Vorticity of viscous electronic flow in graphene

Abstract

In ultra-pure materials electrons may exhibit a collective motion similar to the hydrodynamic flow of a viscous fluid, the phenomenon with far reaching consequences in a wide range of many body systems from black holes to high-temperature superconductivity. Yet the definitive detection of this intriguing behavior remains elusive. Until recently, experimental techniques for observing hydrodynamic behavior in solids were based on measuring macroscopic transport properties, such as the "nonlocal" (or "vicinity") resistance, which may allow alternative interpretation. Earlier this year two breakthrough experiments demonstrated two distinct imaging techniques making it possible to "observe" the electronic flow directly. We demonstrate that a hydrodynamic flow in a long Hall bar (in the absence of magnetic field) exhibits a nontrivial vortex structure accompanied by a sign-alternating nonlocal resistance. An experimental observation of such unique flow pattern could serve a definitive proof of electronic hydrodynamics.Traditional fluid mechanics 1 describes long-distance properties of conventional (e.g., water, oil, etc.) and quantum (e.g., 3 He) fluids equally well 2,3 . The key feature uniting these diverse many body systems is the short-ranged or collision-like nature of interactions between the constituent particles that conserve momentum. In the simplest case of a dilute gas (e.g., air) the hydrodynamic equations can be derived from the kinetic theory 4 . The resulting theory is however more general than the derivation: the hydrodynamic equations provide a universal description applicable to any system within the same symmetry class.The usual theory of the electron transport in solids also relies on the kinetic theory 5 , but with momentumrelaxing scattering processes typically dominating over the momentum-conserving electron-electron interaction. Unlike the conventional fluids, electrons in solids exist in the environment created by a crystal lattice where scattering off either lattice imperfections (or "disorder") or lattice vibrations ("phonons") does not conserve momentum. At length scales exceeding the mean free path dis (or e−ph ) the electrons exhibit diffusive motion 2,5 . In relatively small, mesoscopic samples of the size smaller than (or comparable to) the mean free path, L dis , e−ph , the electrons can cross the sample ballistically 6,7 .In contrast, should one manage to fabricate a sample, where the momentum-conserving electron-electron interaction were the dominant scattering process, the macroscopic flow of electrons would be hydrodynamic 8-10 . Envisioned by Gurzhi 10 long time ago, this idea got traction only with the emergence of ultra-pure materials 11-20 . Yet, while it has been established that transport properties of such systems deviate significantly from the traditional expectation 5 , the "hydrodynamic" interpretation of the observed results may still be considered as controversial. In particular, the nonlocal resistance (a tool often used to uncover hydrodynamic transport 14,15,20 ) has ...

Heat vortex in hydrodynamic phonon transport of two-dimensional materials

“…In addition, as normal scattering dominates the heat conduction, the corresponding macroscopic Guyer-Krumhansl (G-K) equation [14,22,30,[45][46][47] is similar to the Navier-Stokes equation in fluid dynamics [36,38]. Hence, will phonon transport like the vortexes in fluid dynamics [36][37][38] or viscous electron flow in hall bar geometries [48][49][50][51]?…”

“…In this work, motivated by the viscous fluid dynamics [36][37][38] or viscous electron flow [48][49][50][51], the heat vortexes in two different structures (porous (Fig. 2) and ribbon ( Fig.…”

Giant nonlocality in nearly compensated two-dimensional semimetals

“…2 and Ref. [17]). The neutral current appearing in the two-fluid system is decoupled from the electric current and is practically undetectable.…”

“…Traditionally, such patterns were detected using nonlocal transport measurements [1][2][3][4][5][6][7], i.e., by measuring voltage drops between various leads other than the source and drain. Devised to study ballistic propagation of charge carriers in mesoscopic systems, these techniques were recently applied to investigate possible hydrodynamic behavior in ultrapure conductors [8][9][10][11][12], where the unusual behavior of the nonlocal resistance is often associated with viscosity of the electronic system [13][14][15][16][17].…”

“…To highlight the difference between the one-and twocomponent systems, we briefly recall the macroscopic description of electronic transport in the standard (former) case. Allowing for nonuniform charge density, the linear relation between the electric current J and the external fields E, B could be formulated as [17,32,33]…”