Hydrodynamic electron transport and nonlinear waves in graphene

Svintsov, Dmitry; Vyurkov, V.; Ryzhii, V.; Otsuji, T.

doi:10.1103/physrevb.88.245444

Cited by 86 publications

(107 citation statements)

References 38 publications

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“…In contrast to conventional metals and semiconductors, graphene is characterized by a linear excitation spectrum, which makes the system explicitly non-Galilean-invariant [6][7][8]12,13]. Consequently, the transport scattering time in graphene is strongly affected by the electron-electron interaction [14], which has to be taken into account on equal footing with disorder.…”

Section: Introductionmentioning

confidence: 99%

“…Consequently, the transport scattering time in graphene is strongly affected by the electron-electron interaction [14], which has to be taken into account on equal footing with disorder. At the same time, due to the classical nature of the Coulomb interaction between charge carriers in graphene, the system is also non-Lorentz-invariant [6][7][8]12,13]. As a result, the standard derivation [1,10,12,13] of the hydrodynamic equations has to be revisited [5][6][7].…”

Section: Introductionmentioning

confidence: 99%

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Hydrodynamics in graphene: Linear-response transport

et al. 2015

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We develop a hydrodynamic description of transport properties in graphene-based systems, which we derive from the quantum kinetic equation. In the interaction-dominated regime, the collinear scattering singularity in the collision integral leads to fast unidirectional thermalization and allows us to describe the system in terms of three macroscopic currents carrying electric charge, energy, and quasiparticle imbalance. Within this "three-mode" approximation, we evaluate transport coefficients in monolayer graphene as well as in double-layer graphene-based structures. The resulting classical magnetoresistance is strongly sensitive to the interplay between the sample geometry and leading relaxation processes. In small, mesoscopic samples, the macroscopic currents are inhomogeneous, which leads to a linear magnetoresistance in classically strong fields. Applying our theory to double-layer graphene-based systems, we provide a microscopic foundation for a phenomenological description of giant magnetodrag at charge neutrality and find the magnetodrag and Hall drag in doped graphene.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Hydrodynamics in graphene: Linear-response transport

et al. 2015

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“…This is the starting point for derivation of the nonlinear hydrodynamics, which is valid at time scales much longer than τ ee . In view of conservation of the particle number, energy, and momentum, as well as independent conservation of the number of particles in the two bands in graphene, we may write the local equilibrium distribution function as [12,14] where ε λ,k = λv g k denotes the energies of the electronic states with the momentum k in the band λ = ±, μ λ (r) the local chemical potential, the local temperature is encoded in β(r) = 1/T (r), and u(r) is the hydrodynamic velocity field which we define in the following (this field should not be confused with quasiparticle velocities v). The distribution function (1) follows from the standard argument similar to the Boltzmann's H-theorem [2]: the equilibrium state is characterized by time-independent entropy.…”

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confidence: 99%

Collision-dominated nonlinear hydrodynamics in graphene

et al. 2015

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U. BRISKOT et al. PHYSICAL REVIEW B 92, 115426 (2015) and therefore is not a conserved quantity. However, it is conserved in the collinear scattering processes and hence the corresponding relaxation rate does not contain the logarithmic enhancement. Finally, the imbalance current j I is proportional to the sign of the quasiparticle energy and to the velocity. Similarly to the electric current, it does not experience logarithmically enhanced relaxation. The imbalance current is related to the quasiparticle number or imbalance density [10] n I = n + + n − , where n + and n − are the particle numbers in the upper (conduction) and lower (valence) bands. Neglecting the Auger processes, quasiparticle recombination due to, e.g., electron-phonon interaction, and three-particle collisions due to weak coupling, one finds that n + and n − are conserved independently. In this case, which will be considered in the rest of the paper, not only the total charge density n = n + − n − , but also the quasiparticle density n I is conserved.At times longer than τ g , physical observables can be described within the macroscopic (or hydrodynamic) approach. The existence of the three slow-relaxing modes in graphene implies a peculiar two-step thermalization.Short-time electron-electron scattering (at time scales up to τ g ) establishes the so-called "unidirectional thermalization" [24]: the collinear scattering singularity implies that the electron-electron interaction is more effective along the same direction. Within linear response [18], one can express the nonequilibrium distribution function in terms of the three macroscopic currents j , j E , and j I . The currents can then be found from the macroscopic equations. The currents j and j I are not conserved and can be relaxed by the electron-electron interaction. Close to charge neutrality, the corresponding relaxation rates can be estimated as [6,40] g . These rates enter the macroscopic equations as frictionlike terms. The macroscopic linear-response theory has the same form on time scales shorter or longer than τ ee .Beyond linear response, the scattering processes characterized by the time scale τ ee play an important role in thermalizing quasiparticles moving in different directions and thus lead to establishing the local equilibrium. This is the starting point for derivation of the nonlinear hydrodynamics, which is valid at time scales much longer than τ ee . In view of conservation of the particle number, energy, and momentum, as well as independent conservation of the number of particles in the two bands in graphene, we may write the local equilibrium distribution function as [12,14] where ε λ,k = λv g k denotes the energies of the electronic states with the momentum k in the band λ = ±, μ λ (r) the local chemical potential, the local temperature is encoded in β(r) = 1/T (r), and u(r) is the hydrodynamic velocity field which we define in the following (this field should not be confused with quasiparticle velocities v). The distribution function (1) follows from the sta...

