Direct observation of vortices in an electron fluid

  • Bandurin, D. A. et al. Negative local resistance caused by viscous electron backflow in graphene. Science 351, 1055–1058 (2016).

    ADS 
    CAS 

    Google Scholar 

  • Levin, A. D., Gusev, G. M., Levinson, E. V., Kvon, Z. D. & Bakarov, A. K. Vorticity-induced negative nonlocal resistance in a viscous two-dimensional electron system. Phys. Rev. B 97, 245308 (2018).

    ADS 
    CAS 

    Google Scholar 

  • Bandurin, D. A. et al. Fluidity onset in graphene. Nat. Commun. 9, 4533 (2018).

    ADS 

    Google Scholar 

  • Gupta, A. et al. Hydrodynamic and ballistic transport over large length scales in GaAs/AlGaAs. Phys. Rev. Lett. 126, 076803 (2021).

    ADS 
    CAS 

    Google Scholar 

  • Krishna Kumar, R. et al. Superballistic flow of viscous electron fluid through graphene constrictions. Nat. Phys. 13, 1182–1185 (2017).

    CAS 

    Google Scholar 

  • Ginzburg, L. V. et al. Superballistic electron flow through a point contact in a Ga[Al]As heterostructure. Phys. Rev. Res. 3, 023033 (2021).

    CAS 

    Google Scholar 

  • Kumar, C. et al. Imaging hydrodynamic electrons flowing without Landauer–Sharvin resistance. Preprint at https://doi.org/10.48550/arXiv.2111.06412 (2021).

  • Sulpizio, J. A. et al. Visualizing Poiseuille flow of hydrodynamic electrons. Nature 576, 75–79 (2019).

    ADS 
    CAS 

    Google Scholar 

  • Ku, M. J. H. et al. Imaging viscous flow of the Dirac fluid in graphene. Nature 583, 537–541 (2020).

    ADS 
    CAS 

    Google Scholar 

  • Vool, U. et al. Imaging phonon-mediated hydrodynamic flow in WTe2. Nat. Phys. 17, 1216–1220 (2021).

    CAS 

    Google Scholar 

  • Crossno, J. et al. Observation of the Dirac fluid and the breakdown of the Wiedemann–Franz law in graphene. Science 351, 1058–1061 (2016).

    ADS 
    CAS 

    Google Scholar 

  • Vasyukov, D. et al. A scanning superconducting quantum interference device with single electron spin sensitivity. Nat. Nanotechnol. 8, 639–644 (2013).

    ADS 
    CAS 

    Google Scholar 

  • Gurzhi, R. N. Hydrodynamic effects in solids at low temperature. Sov. Phys. Usp. 11, 255–270 (1968).

    ADS 

    Google Scholar 

  • Landau, L. D. & Lifshitz, E. M. Fluid Mechanics (Elsevier, 1987).

  • Mayzel, J., Steinberg, V. & Varshney, A. Stokes flow analogous to viscous electron current in graphene. Nat. Commun. 10, 937 (2019).

    ADS 

    Google Scholar 

  • Molenkamp, L. W. & de Jong, M. J. M. Observation of Knudsen and Gurzhi transport regimes in a two-dimensional wire. Solid State Electron. 37, 551–553 (1994).

    ADS 
    CAS 

    Google Scholar 

  • de Jong, M. J. M. & Molenkamp, L. W. Hydrodynamic electron flow in high-mobility wires. Phys. Rev. B 51, 13389–13402 (1995).

    ADS 

    Google Scholar 

  • Taubert, D. et al. An electron jet pump: the Venturi effect of a Fermi liquid. J. Appl. Phys. 109, 102412 (2011).

    ADS 

    Google Scholar 

  • Moll, P. J. W., Kushwaha, P., Nandi, N., Schmidt, B. & Mackenzie, A. P. Evidence for hydrodynamic electron flow in PdCoO2. Science 351, 1061–1064 (2016).

    ADS 
    CAS 

    Google Scholar 

  • Braem, B. A. et al. Scanning gate microscopy in a viscous electron fluid. Phys. Rev. B 98, 241304 (2018).

