Hydrodynamic electron transport and nonlinear waves in graphene

Abstract

We derive the system of hydrodynamic equations governing the collective motion of massless fermions in graphene. The obtained equations demonstrate the lack of Galilean- and Lorentz invariance, and contain a variety of nonlinear terms due to quasi-relativistic nature of carriers. Using those equations, we show the possibility of soliton formation in electron plasma of gated graphene. The quasi-relativistic effects set an upper limit for soliton amplitude, which marks graphene out of conventional semiconductors. The lack of Galilean and Lorentz invariance of hydrodynamic equations is revealed in spectra of plasma waves in the presence of steady flow, which no longer obey the relations of Doppler shift. The possibility of plasma wave excitation by direct current in graphene channels is also discussed.

8 pages, 3 figures

References in corpus (12)

• Graphene plasmonics
• Graphene field effect transistors as room-temperature Terahertz detectors
• Quantum critical transport in clean graphene
• Collective modes of the massless Dirac plasma
• Quantum-critical relativistic magnetotransport in graphene
• Drude weight, plasmon dispersion, and a.c. conductivity in doped graphene sheets
• Conductivity of the defectless Graphene
• Voltage and temperature dependencies of conductivity in gated graphene
• Theory of the plasma-wave photoresponse of a gated graphene sheet
• Coulomb interaction in graphene: Relaxation rates and transport
• Hydrodynamic Model for Conductivity in Graphene
• Electrical excitation of shock and soliton-like waves in two-dimensional electron channels

Cited by in corpus (41)

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• Hydrodynamics in graphene: Linear-response transport
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• Fizeau Drag in Graphene Plasmonics
• Collision-dominated nonlinear hydrodynamics in graphene
• Hydrodynamic approach to two-dimensional electron systems
• Magnetoresistance of compensated semimetals in confined geometries
• Emission of plasmons by drifting Dirac electrons: where hydrodynamics matters
• Emission and amplification of surface plasmons in resonant - tunneling van der Waals heterostructures
• Plasmons in tunnel-coupled graphene layers: backward waves with quantum cascade gain
• Hydrodynamic theory of the Dyakonov-Shur instability in graphene transistors
• Drift-induced modifications to the dynamical polarization of graphene
• Hydrodynamical study of Terahertz emission in magnetized graphene field-effect transistors
• Terahertz Laser Combs in Graphene Field-Effect Transistors
• Thermal transport in compensated semimetals: a mystery explained
• S-shaped current-voltage characteristics of n+-i-n-n+ graphene field-effect transistors due the Coulomb drag of quasi-equilibrium electrons by ballistic electrons
• Beyond Ohm's law -- Bernoulli effect and streaming in electron hydrodynamics
• Electrical plasmon detection in graphene waveguides
• Comment on "Negative Landau damping in bilayer graphene"
• Spin generalizations of the Benjamin-Ono equation
• Coulomb electron drag mechanism of terahertz plasma instability in n+-i-n-n+ graphene FETs with ballistic injection
• Graphene as a source of entangled plasmons
• Resonant plasmonic detection of terahertz radiation in field-effect transistors with the graphene channel and the black-As${}_x$P${}_{1-x}$ gate layer
• Plasma Instability and Amplified Mode Switching Effect in THz Field Effect Transistors with Grating Gate
• Plasmon Fizeau drag in 3D Dirac and Weyl semimetals
• Effect of Coulomb carrier drag and terahertz plasma instability in p+-p-i-n-n+ graphene tunneling transistor structures
• Electro-Optics of Current-carrying Graphene
• Nonlinear density waves on graphene electron fluids
• Terahertz Radiation from the Dyakonov-Shur Instability of Hydrodynamic Electrons in a Corbino Geometry
• Ballistic injection terahertz plasma instability in graphene n+-i-n-n+ field-effect transistors and lateral diodes
• Strong suppression of electron convection in Dirac and Weyl semimetals
• Dipole excitation of collective modes in viscous two-dimensional electron systems
• Effects of Dissipation on Solitons in the Hydrodynamic Regime of Graphene
• Spatially dispersive dynamical response of hot carriers in doped graphene
• Hydrodynamics of the electronic Fermi liquid: a pedagogical overview
• Origin of the Temperature Collapse of the Electric Conductivity in Bilayer Graphene
• Plasma solitons in gated two-dimensional electron systems: exactly solvable analytical model for the regime beyond weak non-linearity
• Thermal dissipation in two dimensional relativistic Fermi gases with a relaxation time model
• Hydrodynamic electrons in Graphene: a viscous boundary-layer description
• Dissipation in 2D degenerate gases with non-vanishing rest mass
• Entropy Wave Instability in Dirac and Weyl Semimetals