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“…This idea has stimulated the re-examination of various 'classical' plasma instabilities in graphene, including the beam and resistive instabilities [18], Dyakonov-Shur self-excitation [10,11], and generation due to the negative differential conductance [19]. On the other hand, the plasmon gain can be provided by the photogenerated electrons and holes recombining with plasmon emission [20], which opens up the prospects of graphene-based spasers [21].…”

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confidence: 99%

“…Among more sophisticated predictions there stand the existence of weakly damped transverse electric plasmons [6] and quasi-neutral electron-hole sound waves near the neutrality point [7,8]. Some peculiar types of plasmons can be excited in the graphene p − n junctions [9], field-effect transistors [10,11], optoelectronic modulators [12], and nanomechanical resonators [13] engaging for the improved device performance at the terahertz frequencies.Unfortunately, the experimental studies of graphene plasmons are yet unable to confirm or refute many of these predictions. To achieve an extreme plasmon confinement, one has to sacrifice their propagation length.…”

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confidence: 99%

Plasmons in tunnel-coupled graphene layers: Backward waves with quantum cascade gain

et al. 2016

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We predict a new mechanism of surface plasmon amplification in graphene-insulator-graphene van der Waals heterostructures. The amplification occurs upon the stimulated interlayer electron tunneling accompanied by the emission of a coherent plasmon. The quantum-mechanical calculations of the non-local high-frequency tunnel conductivity show that a relative smallness of the tunneling exponent can be compensated by a strong resonance due to the enhanced tunneling between electron states with collinear momenta in the neighboring graphene layers. With the optimal selection of the barrier layer, the surface plasmon gain due to the inelastic tunneling can compensate or even exceed the loss due to both Drude and interband absorption. The tunneling emission of the surface plasmons is robust against a slight twist of the graphene layers and might explain the electroluminescence from the tunnel-coupled graphene layers observed in the recent experiments.The ultrarelativistic nature of electrons in graphene gives rise to the uncommon properties of their collective excitations -surface plasmons [1][2][3]. The deep subwavelength confinement [3], the unconventional density dependence of frequency [4,5], and the absence of Landau damping [4] are probably the most well-known features of plasmons in graphene-based heterostructures. Among more sophisticated predictions there stand the existence of weakly damped transverse electric plasmons [6] and quasi-neutral electron-hole sound waves near the neutrality point [7,8]. Some peculiar types of plasmons can be excited in the graphene p − n junctions [9], field-effect transistors [10,11], optoelectronic modulators [12], and nanomechanical resonators [13] engaging for the improved device performance at the terahertz frequencies.Unfortunately, the experimental studies of graphene plasmons are yet unable to confirm or refute many of these predictions. To achieve an extreme plasmon confinement, one has to sacrifice their propagation length. The latter is of the order of several micrometers at the infrared frequencies [14,15] and is limited by the interband absorption in intrinsic samples and somewhat lower Drude absorption in the doped ones [16]. The experimentally reported quality factors of graphene plasmons reach only five for graphene on SiO 2 [14, 15], and 25 for graphene encapsulated in hexagonal boron nitride [17] at room temperature. In the latter case, the damping is due to the scattering by the intrinsic acoustic phonons [16] and can be suppressed only by lowering the temperature.Instead of reducing the plasmon loss, it is possible to overcome the damping by introducing the gain medium which can replenish the energy being dissipated upon scattering. This idea has stimulated the re-examination of various 'classical' plasma instabilities in graphene, including the beam and resistive instabilities [18], Dyakonov-Shur self-excitation [10,11], and generation due to the negative differential conductance [19]. On the other hand, the plasmon gain can be provided by the photogenerated ele...

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Hydrodynamic electron transport and nonlinear waves in graphene

Cited by 86 publications

References 38 publications

Hydrodynamics in graphene: Linear-response transport

Hydrodynamics in graphene: Linear-response transport

Collision-dominated nonlinear hydrodynamics in graphene

Plasmons in tunnel-coupled graphene layers: Backward waves with quantum cascade gain

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