Driving viscous hydrodynamics in bulk electron flow in graphene using micromagnets

Bulk electrons; Electron flow; Electron fluid; Hydrodynamic flows; Micromagnets; No-slip boundary conditions; Periodic magnetic fields; Two-dimensional electron gases (2DEG); Viscous boundary layers; Voltage modulations; Electronic, Optical and Magnetic Materials; Condensed Matter Physics; Physics - Mesoscopic Systems and Quantum Hall Effect

Abstract :

[en] We consider the hydrodynamic flow of an electron fluid in a channel formed in a two-dimensional electron gas (2DEG) with no-slip boundary conditions. To generate vorticity in the fluid, the flow is influenced by an array of micromagnets on the top of the 2DEG. We analyze the viscous boundary layer, and we demonstrate anti-Poiseuille behavior in this region. Furthermore, we predict a longitudinal voltage modulation, where a periodic magnetic field generates a voltage term periodic in the direction of transport. From an experimental point of view, we propose a method for a boundary-independent measurement of the viscosity of different electron fluids. The results are applicable to graphene away from the charge-neutrality point and to semiconductors.

Disciplines :

Physics

Author, co-author :

Engdahl, Jack N. ; School of Physics, University of New South Wales, Sydney, Australia

Keser, Aydln Cem ; CSIRO, West Lindfield, Australia

SCHMIDT, Thomas ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS) ; School of Chemical and Physical Sciences, Victoria University of Wellington, Wellington, New Zealand

Sushkov, Oleg P.; School of Physics, University of New South Wales, Sydney, Australia

External co-authors :

yes

Language :

English

Title :

Driving viscous hydrodynamics in bulk electron flow in graphene using micromagnets

Publication date :

15 May 2024

Journal title :

Physical Review. B

ISSN :

2469-9950

eISSN :

2469-9969

Publisher :

American Physical Society

Volume :

109

Issue :

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://link.aps.org/article/10.1103/PhysRevB.109.195402

Funders :

Centre of Excellence in Future Low-Energy Electronics Technologies, Australian Research Council

Funding text :

We acknowledge important discussions with A. Hamilton, Y. A. Alava, O. Klochan, D. Wang, and Z. Krix. This work was supported by the Australian Research Council Centre of Excellence in Future Low-Energy Electronics Technologies (CE170100039).

Commentary :

13 pages, 7 figures. V2: Typos fixed and additional discussion added. Analysis of the bulk flow expanded to include subleading corrections to the Navier-Stokes equation. The solution for the boundary layer has been generalized to finite slip length in Appendix B

Available on ORBilu :

since 17 December 2025

Statistics

Number of views

17 (0 by Unilu)

