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.
Collective behavior is one of the most intriguing aspects of the hydrodynamic approach to electronic transport. Here we provide a consistent, unified calculation of the dispersion relations of the hydrodynamic collective modes in graphene. Taking into account viscous effects, we show that the hydrodynamic sound mode in graphene becomes overdamped at sufficiently large momentum scales. Extending the linearized theory beyond the hydrodynamic regime, we connect the diffusive hydrodynamic charge density fluctuations with plasmons.
In this paper I report a pedagogical derivation of the unconventional electronic hydrodynamics in graphene on the basis of the kinetic theory. While formally valid in the weak coupling limit, this approach allows one to derive the unconventional hydrodynamics in the system which is neither Galilean- nor Lorentz-invariant, such that hydrodynamic equations can not be inferred from symmetry arguments. I generalize earlier work to include external magnetic fields and give explicit expressions for dissipative coefficients, the shear viscosity and electrical conductivity. I also compare the resultin…
The last few years have seen an explosion of interest in hydrodynamic effects in interacting electron systems in ultra-pure materials. One such material, graphene, is not only an excellent platform for the experimental realization of the hydrodynamic flow of electrons, but also allows for a controlled derivation of the hydrodynamic equations on the basis of kinetic theory. The resulting hydrodynamic theory of electronic transport in graphene yields quantitative predictions for experimentally relevant quantities, e.g. viscosity, electrical conductivity, etc. Here I review recent theoretical adv…
Experimental investigation of hydrodynamics in electron fluids is a highly topical research area that emerged during the last few years. A recent measurement of the optical conductivity in graphene [P. Gallagher et.al, Science 364, 158 (2019)] offers a possibility of experimental determination of microscopic time scales describing scattering processes in the electronic fluid. In this paper, I report a theoretical calculation of the optical conductivity in graphene at arbitrary doping levels, within the whole "hydrodynamic" temperature range, and for arbitrary, non-quantizing magnetic fields. T…
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 hi…
We present an effective hydrodynamic theory of electronic transport in graphene in the interaction-dominated regime. We derive the emergent hydrodynamic description from the microscopic Boltzmann kinetic equation taking into account dissipation due to Coulomb interaction and find the viscosity of Dirac fermions in graphene for arbitrary densities. The viscous terms have a dramatic effect on transport coefficients in clean samples at high temperatures. Within linear response, we show that viscosity manifests itself in the nonlocal conductivity as well as dispersion of hydrodynamic plasmons. Bey…
Generic interacting many-body quantum systems are believed to behave as classical fluids on long time and length scales. Due to rapid progress in growing exceptionally pure crystals, we are now able to experimentally observe this collective motion of electrons in solid-state systems, including graphene. We present a review of recent progress in understanding the hydrodynamic limit of electronic motion in graphene, written for physicists from diverse communities. We begin by discussing the "phase diagram" of graphene, and the inevitable presence of impurities and phonons in experimental systems…
Motivated by recent experimental progress in preparing encapsulated graphene sheets with ultra-high mobilities up to room temperature, we present a theoretical study of dc transport in doped graphene in the hydrodynamic regime. By using the continuity and Navier-Stokes equations, we demonstrate analytically that measurements of non-local resistances in multi-terminal Hall bar devices can be used to extract the hydrodynamic shear viscosity of the two-dimensional (2D) electron liquid in graphene. We also discuss how to probe the viscosity-dominated hydrodynamic transport regime by scanning probe…
We show that hydrodynamic collision processes of graphene at the neutrality point can be described in terms of a Fokker-Planck equation with fractional derivative, corresponding to a Lévy flight in momentum space. Thus, electron-electron collisions give rise to frequent small-angle scattering processes that are interrupted by rare large-angle events. The latter give rise to superdiffusive dynamics of collective excitations. We argue that such superdiffusive dynamics is of more general importance to the out-of-equilibrium dynamics of quantum-critical systems.