    ADS 
    CAS 

    Google Scholar 

  • Gusev, G. M., Jaroshevich, A. S., Levin, A. D., Kvon, Z. D. & Bakarov, A. K. Stokes flow around an obstacle in viscous two-dimensional electron liquid. Sci. Rep. 10, 7860 (2020).

    ADS 
    CAS 

    Google Scholar 

  • Raichev, O. E., Gusev, G. M., Levin, A. D. & Bakarov, A. K. Manifestations of classical size effect and electronic viscosity in the magnetoresistance of narrow two-dimensional conductors: theory and experiment. Phys. Rev. B 101, 235314 (2020).

    ADS 
    CAS 

    Google Scholar 

  • Gusev, G. M., Jaroshevich, A. S., Levin, A. D., Kvon, Z. D. & Bakarov, A. K. Viscous magnetotransport and Gurzhi effect in bilayer electron system. Phys. Rev. B 103, 075303 (2021).

    ADS 
    CAS 

    Google Scholar 

  • Krebs, Z. J. et al. Imaging the breaking of electrostatic dams in graphene for ballistic and viscous fluids. Preprint at https://doi.org/10.48550/arXiv.2106.07212 (2021).

  • Samaddar, S. et al. Evidence for local spots of viscous electron flow in graphene at moderate mobility. Nano Lett. 21, 9365–9373 (2021).

    ADS 
    CAS 

    Google Scholar 

  • Govorov, A. O. & Heremans, J. J. Hydrodynamic effects in interacting Fermi electron jets. Phys. Rev. Lett. 92, 026803 (2004).

    ADS 

    Google Scholar 

  • Di Sante, D. et al. Turbulent hydrodynamics in strongly correlated Kagome metals. Nat. Commun. 11, 3997 (2020).

    ADS 

    Google Scholar 

  • Huang, Y. & Wang, M. Nonnegative magnetoresistance in hydrodynamic regime of electron fluid transport in two-dimensional materials. Phys. Rev. B 104, 155408 (2021).

    ADS 
    CAS 

    Google Scholar 

  • Hui, A., Oganesyan, V. & Kim, E. Beyond Ohm’s law: Bernoulli effect and streaming in electron hydrodynamics. Phys. Rev. B 103, 235152 (2021).

    ADS 
    CAS 

    Google Scholar 

  • Narozhny, B. N., Gornyi, I. V. & Titov, M. Anti-Poiseuille flow in neutral graphene. Phys. Rev. B 104, 075443 (2021).

    ADS 
    CAS 

    Google Scholar 

  • Tavakol, O. & Kim, Y. B. Artificial electric field and electron hydrodynamics. Phys. Rev. Res. 3, 013290 (2021).

    CAS 

    Google Scholar 

  • Zhang, G., Kachorovskii, V., Tikhonov, K. & Gornyi, I. Heating of inhomogeneous electron flow in the hydrodynamic regime. Phys. Rev. B 104, 075417 (2021).

    ADS 
    CAS 

    Google Scholar 

  • Li, S., Khodas, M. & Levchenko, A. Conformal maps of viscous electron flow in the Gurzhi crossover. Phys. Rev. B 104, 155305 (2021).

    ADS 
    CAS 

    Google Scholar 

  • Nazaryan, K. G. & Levitov, L. Robustness of vorticity in electron fluids. Preprint at https://doi.org/10.48550/arXiv.2111.09878 (2021).

  • Stern, A. et al. Spread and erase—how electron hydrodynamics can eliminate the Landauer–Sharvin resistance. Preprint at https://doi.org/10.48550/arXiv.2110.15369 (2021).

  • Andreev, A. V., Kivelson, S. A. & Spivak, B. Hydrodynamic description of transport in strongly correlated electron systems. Phys. Rev. Lett. 106, 256804 (2011).

    ADS 
    CAS 

    Google Scholar 

  • Mendoza, M., Herrmann, H. J. & Succi, S. Preturbulent regimes in graphene flow. Phys. Rev. Lett. 106, 156601 (2011).

    ADS 
    CAS 

    Google Scholar 

  • Torre, I., Tomadin, A., Geim, A. K. & Polini, M. Nonlocal transport and the hydrodynamic shear viscosity in graphene. Phys. Rev. B 92, 165433 (2015).