Number of downloads

11 (0 by Unilu)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

OpenAlex citations

WoS citations^™

Bibliography

R. N. Gurzhi, Hydrodynamic effects in solids at low temperature, Sov. Phys. Usp. 11, 255 (1968) 0038-5670 10.1070/PU1968v011n02ABEH003815.
M. Polini and A. K. Geim, Viscous electron fluids, Phys. Today 73, 28 (2020) 0031-9228 10.1063/PT.3.4497.
B. N. Narozhny, Hydrodynamic approach to two-dimensional electron systems, Riv. Nuovo Cimento 45, 661 (2022) 0393-697X 10.1007/s40766-022-00036-z.
R. N. Gurzhi, Minimum of Resistance in Impurity-free Conductors, Sov. Phys. JETP 17, 521 (1963).
M. J. M. de Jong and L. W. Molenkamp, Hydrodynamic electron flow in high-mobility wires, Phys. Rev. B 51, 13389 (1995) 0163-1829 10.1103/PhysRevB.51.13389.
A. Lucas and K. C. Fong, Hydrodynamics of electrons in graphene, J. Phys.: Condens. Matter 30, 053001 (2018) 0953-8984 10.1088/1361-648X/aaa274.
R. N. Gurzhi, A. N. Kalinenko, and A. I. Kopeliovich, Electron-electron collisions and a new hydrodynamic effect in two-dimensional electron gas, Phys. Rev. Lett. 74, 3872 (1995) 0031-9007 10.1103/PhysRevLett.74.3872.
D. A. Bandurin, I. Torre, R. K. Kumar, M. Ben Shalom, A. Tomadin, A. Principi, G. H. Auton, E. Khestanova, K. S. Novoselov, I. V. Grigorieva, L. A. Ponomarenko, A. K. Geim, and M. Polini, Negative local resistance caused by viscous electron backflow in graphene, Science 351, 1055 (2016) 0036-8075 10.1126/science.aad0201.
P. J. W. Moll, P. Kushwaha, N. Nandi, B. Schmidt, and A. P. Mackenzie, Evidence for hydrodynamic electron flow in (Equation presented), Science 351, 1061 (2016) 0036-8075 10.1126/science.aac8385.
P. S. Alekseev, Negative magnetoresistance in viscous flow of two-dimensional electrons, Phys. Rev. Lett. 117, 166601 (2016) 0031-9007 10.1103/PhysRevLett.117.166601.
R. Krishna Kumar, D. A. Bandurin, F. M. D. Pellegrino, Y. Cao, A. Principi, H. Guo, G. H. Auton, M. Ben Shalom, L. A. Ponomarenko, G. Falkovich, K. Watanabe, T. Taniguchi, I. V. Grigorieva, L. S. Levitov, M. Polini, and A. K. Geim, Superballistic flow of viscous electron fluid through graphene constrictions, Nat. Phys. 13, 1182 (2017) 1745-2473 10.1038/nphys4240.
D. A. Bandurin, A. V. Shytov, L. S. Levitov, R. K. Kumar, A. I. Berdyugin, M. Ben Shalom, I. V. Grigorieva, A. K. Geim, and G. Falkovich, Fluidity onset in graphene, Nat. Commun. 9, 4533 (2018) 2041-1723 10.1038/s41467-018-07004-4.
A. C. Keser, D. Q. Wang, O. Klochan, D. Y. H. Ho, O. A. Tkachenko, V. A. Tkachenko, D. Culcer, S. Adam, I. Farrer, D. A. Ritchie, O. P. Sushkov, and A. R. Hamilton, Geometric control of universal hydrodynamic flow in a two-dimensional electron fluid, Phys. Rev. X 11, 031030 (2021) 2160-3308 10.1103/PhysRevX.11.031030.
G. M. Gusev, A. D. Levin, E. V. Levinson, and A. K. Bakarov, Viscous transport and Hall viscosity in a two-dimensional electron system, Phys. Rev. B 98, 161303 (R) (2018) 2469-9950 10.1103/PhysRevB.98.161303.
L. V. Ginzburg, C. Gold, M. P. Röösli, C. Reichl, M. Berl, W. Wegscheider, T. Ihn, and K. Ensslin, Superballistic electron flow through a point contact in a Ga[Al]As heterostructure, Phys. Rev. Res. 3, 023033 (2021) 2643-1564 10.1103/PhysRevResearch.3.023033.
