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.
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…
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.
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…
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…
Collective excitations in graphene monolayer are studied. Equations describing collective properties of electrons in graphene are obtained. The basic ideas of the method of many-particle quantum hydrodynamics are used for the derivation. As starting point of the derivation we use the Dirac equation for massless electrons which is usually used for description of electrons in graphene [D. E. Sheehy and J. Schmalian, Phys. Rev. Lett. 99, 226803 (2007)], where the Coulomb interaction is taken into account. We study dispersion properties of collective excitations by means derived here graphene quan…
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…
We have investigated the Coulomb screening properties and collective excitations in a graphene bilayer. The static screening effect is anisotropic and is much stronger in the undoped graphene bilayer than in a monolayer graphene [1]. The dynamic screening shows the properties of a Dirac gas in the low frequency and that of a Fermi gas in the high frequency. The transition from the Dirac to the Fermi gas is also observed in the plasmon spectrum. Finally, we find that an electron gas in a doped graphene bilayer has quite similar properties as those of a Fermi gas in materials containing two ener…
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…
We predict the formation and superfluidity of polaritons in an optical microcavity formed by excitons in gapped graphene embedded there and microcavity photons. The Rabi splitting related to the creation of an exciton in a graphene layer in the presence of the band gap is obtained. The analysis of collective excitations as well as the sound velocity is presented. We show that the superfluid density and temperature of the Kosterlitz-Thouless phase transition are decreasing functions of the energy gap.
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 breakth…
Bose-Einstein condensation of the excitons in graphene is considered. We suggested the model spinor equation for neutral particles with short range interaction described the microscopic graphene excitons dynamic. Using this equation we derived quantum hydrodynamic equations for description of collective properties of excitons in graphene, particularly for the case when excitons being in the Bose-Einstein condensate (BEC) state. The dispersion of collective excitations in graphene excitons BEC is studied. We shown that frequency of collective excitations is proportional to the square root of th…
We develop the theory of collective modes supported by a Fermi liquid of electrons in pristine graphene. Under reasonable assumptions regarding the electron-electron interaction, all the modes but the plasmon are over-damped. In addition to the $SU(2)$ symmetric spin mode, these include also the valley imbalance modes obeying a $U(1)$ symmetry, and a $U(2)$ symmetric valley spin imbalance mode. We derive the interactions and diffusion constants characterizing the over-damped modes. The corresponding relaxation rates set fundamental constraints on graphene valley- and spintronics applications.
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…
The excitation spectrum and the collective modes of graphene antidot lattices (GALs) are studied in the context of a $π$-band tight-binding model. The dynamical polarizability and dielectric function are calculated within the random phase approximation. The effect of different kinds of disorder, such as geometric and chemical disorder, are included in our calculations. We highlight the main differences of GALs with respect to single-layer graphene (SLG). Our results show that, in addition to the well-understood bulk plasmon in doped samples, inter-band plasmons appear in GALs. We further show …
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…
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.
We have investigated the Coulomb screening properties and plasmon spectrum in a bilayer graphene under a perpendicular electric bias. The bias voltage applied between the two graphene layers opens a gap in the single particle energy spectrum and modifies the many-body correlations and collective excitations. The energy gap can soften the plasmon modes and lead to a crossover of the plasmons from a Landau damped mode to being undamped. Plasmon modes of long lifetime may be observable in experiments and may have potentials for device applications.
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…
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 derive an effective field-theoretical model for the one-dimensional collective mode associated with a domain wall in a quantum Hall ferromagnetic state, as realized in confined graphene systems at zero filling. To this end, we consider the coupling of a quantum spin ladder forming near a kink in the Zeeman field to the spin fluctuations of a neighboring spin polarized two-dimensional environment. It is shown, in particular, that such coupling may induce anisotropy of the exchange coupling in the legs of the ladder. Furthermore, we demonstrate that the resulting ferromagnetic spin-1/2 ladder…
We have studied the temperature effect on collective excitations in biased bilayer graphene within random-phase approximation. From the zeros of temperature dynamical dielectric function of the system we have found one weakly damped plasmon mode. For a given electrostatic potential bias, at low (high) temperature T the plasmon frequency changes slightly (increases remarkably) with T. We have also studied the effects of potential bias and carrier density on the plasmon frequency of the system at finite temperatures.