    ADS 

    Google Scholar 

  • Alekseev, P. S. Negative magnetoresistance in viscous flow of two-dimensional electrons. Phys. Rev. Lett. 117, 166601 (2016).

    ADS 
    CAS 

    Google Scholar 

  • Pellegrino, F. M. D., Torre, I., Geim, A. K. & Polini, M. Electron hydrodynamics dilemma: whirlpools or no whirlpools. Phys. Rev. B 94, 155414 (2016).

    ADS 

    Google Scholar 

  • Galitski, V., Kargarian, M. & Syzranov, S. Dynamo effect and turbulence in hydrodynamic Weyl metals. Phys. Rev. Lett. 121, 176603 (2018).

    ADS 
    CAS 

    Google Scholar 

  • Shytov, A., Kong, J. F., Falkovich, G. & Levitov, L. Particle collisions and negative nonlocal response of ballistic electrons. Phys. Rev. Lett. 121, 176805 (2018).

    ADS 
    CAS 

    Google Scholar 

  • Holder, T. et al. Ballistic and hydrodynamic magnetotransport in narrow channels. Phys. Rev. B 100, 245305 (2019).

    ADS 
    CAS 

    Google Scholar 

  • Levitov, L. & Falkovich, G. Electron viscosity, current vortices and negative nonlocal resistance in graphene. Nat. Phys. 12, 672–676 (2016).

    CAS 

    Google Scholar 

  • Falkovich, G. & Levitov, L. Linking spatial distributions of potential and current in viscous electronics. Phys. Rev. Lett. 119, 066601 (2017).

    ADS 

    Google Scholar 

  • Danz, S. & Narozhny, B. N. Vorticity of viscous electronic flow in graphene. 2D Mater. 7, 035001 (2020).

    CAS 

    Google Scholar 

  • Gabbana, A., Polini, M., Succi, S., Tripiccione, R. & Pellegrino, F. M. D. Prospects for the detection of electronic preturbulence in graphene. Phys. Rev. Lett. 121, 236602 (2018).

    ADS 
    CAS 

    Google Scholar 

  • Meltzer, A. Y., Levin, E. & Zeldov, E. Direct reconstruction of two-dimensional currents in thin films from magnetic-field measurements. Phys. Rev. Appl. 8, 064030 (2017).

    ADS 

    Google Scholar 

  • Kiselev, E. I. & Schmalian, J. Boundary conditions of viscous electron flow. Phys. Rev. B 99, 035430 (2019).

    ADS 
    CAS 

    Google Scholar 

  • Woods, J. M. et al. Suppression of magnetoresistance in thin WTe2 flakes by surface oxidation. ACS Appl. Mater. Interfaces 9, 23175–23180 (2017).

    CAS 

    Google Scholar 

  • Jenkins, A. et al. Imaging the breakdown of ohmic transport in graphene. Preprint at https://doi.org/10.48550/arXiv.2002.05065 (2020).

  • Gooth, J. et al. Thermal and electrical signatures of a hydrodynamic electron fluid in tungsten diphosphide. Nat. Commun. 9, 4093 (2018).

    ADS 
    CAS 

    Google Scholar 

  • Berdyugin, A. I. et al. Measuring Hall viscosity of graphene’s electron fluid. Science 364, 162–165 (2019).

    ADS 
    CAS 

    Google Scholar 

  • Kim, M. et al. Control of electron–electron interaction in graphene by proximity screening. Nat. Commun. 11, 2339 (2020).

    ADS 
    CAS 

    Google Scholar 

  • Geurs, J. et al. Rectification by hydrodynamic flow in an encapsulated graphene Tesla valve. Preprint at https://doi.org/10.48550/arXiv.2008.04862 (2020).

  • Choi, Y.-G., Doan, M., Choi, G. & Chernodub, M. N. Pseudo-hydrodynamic flow of quasiparticles in semimetal WTe2 at room temperature. Preprint at https://doi.org/10.48550/arXiv.2201.08331 (2022).

  • Ali, M. N. et al. Large, non-saturating magnetoresistance in WTe2. Nature 514, 205–208 (2014).

    ADS 
    CAS 

    Google Scholar 

  • Wang, P. et al. Landau quantization and highly mobile fermions in an insulator. Nature 589, 225–229 (2021).

