Quantum aspects of hydrodynamic transport from weak electron-impurity scattering

Abstract

Recent experimental observations of apparently hydrodynamic electronic transport have generated much excitement. However, theoretical understanding of the observed non-local transport (whirlpool) effects and parabolic (Poiseuille-like) current profiles has remained at the level of a phenomenological analogy with classical fluids. A more microscopic account of genuinely hydrodynamic electronic transport is difficult because such behavior requires strong interactions to diffuse momentum. Here, we show that the non-local conductivity effects actually observed in experiments can indeed occur for free fermion systems in the presence of weak disorder. By explicit calculation of the conductivity at finite wavevector σ(q) for selected weakly disordered free fermion systems, we propose experimental strategies for demonstrating distinctive quantum effects in non-local transport at odds with the expectations of classical kinetic theory. Our results imply that the observation of whirlpools or other "hydrodynamic" effects does not guarantee the dominance of electron-electron scattering over electron-impurity scattering. arXiv:1910.14043v2 [cond-mat.str-el]

Conformal maps of viscous electron flow in the Gurzhi crossover

“…We note that quantum aspects of nonlocal transport from weak electron-impurity scattering was discussed recently in Ref. [40]. However, the result for σ(q) was not properly derived in the model, furthermore small-q expansion to q 2 order to generate spatial scale, q 2 → −∇ 2 , simply does not apply in the quasiballistic regime ql 1.…”

“…We thank Aaron Hui and Eun-Ah Kim for the communication regarding Ref. [40]. We are grateful to Igor Burmistrov for the discussions on the diagrammatic evaluation of the localization corrections to the conductivity at finite momentum and to Boris Narozhny for the discussion of boundary conditions in the viscous regime.…”

Beyond Ohm's law -- Bernoulli effect and streaming in electron hydrodynamics

“…However, these results are all in the linear response regime and can be ultimately described using a non-local variant of Ohm's law. Indeed, the linearized Navier-Stokes equation can be simply recast using a nonlocal conductivity σ(q) [25][26][27] . While non-local transport can certainly be couched in the formalism of hydrodynamics, it is also clear that inherently finite length scales of a realistic fermionic system can conspire to produce non-local transport indistinguishable from that implied by the Navier-Stokes equation 27 .…”

“…Indeed, the linearized Navier-Stokes equation can be simply recast using a nonlocal conductivity σ(q) [25][26][27] . While non-local transport can certainly be couched in the formalism of hydrodynamics, it is also clear that inherently finite length scales of a realistic fermionic system can conspire to produce non-local transport indistinguishable from that implied by the Navier-Stokes equation 27 . Other ways of accessing electron hydrodynamics are of great interest as we seek to understand and isolate competing effects.…”

Evidence for Local Spots of Viscous Electron Flow in Graphene at Moderate Mobility

“…Inverted electric fields also appear in the ballistic regime, if current is injected via a constriction. [62][63][64] The dilution of current density in the diffraction pattern behind a constriction naturally leads to current vorticity that eventually causes inverted electric fields via boundary scattering. [62][63][64] We cannot exclude that such effects contribute to the observed field inversion in our experiments, if one substitutes the boundaries by local obstacles.…”