I. V. Gornyi and D. G. Polyakov, Two-dimensional electron hydrodynamics in a random array of impenetrable obstacles: Magnetoresistivity, Hall viscosity, and the Landauer dipole, Phys. Rev. B 108, 165429 (2023) 2469-9950 10.1103/PhysRevB.108.165429.
G. M. Gusev, A. D. Levin, E. V. Levinson, and A. K. Bakarov, Viscous electron flow in mesoscopic two-dimensional electron gas, AIP Adv. 8, 025318 (2018) 2158-3226 10.1063/1.5020763.
Q. Shi, P. D. Martin, Q. A. Ebner, M. A. Zudov, L. N. Pfeiffer, and K. W. West, Colossal negative magnetoresistance in a two-dimensional electron gas, Phys. Rev. B 89, 201301 (R) (2014) 1098-0121 10.1103/PhysRevB.89.201301.
R. G. Mani, A. Kriisa, and W. Wegscheider, Size-dependent giant-magnetoresistance in millimeter scale GaAs/AlGaAs 2D electron devices, Sci. Rep. 3, 2747 (2013) 2045-2322 10.1038/srep02747.
X. Wang, P. Jia, R.-R. Du, L. N. Pfeiffer, K. W. Baldwin, and K. W. West, Hydrodynamic charge transport in gaas/algaas ultrahigh-mobility two-dimensional electron gas, Phys. Rev. B 106, L241302 (2022) 10.1103/PhysRevB.106.L241302.
A. D. Levin, G. M. Gusev, A. S. Yaroshevich, Z. D. Kvon, and A. K. Bakarov, Geometric engineering of viscous magnetotransport in a two-dimensional electron system, Phys. Rev. B 108, 115310 (2023) 2469-9950 10.1103/PhysRevB.108.115310.
J. A. Sulpizio, L. Ella, A. Rozen, J. Birkbeck, D. J. Perello, D. Dutta, M. Ben-Shalom, T. Taniguchi, K. Watanabe, T. Holder, R. Queiroz, A. Principi, A. Stern, T. Scaffidi, A. K. Geim, and S. Ilani, Visualizing Poiseuille flow of hydrodynamic electrons, Nature (London) 576, 75 (2019) 0028-0836 10.1038/s41586-019-1788-9.
M. J. H. Ku, T. X. Zhou, Q. Li, Y. J. Shin, J. K. Shi, C. Burch, L. E. Anderson, A. T. Pierce, Y. Xie, A. Hamo, U. Vool, H. Zhang, F. Casola, T. Taniguchi, K. Watanabe, M. M. Fogler, P. Kim, A. Yacoby, and R. L. Walsworth, Imaging viscous flow of the Dirac fluid in graphene, Nature (London) 583, 537 (2020) 0028-0836 10.1038/s41586-020-2507-2.
L. Ella, A. Rozen, J. Birkbeck, M. Ben-Shalom, D. Perello, J. Zultak, T. Taniguchi, K. Watanabe, A. K. Geim, S. Ilani, and J. A. Sulpizio, Simultaneous voltage and current density imaging of flowing electrons in two dimensions, Nat. Nanotechnol. 14, 480 (2019) 1748-3387 10.1038/s41565-019-0398-x.
A. I. Berdyugin, S. G. Xu, F. M. D. Pellegrino, R. Krishna Kumar, A. Principi, I. Torre, M. Ben Shalom, T. Taniguchi, K. Watanabe, I. V. Grigorieva, M. Polini, A. K. Geim, and D. A. Bandurin, Measuring Hall viscosity of graphene's electron fluid, Science 364, 162 (2019) 0036-8075 10.1126/science.aau0685.
A. O. Govorov and J. J. Heremans, Hydrodynamic effects in interacting Fermi electron jets, Phys. Rev. Lett. 92, 026803 (2004) 0031-9007 10.1103/PhysRevLett.92.026803.
I. I. Kaya, Nonequilibrium transport and the Bernoulli effect of electrons in a two-dimensinoal electron gas, Mod. Phys. Lett. B 27, 1330001 (2013) 0217-9849 10.1142/S0217984913300019.
