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Thomas Scaffidi UC Berkeley

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 ]

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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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