The recent demonstrations of viscous hydrodynamic electron flow in two-dimensional electron systems poses serious questions to the validity of existing transport theories, including the ballistic model, the collision-induced and collisionless hydrodynamics. While the theories of transport at hydrodynamic-to-ballistic crossover for free 2d electrons are well established, the same is not true for electrons in magnetic fields. In this work, we develop an analytically solvable model describing the transition from ballistic to hydrodynamic transport with changing the strength of electron-electron collisions in magnetic fields. Within this model, we find an expression for the high-frequency non-local conductivity tensor of 2d electrons. It is valid at arbitrary relation between frequency of external field $ω$, the cyclotron frequency $ω_c$, and the frequency of e-e collisions $τ^{-1}_{ee}$. We use the obtained expression to study the transformation of 2d magnetoplasmon modes at hydrodynamic-to-ballistic crossover. In the true hydrodynamic regime, $ωτ_{ee} \ll 1$, the 2DES supports a single magnetoplasmon mode that is not split at cyclotron harmonics. In the ballistic regime, $ωτ_{ee} \gg 1$, the plasmon dispersion develops splittings at cyclotron harmonics, forming the Bernstein modes. A formal long-wavelength expansion of kinetic equations ("collisionless hydrodynamics") predicts the first splitting of plasmon dispersion at $ω\approx 2ω_c$. Still, such expansion fails to predict the zero and negative group velocity sections of true magnetoplasmon dispersion, for which the full kinetic model is required.
We study hydrodynamic and ballistic transport regimes through nonlocal resistance measurements and high-resolution kinetic simulations in a mesoscopic structure on a high-mobility two-dimensional electron system in a GaAs/AlGaAs heterostructure. We evince the existence of collective transport phenomena in both regimes and demonstrate that negative nonlocal resistances and current vortices are not exclusive to only the hydrodynamic regime. The combined experiments and simulations highlight the importance of device design, measurement schemes and one-to-one modeling of experimental devices to de…
We develop an exactly solvable classical kinetic model of transport in Dirac materials accounting for strong electron-electron (e-e) and electron-hole (e-h) collisions. We use this model to track the evolution of graphene conductivity and properties of its collective excitations across the hydrodynamic-to-ballistic crossover. We find the relaxation rate of electric current by e-e collisions that is possible due to the lack of Galilean invariance, and introduce a universal numerical measure of this non-invariance in arbitrary dimension. We find the two branches of collective excitations in the …
We theoretically investigate the experimental observable of the ballistic collective group delay (CGD) of all the particles on the Fermi surface in graphene. First, we reveal that, lateral Goos-Hänchen (GH) shifts along barrier interfaces contribute an inherent component in the individual group delay (IGD). Then, by linking the complete IGD to spin precession through a dwell time, we suggest that, the CGD and its GH component can be electrostatically measured by a conductance difference in a spin-precession experiment under weak magnetic fields. Such an approach is feasible for almost arbitrar…
Previous studies have predicted the failure of Fourier's law of thermal conduction due to the existence of wave like propagation of heat with finite propagation speed. This non-Fourier thermal transport phenomenon can appear in both the hydrodynamic and (quasi) ballistic regimes. Hence, it is not easy to clearly distinguish these two non-Fourier regimes only by this phenomenon. In this work, the transient heat propagation in homogeneous thermal system is studied based on the phonon Boltzmann transport equation (BTE) under the Callaway model. Given a quasi-one or quasi-two (three) dimensional s…
In conductors with a very small density of defects, electrons at low temperatures collide predominantly with the edges of a sample. Therefore, the ballistic regime of charge and heat transport is realized. The application of a perpendicular magnetic field substantially modifies the character of ballistic transport. For the case of two-dimensional (2D) electrons in the magnetic fields corresponding to the diameter of the cyclotron trajectories smaller than the sample width a hydrodynamic transport regime is formed. In the latter regime, the flow is mainly controlled by rare electron-electron co…
Strongly interacting electrons can move in a neatly coordinated way, reminiscent of the movement of viscous fluids. Here we show that in viscous flows interactions facilitate transport, allowing conductance to exceed the fundamental Landauer's ballistic limit $G_{\rm ball}$. The effect is particularly striking for the flow through a viscous point contact, a constriction exhibiting the quantum-mechanical ballistic transport at $T=0$ but governed by electron hydrodynamics at elevated temperatures. We develop a theory of the ballistic-to-viscous crossover using an approach based on quasi-hydrodyn…
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…
