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Thomas Scaffidi UC Berkeley

Explore the essential concepts of electron hydrodynamics and Hall viscosity in 2D materials, investigating transport mechanisms through hydrodynamic models. Learn about the universal description of fluids and the interplay of shear viscosity and Hall viscosity in electrical conduction. Dive into the historical perspectives and implications for modern research in the field.

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Thomas Scaffidi UC Berkeley

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  1. Electron Hydrodynamics and Hall Viscosity Hydrodynamic Models for Transport in 2D Materials University of Minnesota [TS, Nandi, Schmidt, Mackenzie, and Moore, Phys. Rev. Lett. 118, 226601] [Holder, Queiroz, TS, Silberstein, Rozen, Sulpizio, Ella, Ilani, Stern, arXiv:1901.08546] [J.A. Sulpizio1†, L. Ella1†, A. Rozen1†, J. Birkbeck2,3, D.J. Perello2,3, D. Dutta1, M. Ben-Shalom2,3,4, T. Taniguchi5, K. Watanabe5, T. Holder1, R. Queiroz1, A. Stern1, T. Scaffidi6, A.K. Geim2,3, and S. Ilani,arXiv:1905.11662 ] Thomas Scaffidi UC Berkeley

  2. Electric conduction versus water flow Water Metal Resistance arises through external scattering due to the lattice (impurities, phonons,…) Theory: Drude • Resistance arises through internal scattering (viscosity) • Theory: Hydrodynamics

  3. Hydrodynamics • Universal description of fluids based on conserved quantities: momentum, energy, charge,… • Works at length/time scales much larger than the microscopic ones • The more interacting, the better! mean free path (internal scattering) Wavelength of perturbation

  4. Why look for hydro in solids? • Novel regime of transport: Access to “exotic” hydrodynamics: Integrable hydro in spin chains Dirac fluid • Available experiments: 300 μm • … • PdCoO2 • Graphene • 2DEGs [Bertini et al] [Bulchandani et al] Crossno et al, Science 351, 1058 (2016) De Jong, Molenkamp(1995),… Bandurin et al, Science 351, 1055-1058 (2016) Moll et al, Science (2016) Crossno et al, Science 351, 1058 (2016),…

  5. Viscous fluid Microscopics Hydrodynamics Navier-Stokes

  6. Hydrodynamic flow of electrons possible if… Sample size • Momentum-relaxing mean free path (“external scattering”): • Impurities • Phonons • Momentum-conserving mean free path (“internal scattering”): • e-e scattering W First proposed by Gurzhi in 1963. Manypaperssincethen...

  7. Ohmic Viscous Classical-Ballistic “Knudsen flow”

  8. Viscous fluid Microscopics Hydrodynamics Navier-Stokes

  9. Viscous electronic fluid Microscopics Hydrodynamics

  10. Two regimes If term dominates If term dominates Ohmic Viscous Non-local relation between current and electric field!

  11. Where did the convection term go? Today:

  12. Outline • Electron hydrodynamics – What and why? • Electron hydrodynamics in good metals • Using magnetic fields to detect hydro effects • Conclusion and outlook

  13. How to identify hydro effects? • Idea: Look at finite size corrections to transport coefficients • Problem: how to distinguish from ballistic effects? • Solution: use magnetic field 300 μm W

  14. Navier-Stokes under magnetic field Add B field Lorentz force Hall viscosity

  15. A tale of two viscosities Shear viscosity Hall viscosity Probed by Probed by

  16. A tale of two viscosities Shear viscosity Hall viscosity Probed by Probed by

  17. Hydrodynamic solution Result from Boltzmann theory for a charged Fermi liquid:

  18. Navier-Stokes is not enough In theory: Navier-Stokes In practice: : quasi-particle density Kinetic theory

  19. Boltzmann equation for quasi-particle density • Non-uniform current density • Collision integral: simplest form which conserves momentum • Momentum-relaxing scattering • Lorentz force

  20. Results from kinetic theory: magnetoresistance

  21. A tale of two viscosities Shear viscosity Hall viscosity Probed by Probed by

  22. Historical perspective on Hall effects Classical Hall Effect [Hall 1879] Quantum Hall Effect [von Klitzing 1980] Classical Viscous Hall Effect Quantum Viscous Hall Effect

  23. Hall resistivity => Hall viscosity W Hall viscosity could be measured by looking at finite-size effects in Hall resistivity Nicer probe than , because bulk value is “universal”

  24. Results of kinetic theory: Hall resistivity (normalized by bulk value)

  25. Hall voltage 0 B

  26. More on this tomorrow: arXiv:1806.01606

  27. Last part of the talk: local properties • So far we’ve only discussed quantities that are averaged over the cross section of the channel • What about their spatial dependence? Any smoking gun features of hydro? • Naïvely, yes: Ohmic Hydro

  28. Last part of the talk: local properties • So far we’ve only discussed quantities that are averaged over the cross section of the channel • What about their spatial dependence? Any smoking gun features of hydro? • Naïvely, yes: But: Ohmic Ballistic Hydro

  29. Magnetic fields are useful again: Ballistic Hydro Current density

  30. Magnetic fields are useful again: Ballistic Hydro Current density Hall electric field

  31. Magnetic fields are useful again: Ballistic Hydro Current density Hall electric field

  32. “Phase diagram” based on profile curvature Hall electric field Current

  33. Measurements Single-electron transistor [J.A. Sulpizio1†, L. Ella1†, A. Rozen1†, J. Birkbeck2,3, D.J. Perello2,3, D. Dutta1, M. Ben-Shalom2,3,4, T. Taniguchi5, K. Watanabe5, T. Holder1, R. Queiroz1, A. Stern1, T. Scaffidi6, A.K. Geim2,3, and S. Ilani,arXiv:1905.11662 ]

  34. Acknowledgements • UC Berkeley: Joel Moore • MPI Dresden: Nabhanila Nandi, Burkhard Schmidt, Philip Moll, PallaviKushwaha, Andrew Mackenzie  • Weizmann institute: Tobias Holder, Raquel Queiroz,Navot Silberstein, AsafRozen, Joseph A. Sulpizio, Lior Ella, ShahalIlani, Ady Stern • Thanks for your attention!

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