    ADS 
    CAS 

    Google Scholar 

  • Kumar, N. et al. Extremely high magnetoresistance and conductivity in the type-II Weyl semimetals WP2 and MoP2. Nat. Commun. 8, 1642 (2017).

    ADS 

    Google Scholar 

  • Wang, L. et al. Tuning magnetotransport in a compensated semimetal at the atomic scale. Nat. Commun. 6, 8892 (2015).

    ADS 

    Google Scholar 

  • Lv, Y.-Y. et al. Experimental observation of anisotropic Adler–Bell–Jackiw anomaly in type-II Weyl semimetal WTe1.98 crystals at the quasiclassical regime. Phys. Rev. Lett. 118, 096603 (2017).

    ADS 

    Google Scholar 

  • Ali, M. N. et al. Correlation of crystal quality and extreme magnetoresistance of WTe2. Europhys. Lett. 110, 67002 (2015).

    ADS 

    Google Scholar 

  • Wu, Y. et al. Temperature-induced Lifshitz transition in WTe2. Phys. Rev. Lett. 115, 166602 (2015).

    ADS 

    Google Scholar 

  • Zhu, Z. et al. Quantum oscillations, thermoelectric coefficients, and the Fermi surface of semimetallic WTe2. Phys. Rev. Lett. 114, 176601 (2015).

    ADS 

    Google Scholar 

  • Xiang, F.-X., Veldhorst, M., Dou, S.-X. & Wang, X.-L. Multiple Fermi pockets revealed by Shubnikov–de Haas oscillations in WTe2. Europhys. Lett. 112, 37009 (2015).

    ADS 

    Google Scholar 

  • Zhang, Q. et al. Lifshitz transitions induced by temperature and surface doping in type‐II Weyl semimetal candidate Td‐WTe2. Phys. Status Solidi Rapid Res. Lett. 11, 1700209 (2017).

    ADS 

    Google Scholar 

  • Luo, Y. et al. Hall effect in the extremely large magnetoresistance semimetal WTe2. Appl. Phys. Lett. 107, 182411 (2015).

    ADS 

    Google Scholar 

  • Kirtley, J. R., Tsuei, C. C. & Moler, K. A. Temperature dependence of the half-integer magnetic flux quantum. Science 285, 1373–1375 (1999).

    CAS 

    Google Scholar 

  • Kalisky, B. et al. Behavior of vortices near twin boundaries in underdoped Ba(Fe1−xCox)2As2. Phys. Rev. B 83, 064511 (2011).

    ADS 

    Google Scholar 

  • Embon, L. et al. Probing dynamics and pinning of single vortices in superconductors at nanometer scales. Sci. Rep. 5, 7598 (2015).

    CAS 

    Google Scholar 

  • Kremen, A. et al. Mechanical control of individual superconducting vortices. Nano Lett. 16, 1626–1630 (2016).

    ADS 
    CAS 

    Google Scholar 

  • Embon, L. et al. Imaging of super-fast dynamics and flow instabilities of superconducting vortices. Nat. Commun. 8, 85 (2017).

    ADS 
    CAS 

    Google Scholar 

  • Zhang, I. P. et al. Imaging anisotropic vortex dynamics in FeSe. Phys. Rev. B 100, 024514 (2019).

    ADS 
    CAS 

    Google Scholar 

  • Anahory, Y. et al. SQUID-on-tip with single-electron spin sensitivity for high-field and ultra-low temperature nanomagnetic imaging. Nanoscale 12, 3174–3182 (2020).

    CAS 

    Google Scholar 

  • Huber, M. E. et al. DC SQUID series array amplifiers with 120 MHz bandwidth. IEEE Trans. Appl. Supercond. 11, 1251–1256 (2001).

    ADS 

    Google Scholar 

  • Finkler, A. et al. Self-aligned nanoscale SQUID on a tip. Nano Lett. 10, 1046–1049 (2010).

    ADS 
    CAS 

    Google Scholar 

  • Finkler, A. et al. Scanning superconducting quantum interference device on a tip for magnetic imaging of nanoscale phenomena. Rev. Sci. Instrum. 83, 073702 (2012).

    ADS 
    CAS 

    Google Scholar 

  • Halbertal, D. et al. Nanoscale thermal imaging of dissipation in quantum systems. Nature 539, 407–410 (2016).