Graphene has generated a lot of research interest due to its special properties, which include a hydrodynamic regime. It is not yet clear however which boundary condition such a hydrodynamic current flow satisfies. The aim of this paper is to investigate the effect of different boundary conditions on the potential in an infinite strip of graphene, in which the electrons can be treated hydrodynamically. The boundary conditions on the current range continuously from no-slip to a free boundary. We analyse the situation for two different orientations of the source and sink, inspired by recent pape…
We study hydrodynamic electron magnetotransport in graphene devices. We show that in these systems a distinct mechanism of magnetoresistance appears, which is absent in systems with Galilean-invariant electron liquid. The resulting magnetoresistance depends on the intrinsic conductivity and viscosity of the electron liquid, and becomes especially pronounced near charge neutrality. We obtain analytic expressions for magnetoransport coefficients of Corbino devices, and obtain estimates for the electrical and thermal magnetoresistances for monolayer and bilayer systems at charge neutrality. Magne…
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 i…
Systems in which interparticle interactions prevail can be described by hydrodynamics. This regime is typically difficult to access in the solid state for electrons. However, the high purity of encapsulated graphene combined with its advantageous phonon properties make it possible, and hydrodynamic corrections to the conductivity of graphene have been observed. Examples include electron whirlpools, enhanced flow through constrictions as well as a Poiseuille flow profile. An electronic device relying specifically on viscous behaviour and acting as a viscometer has however been lacking. Here, we…
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 coeffcients in monolayer graphene as well as in double-layer graphene-based structures. The resulting classical magne…
Recent experiments have revealed that novel nonequilibrium states consistent with the hydrodynamic description of electrons are realized in ultrapure graphene, which hosts the valley degrees of freedom. Here, we formulate a theory of electron hydrodynamics including dissipation processes of the valley angular momentum by employing the concept of micropolar fluids. As a result, our theory proposes a novel strategy to generate a valley polarization by the microrotation. We uncover that the rotational viscosity induces longitudinal valley currents which are second order in electric fields.
Electrons behave like a classical fluid with a momentum distribution function that varies slowly in space and time when the quantum mechanical carrier-carrier scattering dominates over all other scattering processes. Recent experiments in monolayer and bilayer graphene have reported signatures of such hydrodynamic electron behavior in ultra-clean devices. In this theoretical work, starting from a microscopic treatment of electron-electron, electron-phonon and electron-impurity interactions within the Random Phase Approximation, we demonstrate that monolayer and bilayer graphene both host two d…
Several hydrodynamic descriptions of charge transport in graphene have been presented in the late years. We discuss a general hydrodynamic model governing the dynamics of a two-dimensional electron gas in a magnetized field-effect transistor in the slow drift regime. The Dyakonov--Shur instability is investigated including the effect of weak magnetic fields (i.e. away from Landau levels). We show that the gap on the dispersion relation prevents the instability to reach the lower frequencies thus imposing a limit on the Mach number of the electronic flow. Furthermore, we discuss that the presen…
The electrodynamics of a two-dimensional gas of massless fermions in graphene is studied by a collisionless hydrodynamic approach. A low-energy dispersion relation for the collective modes (plasmons) is derived both in the absence and in the presence of a perpendicular magnetic field. The results for graphene are compared to those for a standard two-dimensional gas of massive electrons. We further compare the results within the classical hydrodynamic approach to the full quantum mechanical calculation in the random phase approximation. The low-energy dispersion relation is shown to be a good a…
Imaging flat band electron hydrodynamics in biased bilayer graphene
University of California, Santa Barbara（加州大学圣塔芭芭拉分校）；University of Colorado, Boulder（科罗拉多大学博尔德分校）；National Institute for Materials Science（国立材料研究所）；University of Colorado, Denver（科罗拉多大学丹佛分校）
We present a comprehensive theory of the Dyakonov-Shur (DS) plasma instability in current-biased graphene transistors. Using the hydrodynamic approach, we derive equations describing the DS instability in the two-dimensional electron fluid in graphene at arbitrary values of electron drift velocity. These nonlinear equations together with Maxwell's equations are used for numerical analysis of the spatial and temporal evolution of the graphene electron system after the DS instability is triggered by random current fluctuations. We analyze conditions necessary for the onset of the DS instability …
We consider hydrodynamic electron transport in the Hall-bar geometry. The theory is developed for systems with non-Galilean-invariant electron liquids. We show that inhomogeneity of the electron density induced by long-range disorder and gating leads to mixing between the hydrodynamic transport mode and transport relative to the electron liquid. For graphene systems near charge neutrality, these effects lead to strong coupling of the hydrodynamic flow to charge transport. As a result, the effective electrical conductivity of the system may significantly exceed the intrinsic conductivity of the…