We explore ways in which the close proximity between graphene sheets and monolayers of 2D superconductors can lead to hybridization between their collective excitations. We consider heterostructures formed by combinations of graphene sheets and 2D superconductor monolayers. The broad range of energies in which the graphene plasmon can exist, together with its tunability, makes such heterostrucutres promising platforms for probing the many-body physics of superconductors. We show that the hybridization between the graphene plasmon and the Bardasis-Schrieffer mode of a 2D superconductor results …
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…
This comment pertains the recent manuscript by Morissette {\it et al.} [arXiv:2206.08354v1]. The authors claim to have found signatures of collective excitations in electron spin resonance experiments that would be linked to the correlated structure of magic angle bilayer graphene. However, identical resonance features have already been reported in previous works on mono- and few-layer graphene, voiding their theoretical framework. A straight forward theoretical picture within the single-particle topologically non-trivial band structure of graphene delivers satisfactory explanations for the ob…
Two-dimensional electrons in graphene are known to behave as massless fermions with Dirac-Weyl type linear dispersion near the Dirac crossing points. We have investigated the collective excitations of this system in the presence or absence of an external magnetic field. Unlike in the conventional two-dimensional electron system, the $ν=\frac1m$ fractional quantum Hall state in graphene was found to be most stable in the $n=1$ Landau level. In the zero field case, but in the presence of the spin-orbit interaction, an undamped plasmon mode was found to exist in the gap of the single-particle con…
Twisted bilayer graphene with tiny rotation angles have drawn significant attention due to the observation of the unconventional superconducting and correlated insulating behaviors. In this paper, we employ a full tight-binding model to investigate collective excitations in twisted bilayer graphene near magic angle. The polarization function is obtained from the tight-binding propagation method without diagonalization of the Hamiltonian matrix. With the atomic relaxation considered in the simulation, damped and undamped interband plasmon modes are discovered near magic angle under both room te…
We show that the insulating states of magic-angle twisted bilayer graphene support a series of collective modes corresponding to local particle-hole excitations on triangular lattice sites. Our theory is based on a continuum model of the magic angle flat bands. When the system is insulating at moiré band filling $ν=-3$, our calculations show that the ground state supports seven low-energy modes that lie well below the charge gap throughout the moiré Brillouin zone, one of which couples strongly to THz photons. The low-energy collective modes are faithfully described by a model with a local $SU…
In spin-polarized itinerant electron systems, collective spin-wave modes arise from dynamical exchange and correlation (xc) effects. We here consider spin waves in doped paramagnetic graphene with adjustable Zeeman-type band splitting. The spin waves are described using time-dependent spin-density-functional response theory, treating dynamical xc effects within the Slater and Singwi-Tosi-Land-Sjolander approximations. We obtain spin-wave dispersions and spin stiffnesses as a function of doping and spin polarization, and discuss prospects for their experimental observation.
We show that graphene in a strong magnetic field with partially filled Landau levels sustains charged collective excitations, which are bound states of three-particle complexes. Some of these states are optically bright and may be detected in spectroscopy experiments, enhancing the current understanding of electron-electron interactions in graphene. The states can be classified using the geometrical symmetries - non-commutative magnetic translations and generalized rotations - in addition to the dynamical SU(4) symmetry in graphene. From the SU(4) symmetry point of view, such excitations are 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）
The growing precision of optical and scattering experiments necessitates a better understanding of the influence of damping onto the collective mode of sheet electrons. As spin-polarized systems are of particular interest for spintronic applications, we here report spin-sensitive linear response functions of graphene, which give access to charge- and spin-density related excitations. We further calculate the reflectivity of graphene on an SiO 2 surface, a setup used in s-wave scanning near field microscopy. Increasing the partial spin-polarization of the graphene charge carriers leads to a sig…
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 …
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 theoretically study the dynamic screening properties of bilayer graphene within the random phase approximation assuming quadratic band dispersion and zero gap for the single-particle spectrum. We calculate the frequency dependent dielectric function of the system and obtain the low energy plasmon dispersion and broadening of the plasmon modes from the dielectric function. We also calculate the optical spectral weight (i.e. the dynamical structure factor) for the system. We find that the leading order long wavelength limit of the plasmon dispersion matches with the classical result for 2D el…
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…
Individual electrons in graphene behave as massless quasiparticles. In surprising twist, it is inferred from plasmonic investigations that collectively excited graphene electrons must exhibit non-zero mass and its inertial acceleration is essential for graphene plasmonics. Despite such importance, this collective mass has defied direct unequivocal measurement. It may be directly measured by accelerating it with a time-varying voltage and quantifying the phase delay of the resulting current; this voltage-current phase relation would manifest as kinetic inductance, representing the collective in…
We discuss novel transverse plasmon-polaritons that are hosted by AA- and AB-stacked bilayer graphene due to perfect nesting. They are composed of oscillating counterflow currents in between the layers, giving a clear interpretation for these collective modes as magnetic excitations carrying magnetic moment parallel to the planes. For AA-stacked bilayer graphene, these modes can reach zero frequency at the neutrality point and we thus predict a symmetry broken ground-state leading to in-plane orbital ferromagnetism. Even though it could be hard to detect them in real solid-state devices, these…
We study optically-induced collective excitations of graphene in the presence of a strong perpendicular magnetic field and a single impurity. We determine the energies and absorption strengths of these excitations, which become localised on the impurity. Two different types of impurity are considered i. the long-range Coulomb impurity, ii. a delta-function impurity located at either an A or B graphene sublattice site. Both impurity types result in some bound states appearing both above and below the magnetoplasmon continuum, although the effect of the short-range impurity is less pronounced. T…
In a magnetic field two-dimensional (2d) electron systems host, with quenched kinetic energy, a variety of many-body correlation phenomena, such as interaction-driven new states and associated collective excitations over them. In a magnetic field the two-body operators pertinent to the 2d Coulomb interaction obey a crossing relation, with which the Coulomb interaction is also cast into the form of manifest exchange interaction. It is shown that active use of this direct/exchange duality of the interaction allows one to develop, within the framework of the single-mode approximation, a new effic…
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…
Graphene subject to a strong, tilted magnetic field exhibits an insulator-metal transition tunable by tilt-angle, attributed to the transition from a canted antiferromagnetic (CAF) to a ferromagnetic (FM) bulk state at filling factor zero. We develop a theoretical description for the spin and valley edge textures in the two phases, and the implied evolution in the nature of edge modes through the transition. In particular, we show that the CAF has gapless neutral modes in the bulk, but supports gapped charged edge modes. At the transition to the FM state the charged edge modes become gapless a…
We devote this work to the study of the mean-field phase diagram of the $ν=0$ quantum Hall state in bilayer graphene and the computation of the corresponding neutral collective modes, extending the results of recent works in the literature. Specifically, we provide a detailed classification of the complete orbital-valley-spin structure of the collective modes and show that phase transitions are characterized by singlet modes in orbital pseudospin, which are independent of the Coulomb strength and suffer strong many-body corrections from short-range interactions at low momentum. We describe the…
