards the ultimate conservative difference scheme. IV. J Comput Phys. 1977;23(3):276-299.
    [DOI]
  • 64. Yoon S, Jameson A. Lower-upper symmetric-gauss-seidel method for the euler and navier-stokes equations. AIAA J. 1988;26(9):1025-1026.
    [DOI]
  • 65. Gupta A, Heremans JJ, Kataria G, Chandra M, Fallahi S, Gardner GC, et al. Hydrodynamic and ballistic transport over large length scales in GaAs/AlGaAs. Phys Rev Lett. 2021;126(7):076803.
    [DOI] [PubMed]
  • 66. Zhang Y, Fan A, Ma W, Zhang X. Interfacial heat transport in two-dimensional heterostructures: From formation to functionality. Thermo-X, 2026, 2(3): 202620.
    [DOI]
  • 67. Yao Y, Yang H, Yang R, Qian X. Imaging thermal properties of thermal interface materials using frequency-domain thermoreflectance microscopy. Thermo-X. 2026;2:202612.
    [DOI]
  • 68. Miao W, Guo Y, Ran X, Wang M. Deviational monte carlo scheme for thermal and electrical transport in metal nanostructures. Phys Rev B. 2019;99(20):205433.
    [DOI]
  • 69. Fuchs K. The conductivity of thin metallic films according to the electron theory of metals. Math Proc Camb Phil Soc. 1938;34(1):100-108.
    [DOI]
  • 70. Sondheimer EH. The mean free path of electrons in metals. Adv Phys. 1952;1(1):1-42.
    [DOI]

© The Author(s) 2026. This is an Open Access article licensed under a Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, sharing, adaptation, distribution and reproduction in any medium or format, for any purpose, even commercially, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Publisher’s Note

Science Exploration remains a neutral stance on jurisdictional claims in published maps and institutional affiliations. The views expressed in this article are solely those of the author(s) and do not reflect the opinions of the Editors or the publisher.

Share And Cite

Science Exploration Style
Zhang C, Lian M, Liang H, Li X, Guo Z, Lü JT. Kinetic simulation of magnetic-field-tuned hydro-dynamic electron transport in a graphene Corbino disk. Thermo-X. 2026;2:Thermo-X_202613. https://doi.org/10.70401/tx.2026.0028

Submit a Manuscript
Author Instructions
Cite this Article
Export Citation
Article Metrics
0
View
0
Download
Cited
Article Updates
Citation Icon Get citation