Optical conductivity in graphene: Hydrodynamic regime

Narozhny, B. N.

doi:10.1103/physrevb.100.115434

Cited by 17 publications

(31 citation statements)

References 52 publications

(205 reference statements)

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“…where η is the shear viscosity 14,20,32 , n is the carrier density, E is the electric field, v g is the Fermi velocity, P is the thermodynamic pressure, µ is the chemical potential, and τ dis is the disorder mean free time, see Appendix A for details. At high enough densities, the electric current is proportional to the hydrodynamic velocity, J = enu.…”

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“…where ν is the kinematic viscosity 1,14,20,32 and l is the typical length scale in the problem (e.g., the width of the graphene strip) in analogy to the standard composition of the Reynolds number 1 . For small values of the Gurzhi number the electrons propagate ballistically with a flat velocity profile across the bulk of the sample, while large values of Gu correspond to a Poiseuille-like flow with a nonuniform velocity distribution.…”

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“…where η is the shear viscosity 14,20,32 , n is the carrier density, E is the electric field, v g is the Fermi velocity in graphene, and τ dis is the disorder mean free time. The enthalpy W and pressure P are related to the energy density n E in graphene by the "equation of state" 30,31…”

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Vorticity of viscous electronic flow in graphene

Danz

Narozhny

2020

2D Mater.

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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 ...

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Vorticity of viscous electronic flow in graphene

Danz

Narozhny

2020

2D Mater.

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“…Secondly, the so-called collinear scattering singularity [10][11][12][15][16][17][18][19] allows for a non-perturbative solution to the kinetic equation focusing on the three hydrodynamic modes [19][20][21]. This yields the general form of the hydrodynamic equations and the kinetic coefficients [21][22][23]. To be of any practical value, the latter calculation has to be combined with the renormalization group approach [24] since the effective coupling constant in real graphene (either encapsulated or put on a dielectric substrate) is not too small, α g ≈ 0.2 − 0.3 [25,26].…”

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Hydrodynamic Approach to Electronic Transport in Graphene

et al. 2017

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The last few years have seen an explosion of interest in hydrodynamic effects in interacting electron systems in ultra-pure materials. In this paper we briefly review the recent advances, both theoretical and experimental, in the hydrodynamic approach to electronic transport in graphene, focusing on viscous phenomena, Coulomb drag, non-local transport measurements, and possibilities for observing nonlinear effects.Hydrodynamics describes a great variety of phenomena around (and inside) us, including, e.g., the flow of water in rivers, seas, and oceans, atmospheric phenomena, aircraft motion, the flow of petroleum in pipelines, or the blood flow through blood vessels in humans and animals. It has been realized a long time ago that the flow of electrons in a conductor should, under certain circumstances, also obey the laws of hydrodynamics. In particular, Gurzhi 1,2 predicted that electrons can exhibit a Poiseuille-type flow 3,4 analogous to that of liquids in pipes. This should result in an initial power-law decrease of resistivity with the transverse cross-section of a sample and temperature, leading to a pronounced minimum. It has turned out, however, that an experimental realization of such a regime in a metal or a semiconductor is a highly non-trivial task. Three decades have passed before de Jong and Molenkamp 5 observed the Gurzhi effect, and even in that work the magnitude of the effect did not exceed 20%.Why is it so difficult to implement electron hydrodynamics in a laboratory experiment? In contrast to molecules of a conventional liquid, electrons move in the environment formed by the crystal lattice. Therefore, the electrons experience not only collisions among themselves, but also scatter off thermally excited lattice vibrations -phonons -as well as various lattice imperfections (impurities). The hydrodynamic regime is realized when the frequency of electron-electron collisions is much larger than the rates of both, electron-phonon and electron-impurity scattering. These two requirements limit the temperature window for the hydrodynamic flow both from above and from below, and may even be in a conflict with each other. In a typical solid, the elastic impurity scattering dominates electronic transport at low temperatures, whereas at high temperatures the leading mechanism is the electron-phonon scattering. Thus, the requirement of the electron-electron scattering being the fastest process -which is the key condition for the hydrodynamics -may only be satisfied, if at all, in an intermediate temperature range. It turns out that this regime is not well developed in conventional conductors, with the possible exception of the ultrahigh-mobility GaAs quantum wells 6-8 exhibiting negative magnetoresistance 9 and ultra-pure palladium cobaltate 10 . The experimental discovery of graphene 11 has given a new boost to the research in the field of quantum transport. In particular, it has been realized that, among other remarkable properties, graphene is an excellent material for the realization of hydrodynamic flo...

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“…Secondly, the so-called collinear scattering singularity [7][8][9][10][11][12][13][14] allows for a non-perturbative solution to the kinetic (Boltzmann) equation focusing on the three hydrodynamic modes [13,15,16]. As a result, one can determine the general form of the hydrodynamic equations and evaluate the kinetic coefficients [16][17][18]. To be of any practical value, the latter calculation has to be combined with the renormalization group approach [19] since the effective coupling constant in real graphene (either encapsulated or put on a dielectric substrate) is not too small, α g ≈ 0.2 − 0.3 [20,21].…”

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Hydrodynamic Approach to Electronic Transport in Graphene: Energy Relaxation

Narozhny

Gornyi

2021

Front. Phys.

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In nearly compensated graphene, disorder-assisted electron-phonon scattering or “supercollisions” are responsible for both quasiparticle recombination and energy relaxation. Within the hydrodynamic approach, these processes contribute weak decay terms to the continuity equations at local equilibrium, i.e., at the level of “ideal” hydrodynamics. Here we report the derivation of the decay term due to weak violation of energy conservation. Such terms have to be considered on equal footing with the well-known recombination terms due to nonconservation of the number of particles in each band. At high enough temperatures in the “hydrodynamic regime” supercollisions dominate both types of the decay terms (as compared to the leading-order electron-phonon interaction). We also discuss the contribution of supercollisions to the heat transfer equation (generalizing the continuity equation for the energy density in viscous hydrodynamics).

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Optical conductivity in graphene: Hydrodynamic regime

Cited by 17 publications

References 52 publications

Vorticity of viscous electronic flow in graphene

Vorticity of viscous electronic flow in graphene

Hydrodynamic Approach to Electronic Transport in Graphene

Hydrodynamic Approach to Electronic Transport in Graphene: Energy Relaxation

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