    ADS 
    CAS 

    Google Scholar 

  • Broadway, D. A. et al. Improved current density and magnetization reconstruction through vector magnetic field measurements. Phys. Rev. Appl. 14, 024076 (2020).

    ADS 
    CAS 

    Google Scholar 

  • Guerrero-Becerra, K. A., Pellegrino, F. M. D. & Polini, M. Magnetic hallmarks of viscous electron flow in graphene. Phys. Rev. B 99, 041407 (2019).

    ADS 
    CAS 

    Google Scholar 

  • Hasdeo, E. H., Ekström, J., Idrisov, E. G. & Schmidt, T. L. Electron hydrodynamics of two-dimensional anomalous Hall materials. Phys. Rev. B 103, 125106 (2021).

    ADS 
    CAS 

    Google Scholar 

  • Guo, H., Ilseven, E., Falkovich, G. & Levitov, L. S. Higher-than-ballistic conduction of viscous electron flows. Proc. Natl Acad. Sci. USA 114, 3068–3073 (2017).

    ADS 
    CAS 

    Google Scholar 

  • Müller, M., Schmalian, J. & Fritz, L. Graphene: a nearly perfect fluid. Phys. Rev. Lett. 103, 2–5 (2009).

    Google Scholar 

  • Principi, A., Vignale, G., Carrega, M. & Polini, M. Bulk and shear viscosities of the two-dimensional electron liquid in a doped graphene sheet. Phys. Rev. B 93, 125410 (2016).

    ADS 

    Google Scholar 

  • Scaffidi, T., Nandi, N., Schmidt, B., Mackenzie, A. P. & Moore, J. E. Hydrodynamic electron flow and Hall viscosity. Phys. Rev. Lett. 118, 226601 (2017).

    ADS 

    Google Scholar 

  • Svintsov, D. Hydrodynamic-to-ballistic crossover in Dirac materials. Phys. Rev. B 97, 121405 (2018).

    ADS 
    CAS 

    Google Scholar 

  • Burmistrov, I. S., Goldstein, M., Kot, M., Kurilovich, V. D. & Kurilovich, P. D. Dissipative and Hall viscosity of a disordered 2D electron gas. Phys. Rev. Lett. 123, 26804 (2019).

    ADS 
    CAS 

    Google Scholar 

  • Ledwith, P., Guo, H., Shytov, A. & Levitov, L. Tomographic dynamics and scale-dependent viscosity in 2D electron systems. Phys. Rev. Lett. 123, 116601 (2019).

    ADS 
    CAS 

    Google Scholar 

  • Narozhny, B. N. & Schütt, M. Magnetohydrodynamics in graphene: Shear and Hall viscosities. Phys. Rev. B 100, 035125 (2019).

    ADS 
    CAS 

    Google Scholar 

  • Alekseev, P. S. & Dmitriev, A. P. Viscosity of two-dimensional electrons. Phys. Rev. B 102, 241409 (2020).

    ADS 
    CAS 

    Google Scholar 

  • Toshio, R., Takasan, K. & Kawakami, N. Anomalous hydrodynamic transport in interacting noncentrosymmetric metals. Phys. Rev. Res. 2, 032021 (2020).

    CAS 

    Google Scholar 

  • Narozhny, B. N., Gornyi, I. V. & Titov, M. Hydrodynamic collective modes in graphene. Phys. Rev. B 103, 115402 (2021).

    ADS 
    CAS 

    Google Scholar 

  • Alekseev, P. S. et al. Counterflows in viscous electron-hole fluid. Phys. Rev. B 98, 125111 (2018).

    ADS 
    CAS 

    Google Scholar 

  • Alekseev, P. S. et al. Nonmonotonic magnetoresistance of a two-dimensional viscous electron-hole fluid in a confined geometry. Phys. Rev. B 97, 085109 (2018).

    ADS 
    CAS 

    Google Scholar 

  • Dell’Anna, L. & Metzner, W. Fermi surface fluctuations and single electron excitations near Pomeranchuk instability in two dimensions. Phys. Rev. B 73, 045127 (2006).

    ADS 

    Google Scholar 

  • About the Author: AKDSEO

    You May Also Like