Phase transitions are characterized by a sharp change in the type of dynamics of microparticles, and their description usually requires quantum mechanics. Recently, a peculiar type of conductors was discovered in which two-dimensional (2D) electrons form a viscous fluid. In this work we reveal that such electron fluid in high-quality samples can be formed from ballistic electrons via a phase transition. For this purpose, we theoretically study the evolution of a ballistic flow of 2D weakly interacting electrons with an increase of magnetic field and trace an emergence of a fluid fraction at a …
An increasing number of low carrier density materials exhibit a surprisingly large transport mean free path due to inefficient momentum relaxation. Consequently, charge transport in these systems is markedly non-ohmic but rather ballistic or hydrodynamic, features which can be explored by driving current through narrow channels. Using a kinetic equation approach we theoretically investigate how a non-quantizing magnetic field discerns ballistic and hydrodynamic transport, in particular in the spatial dependence of the transverse electric field, $E_y$: We find that $E_y$ is locally enhanced whe…
In this work, the heat vortexes in two-dimensional porous or ribbon structures are investigated based on the phonon Boltzmann transport equation (BTE) under the Callaway model. First, the separate thermal effects of normal (N) scattering and resistive (R) scattering are investigated with frequency-independent assumptions. And then the heat vortexes in graphene are studied as a specific example. It is found that the heat vortexes can appear in both ballistic (rare R/N scattering) and hydrodynamic (N scattering dominates) regimes but disappear in the diffusive (R scattering dominates) regime. As…
We numerically solve semiclassical kinetic equations and compute the growth rate of the Dyakonov-Shur instability of a two-dimensional Fermi liquid in a finite length cavity. When electron-electron scattering is fast, we observe the well-understood hydrodynamic instability, and its disappearance due to viscous dissipation. When electron-electron scattering is negligible, we find that the instability re-emerges for certain boundary conditions, but not for others. We discuss the implications of these findings for experiments.
A theory of the valley and spin Hall effects and resulting accumulation of the valley and spin polarization is developed for ultraclean channels made of two-dimensional semiconductors where the electron mean free path due to the residual disorder or phonons exceeds the channel width. Both ballistic and hydrodynamic regimes of the electron transport are studied. The polarization accumulation is determined by interplay of the anomalous velocity, side-jump and skew scattering effects. In the hydrodynamic regime, where the electron-electron scattering is dominant, the valley and spin current gener…
Carrier transport in materials is often diffusive due to momentum-relaxing scattering with phonons and defects. Suppression of momentum-relaxing scattering can lead to the ballistic and hydrodynamic transport regimes, wherein complex non-Ohmic current flow patterns, including current vortices, can emerge. In the ballistic regime addressed here, transverse magnetic focusing is habitually understood in a familiar single-particle picture of carriers injected from a source, following ballistic cyclotron orbits and reaching a detector. We report on a distinctive nonlocal magnetoresistance phenomeno…
Direct current in clean semiconductors and metals was recently shown to obey the laws of hydrodynamics in a broad range of temperatures and sample dimensions. However, the determination of frequency window for hydrodynamic phenomena remains challenging. Here, we reveal a phenomenon being a hallmark of high-frequency hydrodynamic transport, the Cerenkov emission of plasmons by drifting Dirac electrons. The effect appears in hydrodynamic regime only due to reduction of plasmon velocity by electron-electron collisions below the velocity of carrier drift. To characterize the Cerenkov effect quanti…
Electron transport in clean 2D systems with weak electron-phonon (e-ph) coupling can transition from an Ohmic to a ballistic or a hydrodynamic regime. The ballistic regime occurs when electron-electron (e-e) scattering is weak whereas the hydrodynamic regime arises when this scattering is strong. Despite this difference, we find that vortices and a negative nonlocal resistance believed to be quintessentially hydrodynamic are equally characteristic of the ballistic regime. These non-Ohmic regimes cannot be distinguished in DC transport without changing experimental conditions. Further, as our k…
A self-consistent theory of the admittance of a perfect ballistic, locally charge neutral wire is proposed. Compared to a non-interacting theory, screening effects drastically change the frequency behavior of the conductance. In the single-channel case the frequency dependence of the admittance is monotonic, while for two or more channels collective interchannel excitations lead to resonant structures in the admittance. The imaginary part of the admittance is typically positive, but can become negative near resonances.