We determine the information scrambling rate $λ_{L}$ due to electron-electron Coulomb interaction in graphene. $λ_{L}$ characterizes the growth of chaos and has been argued to give information about the thermalization and hydrodynamic transport coefficients of a many-body system. We demonstrate that $λ_{L}$ behaves for strong coupling similar to transport and energy relaxation rates. A weak coupling analysis, however, reveals that scrambling is related to dephasing or single particle relaxation. Furthermore, $λ_{L}$ is found to be parametrically larger than the collision rate relevant for hydr…
We propose a hydrodynamic model describing steady-state and dynamic electron and hole transport properties of graphene structures which accounts for the features of the electron and hole spectra. It is intended for electron-hole plasma in graphene characterized by high rate of intercarrier scattering compared to external scattering (on phonons and impurities), i.e., for intrinsic or optically pumped (bipolar plasma), and gated graphene (virtually monopolar plasma). We demonstrate that the effect of strong interaction of electrons and holes on their transport can be treated as a viscous frictio…
Hydrodynamic behavior in electronic systems is commonly accepted to be associated with extremely clean samples such that electron-electron collisions dominate and total momentum is conserved. Contrary to this, we show that in monolayer graphene the presence of disorder is essential to enable an unconventional hydrodynamic regime which exists near the charge neutrality point and is characterized by a large enhancement of the Wiedemann-Franz ratio. Although the enhancement becomes more pronounced with decreasing disorder, the very possibility of observing the effect depends crucially on the pres…
Based on the recently developed picture of an electronic ideal relativistic fluid at the Dirac point, we present an analytical model for the conductivity in graphene that is able to describe the linear dependence on the carrier density and the existence of a minimum conductivity. The model treats impurities as submerged rigid obstacles, forming a disordered medium through which graphene electrons flow, in close analogy with classical fluid dynamics. To describe the minimum conductivity, we take into account the additional carrier density induced by the impurities in the sample. The model, whic…
We previously show [JETP Letters, {\bf 114}, 763 (2021)] that a graphene sample placed on a ferromagnetic substrate demonstrates a cooperative magnetoelectronic instability. The instability induces a gap in the electronic spectrum and a canting deformation of the magnetization near the graphene-substrate interface. In this paper we prove that the interaction between the electrons in graphene strongly enhances the instability. Our estimates suggest that in the presence of even a moderate interaction the instability can be sufficiently pronounced to be detected experimentally in a realistic sett…
Graphene, the two-dimensional form of carbon presents outstanding electronic and transport properties. This gives hope for the development of applications in nanoelectronics. However, for industrial purpose, graphene has to be supported by a substrate. We focus here on the graphene-on-SiC system to discuss how the SiC substrate interacts with the graphene layer and to show the effect of the interface on graphene atomic and electronic structures.
We apply the semi-classical quantum Boltzmann formalism for the computation of transport properties to multilayer graphene. We compute the electrical conductivity as well as the thermal conductivity and thermopower for Bernal-stacked multilayers with an even number of layers. We show that the window for hydrodynamic transport in multilayer graphene is similar to the case of bilayer graphene. We introduce a simple hydrodynamic model which we dub the multi-fluid model and which can be used to reproduce the results for the electrical conductivity and thermopower from the quantum Boltzmann equatio…
We probe the local inhomogeneities of the electronic properties of graphene at the nanoscale using scanning probe microscopy techniques. First, we focus on the study of the electronic inhomogeneities caused by the graphene-substrate interaction in graphene samples exfoliated on silicon oxide. We find that charged impurities, present in the graphene-substrate interface, perturb the carrier density significantly and alter the electronic properties of graphene. This finding helps to understand the observed device-to-device variation typically observed in graphene-based electronic devices. Second,…
Graphene revealed a number of unique properties beneficial for electronics, including exceptionally high electron mobility and widely tunable Fermi level. However, graphene does not have an electron energy band gap, which presents a serious hurdle for its applications in digital electronics. A possible route for practical use of graphene in electronics is utilization of its exceptionally high thermal conductivity and electron current conducting properties. This invited review outlines the thermal properties of graphene and describes prospective graphene technologies that are not affected by th…
Using full potential density functional theory calculations we have investigated the structural and electronic properties of graphene and some other graphene-like materials, viz., monolayer of SiC, GeC, BN, AlN, GaN, ZnO, ZnS and ZnSe. We hope, with the advancement of material synthesis techniques, some these new materials will be synthesized in the near future for potential applications in various nano-devices.
