Counterflows in viscous electron-hole fluid

Abstract

In ultra-pure conductors, collective motion of charge carriers at relatively high temperatures may become hydrodynamic such that electronic transport may be described similarly to a viscous flow. In confined geometries (e.g., in ultra-high quality nanostructures), the resulting flow is Poiseuille-like. When subjected to a strong external magnetic field, the electric current in semimetals is pushed out of the bulk of the sample towards the edges. Moreover, we show that the interplay between viscosity and fast recombination leads to the appearance of counterflows. The edge currents possess a non-trivial spatial profile and consist of two stripe-like regions: the outer stripe carrying most of the current in the direction of the external electric field and the inner stripe with the counterflow.Recently, signatures of the hydrodynamic behavior of charge carriers have been observed in graphene 1-3 , palladium cobaltate 4 , and the Weyl semimetal WP 2 5 . This phenomenon occurs in the intermediate temperature regime, where the typical length scale of electronelectron interaction, ee , is much shorter than any other relevant scale in the problem including those characterizing scattering off potential disorder and electron-phonon scattering, ee dis , ph . In this case, the independent particle approximation is violated, the motion of charge carriers becomes collective, and transport properties of the system are determined by interaction 6,7 .Viscous electronic fluids exhibit unusual transport properties 6,7 , such as superballistic transport 3,8,9 , nonlocal resistivity 1,10 , and negative magnetoresistance 5,11-14 . The latter effect may also occur in two-component systems (e.g., semimetals or narrow-band semiconductors) near the charge neutrality point 15 . In such systems, response of the charge carriers to the external magnetic field is non-universal depending on the interplay between inelastic scattering processes and sample geometry.In the hydrodynamic regime, electronic transport can be described with the help of the linearized hydrodynamic theory 12-15 generalizing the standard Navier-Stokes equation 16 . The parameters of the theory, including the shear viscosity coefficient, η xx , and quasiparticle recombination time, τ R , can be derived, at least in principle, from the kinetic equation approach (for a particular case of graphene, see Ref. 17). Due to the above two processes, the electric current density in a finite-sized sample is nonuniform. In long samples (where the length is much larger than the width, L W ), viscous effects tend to form a Poiseuille-like flow. The actual profile of the current density depends on the ratio of the typical length scale describing the viscous effects, the so-called Gurzhi length 15 , G (B), and the sample width, W . In the limit where the Gurzhi length exceeds the width, G W , the current density profile is parabolic, simi-FIG. 1: Schematic plot of the inhomogeneous electric current density in the regime of fast recombination and strong enough magnetic field. The color map e...

Optical conductivity in graphene: Hydrodynamic regime

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