Exploiting vibrational excitation for the dynamic control of material properties is an attractive goal with wide-ranging technological potential. Most metal-to-insulator transitions are mediated by few structural modes and are thus ideal candidates for the selective driving towards a desired electronic phase. Such targeted navigation within a generally multi-dimensional potential energy landscape requires microscopic insight into the non equilibrium pathway. However, the exact role of coherent inertial motion across the transition state has remained elusive. Here, we demonstrate mode-selective…
We study optical spectra of finite electronic quantum systems at frequencies smaller than the plasma frequency using a quasi-classical approach. This approach includes collective effects and enables us to analyze how the nature of the (single-particle) electron dynamics influences the optical spectra in finite electronic quantum systems. We derive an analytical expression for the low-frequency absorption coefficient of electro-magnetic radiation in a finite quantum system with ballistic electron dynamics and specular reflection at the boundaries: a two-dimensional electron gas confined to a st…
In ultra-high quality two-dimensional (2D) materials the mean free paths of phonons and electrons relative to all mechanisms of scattering can be much greater than a size of a sample. In this case the most intensive type of scattering of particles is their collisions with sample edges and the ballistic regime of heat and charge transport is realized. We study the ballistic transport of classical interacting 2D particles in a long narrow sample. We show that the inter-particle scattering conserving momentum leads to a positive hydrodynamic correction to the ballistic conductance, which is a pre…
Materials in which heat and entropy can be transmitted by directed ballistic pulses can trigger new approaches to energy transduction in solids. We predict that a ballistic energy transfer mode, with heat propagation governed by a wave equation rather than a diffusion equation, can be realized for a thermal electron-hole plasma in graphene. The new behavior originates from rapid exchange of energy and momentum in particle collisions leading to energy propagation as a collective weakly-damped oscillation. Due to the electronic nature of this mode, the estimated propagation velocity can be ~10^3…
An electric field that builds in the direction against current, known as negative nonlocal resistance, arises naturally in viscous flows and is thus often taken as a telltale of this regime. Here we predict negative resistance for the ballistic regime, wherein the ee collision mean free path is greater than the length scale at which the system is being probed. Therefore, negative resistance alone does not provide strong evidence for the occurrence of the hydrodynamic regime; it must thus be demoted from the rank of a smoking gun to that of a mere forerunner. Furthermore, we find that negative …
Within a Monte Carlo simulation we investigate the statistical properties of an electron flow injected with a Poissonian distribution and transmitted under ballistic regime in the presence of long-range Coulomb interaction. Electrons are shown to exhibit a motional squeezing which tends to space them more regularly rather than strictly at random, and evidence a sub-Poissonian statistics with a substantially reduced Fano factor $F_n\ll 1$. The temporal (anti)correlation among carriers is demonstrated to be a collective effect which persists over the transit of several successive electrons and r…
Geometric oscillations of local Hall and Nernst effects in ballistic graphene at weak magnetic fields
Abrikosov Center for Theoretical Physics, MIPT（莫斯科物理技术学院阿布里科索夫理论物理中心）；Institute of Physics of DFRS of the RAS（俄罗斯科学院达吉斯坦共和国科学中心物理研究所）；School of Science, Westlake University（西湖大学理学院）
Considering theoretically the transition between hydrodynamic and ballistic regimes in 2D semiconductors, we show that electrons in high-mobility 2D GaAs are by far the best system for the direct observation of collective hydrodynamic effects even in bulk transport properties independent of complicated transport features in narrow constrictions and small systems where Gurzhi phenomena are typically studied experimentally. We predict a strong hydrodynamics-induced generic violation of the Wiedeman-Franz law in bulk 2D GaAs systems for mobilities as modest as $10^6 \mathrm{cm}^2/Vs$ and densitie…
In absence of time-reversal symmetry, viscous electron flow hosts a number of interesting phenomena, of which we focus here on the Hall viscosity. Taking a step beyond the hydrodynamic definition of the Hall viscosity, we derive a generalized relation between Hall viscosity and transverse electric field using a kinetic equation approach. We explore two different geometries where the Hall viscosity is accessible to measurement. For hydrodynamic flow of electrons in a narrow channel, we find that the viscosity may be measured by a local probe of the transverse electric field near the center of t…
Recent experiments have observed hints of hydrodynamic electron flow in a number of materials, not all of which have an isotropic Fermi surface. We revisit these experiments in $\mathrm{PdCoO}_2$, a quasi-two-dimensional material whose Fermi surface is a rounded hexagon, and observe that the data appears quantitatively consistent with a non-hydrodynamic interpretation. Nevertheless, motivated by such experiments, we develop a simple model for the low temperature kinetics and hydrodynamics of a two-dimensional Fermi liquid with a polygonal Fermi surface. A geometric effect leads to a finite num…