Engineering the electronic properties of graphene has triggered great interest for potential applications in electronics and opto-electronics. Here we demonstrate the possibility to tune the electronic transport properties of graphene monolayers and multilayers by functionalisation with fluorine. We show that by adjusting the fluorine content different electronic transport regimes can be accessed. For monolayer samples, with increasing the fluorine content, we observe a transition from electronic transport through Mott variable range hopping in two dimensions to Efros - Shklovskii variable ran…
Since its inception in 2001, the science and technology of epitaxial graphene on hexagonal silicon carbide has matured into a major international effort and is poised to become the first carbon electronics platform. A historical perspective is presented and the unique electronic properties of single and multilayered epitaxial graphenes on electronics grade silicon carbide are reviewed. Early results on transport and the field effect in Si-face grown graphene monolayers provided proof-of-principle demonstrations. Besides monolayer epitaxial graphene, attention is given to C-face grown multilaye…
Previous studies of electron-phonon interaction in impure graphene have found that static disorder can give rise to an enhancement of electronic cooling. We investigate the effect of dynamic disorder and observe over an order of magnitude suppression of electronic cooling compared with clean graphene. The effect is stronger in graphene with more vacancies, confirming its vacancy-induced nature. The dependence of the coupling constant on the phonon temperature implies its link to the dynamics of disorder. Our study highlights the effect of disorder on electron-phonon interaction in graphene. In…
We report the direct observation of polarization resolved electronic Raman scattering in a gated monolayer graphene device. The evolution of the electronic Raman scattering spectra with gate voltage and its polarization dependence are in full agreement with theoretical expectations for non-resonant Raman processes involving interband electron-hole excitations across the Dirac cone. We further show that the spectral dependence of the electronic Raman scattering signal can be simply described by the dynamical polarizability of graphene in the long wavelength limit. The possibility to directly ob…
Using a semi-classical approach and input from experiments on the conductivity of graphene, we determine the electronic density dependence of the electronic transport coefficients -- conductivity, thermal conductivity and thermopower -- of doped graphene. Also the electronic density dependence of the optical conductivity is obtained. Finally we show that the classical Hall effect (low field) in graphene has the same form as for the independent electron case, characterized by a parabolic dispersion, as long as the relaxation time is proportional to the momentum.