B. A. Braem, F. M. D. Pellegrino, A. Principi, M. Röösli, C. Gold, S. Hennel, J. V. Koski, M. Berl, W. Dietsche, W. Wegscheider, M. Polini, T. Ihn, and K. Ensslin, Scanning gate microscopy in a viscous electron fluid, Phys. Rev. B 98, 241304 (R) (2018) 2469-9950 10.1103/PhysRevB.98.241304.
S. Samaddar, J. Strasdas, K. Janßen, S. Just, T. Johnsen, Z. Wang, B. Uzlu, S. Li, D. Neumaier, M. Liebmann, and M. Morgenstern, Evidence for local spots of viscous electron flow in graphene at moderate mobility, Nano Lett. 21, 9365 (2021) 1530-6984 10.1021/acs.nanolett.1c01145.
Y.-T. Tu and S. Das Sarma, Wiedemann-Franz law in graphene, Phys. Rev. B 107, 085401 (2023) 2469-9950 10.1103/PhysRevB.107.085401.
J. Crossno, J. K. Shi, K. Wang, X. Liu, A. Harzheim, A. Lucas, S. Sachdev, P. Kim, T. Taniguchi, K. Watanabe, T. A. Ohki, and K. C. Fong, Observation of the Dirac fluid and the breakdown of the Wiedemann-Franz law in graphene, Science 351, 1058 (2016) 0036-8075 10.1126/science.aad0343.
J. Gooth, F. Menges, N. Kumar, V. Süss, C. Shekhar, Y. Sun, U. Drechsler, R. Zierold, C. Felser, and B. Gotsmann, Thermal and electrical signatures of a hydrodynamic electron fluid in tungsten diphosphide, Nat. Commun. 9, 4093 (2018) 2041-1723 10.1038/s41467-018-06688-y.
A. Lucas and S. Das Sarma, Electronic hydrodynamics and the breakdown of the Wiedemann-Franz and Mott laws in interacting metals, Phys. Rev. B 97, 245128 (2018) 2469-9950 10.1103/PhysRevB.97.245128.
A. Jaoui, B. Fauqué, and K. Behnia, Thermal resistivity and hydrodynamics of the degenerate electron fluid in antimony, Nat. Commun. 12, 195 (2021) 2041-1723 10.1038/s41467-020-20420-9.
S. Ahn and S. Das Sarma, Hydrodynamics, viscous electron fluid, and Wiedeman-Franz law in two-dimensional semiconductors, Phys. Rev. B 106, L081303 (2022) 2469-9950 10.1103/PhysRevB.106.L081303.
Y. Dai, R. R. Du, L. N. Pfeiffer, and K. W. West, Observation of a cyclotron harmonic spike in microwave-induced resistances in ultraclean (Equation presented) quantum wells, Phys. Rev. Lett. 105, 246802 (2010) 0031-9007 10.1103/PhysRevLett.105.246802.
A. T. Hatke, M. A. Zudov, L. N. Pfeiffer, and K. W. West, Giant microwave photoresistivity in high-mobility quantum Hall systems, Phys. Rev. B 83, 121301 (R) (2011) 1098-0121 10.1103/PhysRevB.83.121301.
M. Białek, J. Łusakowski, M. Czapkiewicz, J. Wróbel, and V. Umansky, Photoresponse of a two-dimensional electron gas at the second harmonic of the cyclotron resonance, Phys. Rev. B 91, 045437 (2015) 1098-0121 10.1103/PhysRevB.91.045437.
P. S. Alekseev and A. P. Alekseeva, Transverse magnetosonic waves and viscoelastic resonance in a two-dimensional highly viscous electron fluid, Phys. Rev. Lett. 123, 236801 (2019) 0031-9007 10.1103/PhysRevLett.123.236801.
P. Gallagher, C.-S. Yang, T. Lyu, F. Tian, R. Kou, H. Zhang, K. Watanabe, T. Taniguchi, and F. Wang, Quantum-critical conductivity of the Dirac fluid in graphene, Science 364, 158 (2019) 0036-8075 10.1126/science.aat8687.
G. Varnavides, A. S. Jermyn, P. Anikeeva, C. Felser, and P. Narang, Electron hydrodynamics in anisotropic materials, Nat. Commun. 11, 4710 (2020) 2041-1723 10.1038/s41467-020-18553-y.