The discovery of the hydrodynamic electron liquid (HEL) in graphene [D. Bandurin \emph{et al.}, Science {\bf 351}, 1055 (2016) and J. Crossno \emph{et al.}, Science {\bf 351}, 1058 (2016)] has marked the birth of the solid-state HEL which can be probed near room temperature in a table-top setup. Here we examine the terahertz (THz) magneto-optical (MO) properties of a graphene HEL. Considering the case where the magnetic length $l_B=\sqrt{\hbar/eB}$ is comparable to the mean-free path $l_{ee}$ for electron-electron interaction in graphene, the MO conductivities are obtained by taking a momentum…
We review progress in developing epitaxial graphene as a material for carbon electronics. In particular, improvements in epitaxial graphene growth, interface control and the understanding of multilayer epitaxial graphene's electronic properties are discussed. Although graphene grown on both polar faces of SiC is addressed, our discussions will focus on graphene grown on the (000-1) C-face of SiC. The unique properties of C-face multilayer epitaxial graphene have become apparent. These films behave electronically like a stack of nearly independent graphene sheets rather than a thin Bernal-stack…
Hydrodynamic phonon transport was recently predicted as an important regime for phonon transport in graphitic materials. Many of past studies on hydrodynamic phonon transport have focused on the cases where the hydrodynamic regime predominates over other regimes such that hydrodynamic features can be clearly observed. However, this often requires stringent conditions of temperature and sample size. In many cases, a single regime does not dominate other regimes, but all three regimes - ballistic, hydrodynamic, and diffusive regimes - exist to some extent. Here we assess the extent of three regi…
We review thermal properties of graphene and few-layer graphene, and discuss applications of these materials in thermal management of advanced electronics. The intrinsic thermal conductivity of graphene - among the highest of known materials - is dominated by phonons near the room temperature. The examples of thermal management applications include the few-layer graphene heat spreaders integrated near the heat generating areas of the high-power density transistors. It has been demonstrated that few-layer graphene heat spreaders can lower the hot-spot temperature during device operation resulti…
Electronic structures of graphene sheet with different defective patterns are investigated, based on the first principles calculations. We find that defective patterns can tune the electronic structures of the graphene significantly. Triangle patterns give rise to strongly localized states near the Fermi level, and hexagonal patterns open up band gaps in the systems. In addition, rectangular patterns, which feature networks of graphene nanoribbons with either zigzag or armchair edges, exhibit semiconducting behaviors, where the band gap has an evident dependence on the width of the nanoribbons…
Magnetotransport measurements on Hall bar devices fabricated on purely monolayer epitaxial graphene on Silicon Carbide (SiC/G) show a very tight spread in carrier concentration and mobility across wafer- size dimensions. In contrast, SiC/G devices containing bilayer graphene domains display variations in their electronic properties linked to the amount of bilayer content.
The article presents the work on the investigation of the surface structure as well as electronic and magnetic properties of graphene layer on a lattice matched surface of a ferromagnetic material, Ni(111).
By using the first-principles method based on density of functional theory, we study the electronic properties of twisted bilayer graphene with some specific twist angles and interlayer spacings. With the decrease of the twist angle(the unit cell becomes larger), the energy band becomes narrower and Coulomb repulsion increases, leading to the enhancement of electronic correlation; On the other hand, as the interlayer spacing decreases and the interlayer coupling becomes stronger, the correlation becomes stronger. By tuning the interlayer coupling, we can realize the strongly correlated state w…
Using the hydrodynamic model in the electrostatic approximation, we describe the formation of graphene surface plasmons when a charge is in motion either perpendicular or parallel to a graphene sheet. In the first case, the electron-energy loss (EEL) spectrum of the electron is computed, showing that the resonances in the spectrum are linked to the frequency of the graphene surface plasmons. In the second case, we discuss the formation of plasmonic wakes due to the dragging of the surface plasmons induced by the motion of the charge. This effect is similar to Coulomb drag between two electron …
We study the electronic structure of multilayer graphene using a $π$-orbital continuum model with nearest-neighbor intralayer and interlayer tunneling. Using degenerate state perturbation theory, we show that the low-energy electronic structure of arbitrarily stacked graphene multilayers consists of chiral pseudospin doublets with a conserved chirality sum.
We theoretically demonstrate the capability of a ferromagnetic-normal (FN) interface in graphene to focus an electron-wave with a certain spin direction. The essential feature is the negative refraction Klein tunneling, which is spin-resolved when the exchange energy of F graphene exceeds its Fermi energy. Exploiting this property, we propose a graphene NFN electronic spin lens through which an unpolarized electronic beam can be collimated with a finite spin-polarization. Our study reveals that magnetic graphene has the potential to be the electronic counterpart of the recently discovered phot…
We show how the trigonal warping effect in doped graphene can be used to produce fully valley polarized currents. We propose a device that acts both as a beam splitter and a collimator of these electronic currents. The result is demonstrated trough an optical analogy using two dimensional photonic crystals.
Electronic properties of two-dimensional allotropes of carbon, such as graphene and its bilayer, multi-layer epitaxial graphene, few-layer Bernal-stacked graphene, as well as of three-dimensional bulk graphite are reviewed from the viewpoint of recent optical spectroscopy studies. Attention is focused on relativistic-like character of quasi particles in these systems, which are referred to as massless or massive Dirac fermions.