J. M. Link, B. N. Narozhny, E. I. Kiselev, and J. Schmalian, Out-of-Bounds Hydrodynamics in anisotropic Dirac fluids, Phys. Rev. Lett. 120, 196801 (2018) 0031-9007 10.1103/PhysRevLett.120.196801.
A. Stern, T. Scaffidi, O. Reuven, C. Kumar, J. Birkbeck, and S. Ilani, How electron hydrodynamics can eliminate the Landauer-Sharvin resistance, Phys. Rev. Lett. 129, 157701 (2022) 10.1103/PhysRevLett.129.157701.
V. Galitski, M. Kargarian, and S. Syzranov, Dynamo effect and turbulence in hydrodynamic Weyl metals, Phys. Rev. Lett. 121, 176603 (2018) 0031-9007 10.1103/PhysRevLett.121.176603.
G. Tatara, Hydrodynamic theory of vorticity-induced spin transport, Phys. Rev. B 104, 184414 (2021) 2469-9950 10.1103/PhysRevB.104.184414.
R. J. Doornenbal, M. Polini, and R. A. Duine, Spin-vorticity coupling in viscous electron fluids, J. Phys.: Mater. 2, 015006 (2019) 2515-7639 10.1088/2515-7639/aaf8fb.
M. Matsuo, D. A. Bandurin, Y. Ohnuma, Y. Tsutsumi, and S. Maekawa, Spin hydrodynamic generation in graphene, arXiv:2005.01493.
R. Takahashi, M. Matsuo, M. Ono, K. Harii, H. Chudo, S. Okayasu, J. Ieda, S. Takahashi, S. Maekawa, and E. Saitoh, Spin hydrodynamic generation, Nat. Phys. 12, 52 (2016) 1745-2473 10.1038/nphys3526.
R. Takahashi, H. Chudo, M. Matsuo, K. Harii, Y. Ohnuma, S. Maekawa, and E. Saitoh, Giant spin hydrodynamic generation in laminar flow, Nat. Commun. 11, 3009 (2020) 2041-1723 10.1038/s41467-020-16753-0.
P. S. Alekseev, A. P. Dmitriev, I. V. Gornyi, V. Y. Kachorovskii, B. N. Narozhny, and M. Titov, Counterflows in viscous electron-hole fluid, Phys. Rev. B 98, 125111 (2018) 2469-9950 10.1103/PhysRevB.98.125111.
P. S. Alekseev, A. P. Dmitriev, I. V. Gornyi, V. Y. Kachorovskii, B. N. Narozhny, and M. Titov, Nonmonotonic magnetoresistance of a two-dimensional viscous electron-hole fluid in a confined geometry, Phys. Rev. B 97, 085109 (2018) 2469-9950 10.1103/PhysRevB.97.085109.
B. N. Narozhny, I. V. Gornyi, and M. Titov, Anti-Poiseuille flow in neutral graphene, Phys. Rev. B 104, 075443 (2021) 2469-9950 10.1103/PhysRevB.104.075443.
J. N. Engdahl, A. C. Keser, and O. P. Sushkov, Micromagnets dramatically enhance effects of viscous hydrodynamic flow in a two-dimensional electron fluid, Phys. Rev. Res. 4, 043175 (2022) 2643-1564 10.1103/PhysRevResearch.4.043175.
L. Landau and E. Lifshitz, Fluid Mechanics (Elsevier Science, Kidlington, Oxfordshire, UK, 2013), Vol. 6.
A. C. Keser and O. Sushkov, Magnetic response of a two-dimensional viscous electron fluid, Turk. J. Phys. 47, 28 (2023) 1300-0101 10.55730/1300-0101.2736.
T. Scaffidi, N. Nandi, B. Schmidt, A. P. Mackenzie, and J. E. Moore, Hydrodynamic electron flow and Hall viscosity, Phys. Rev. Lett. 118, 226601 (2017) 0031-9007 10.1103/PhysRevLett.118.226601.
H. Lantangen and A. Logg, Solving PDEs in Python (Springer, Cham, Switzerland, 2017).
Magnetic Materials, in Handbook of Magnetic Measurements, Series in Sensors (CRC, Boca Raton, FL, 2011), Vol. 20110781, pp. 117-158.
E. I. Kiselev and J. Schmalian, Boundary conditions of viscous electron flow, Phys. Rev. B 99, 035430 (2019) 2469-9950 10.1103/PhysRevB.99.035430.