We consider the quantum centipede made of $N$ fermionic quantum walkers on the one-dimensional lattice interacting by means of the simplest of all hard-bound constraints: the distance between two consecutive fermions is either one or two lattice spacings. This composite quantum walker spreads ballistically, just as the simple quantum walk. However, because of the interactions between the internal degrees of freedom, the distribution of its center-of-mass velocity displays numerous ballistic fronts in the long-time limit, corresponding to singularities in the empirical velocity distribution. Th…
Hydrodynamics is a general description for the flow of a fluid, and is expected to hold even for fundamental particles such as electrons when inter-particle interactions dominate. While various aspects of electron hydrodynamics were revealed in recent experiments, the fundamental spatial structure of hydrodynamic electrons, the Poiseuille flow profile, has remained elusive. In this work, we provide the first real-space imaging of Poiseuille flow of an electronic fluid, as well as visualization of its evolution from ballistic flow. Utilizing a scanning nanotube single electron transistor, we im…
We have measured the collective excitation spectrum of interacting electrons in one-dimension. The experiment consists of controlling the energy and momentum of electrons tunneling between two clean and closely situated, parallel quantum wires in a GaAs/AlGaAs heterostructure while measuring the resulting conductance. We measure excitation spectra that clearly deviate from the non-interacting spectrum, attesting to the importance of Coulomb interactions. Notable is an observed 30% enhancement of the velocity of the main excitation branch relative to non-interacting electrons with the same dens…
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.
We present the theory of quasiparticle transport in perturbatively small inhomogeneous magnetic fields across the ballistic-to-hydrodynamic crossover. In the hydrodynamic limit, the resistivity $ρ$ generically grows proportionally to the rate of momentum-conserving electron-electron collisions at large enough temperatures $T$. In particular, the resulting flow of electrons provides a simple scenario where viscous effects suppress conductance below the ballistic value. This new mechanism for $ρ\propto T^2$ resistivity in a Fermi liquid may describe low $T$ transport in single-band $\mathrm{SrTi…
Electronic transport in Fermi liquids is usually Ohmic, because of momentum-relaxing scattering due to defects and phonons. These processes can become sufficiently weak in two-dimensional materials, giving rise to either ballistic or hydrodynamic transport, depending on the strength of electron-electron scattering. We show that the ballistic regime is a quantum critical point (QCP) on the regime boundary separating Ohmic and hydrodynamic transport. The QCP corresponds to a \emph{free} conformal field theory (CFT) with a dynamical scaling exponent $z = 1$. Its nontrivial aspects emerge in devic…
Electrical resistance usually originates from lattice imperfections. However, even a perfect lattice has a fundamental resistance limit, given by the Landauer conductance caused by a finite number of propagating electron modes. This resistance, shown by Sharvin to appear at the contacts of electronic devices, sets the ultimate conductance limit of non-interacting electrons. Recent years have seen growing evidence of hydrodynamic electronic phenomena, prompting recent theories to ask whether an electronic fluid can radically break the fundamental Landauer-Sharvin limit. Here, we use single-elec…
We propose a hydrodynamics theory of collective quantum Hall states, which describes incompressible liquids, hexatic liquid crystals, a bubble solid and a Wigner crystal states within a unified framework. The structure of the theory is uniquely determined by the space-time symmetry, and a symmetry with respect to static shear deformations. In agreement with recent experiments the theory predicts two gapped collective modes for incompressible liquids. We argue that the presence of the above two modes is a universal property of a magnetized two-dimensional collective liquid.
We present the theory of thermoelectric transport in metals with long-lived quasiparticles, carefully addressing the interplay of electron-electron scattering as well as electron-impurity scattering, but neglecting electron-phonon scattering. In Fermi liquids with a large Fermi surface and weak electron-impurity scattering, we provide universal and simple formulas for the behavior of the thermoelectric conductivities across the ballistic-to-hydrodynamic crossover. In this regime, the electrical conductivity is relatively unchanged by hydrodynamic effects. In contrast, the thermal conductivity …
The formation of the beam halo in charged particle accelerators is studied in the framework of a stochastic-hydrodynamic model for the collective motion of the particle beam. In such a stochastic-hydrodynamic theory the density and the phase of the charged beam obey a set of coupled nonlinear hydrodynamic equations with explicit time-reversal invariance. This leads to a linearized theory that describes the collective dynamics of the beam in terms of a classical Schrödinger equation. Taking into account space-charge effects, we derive a set of coupled nonlinear hydrodynamic equations. These equ…
Recent experiments have elucidated that novel nonequilibrium states inherent in the so-called hydrodynamic regime are realized in ultrapure metals with sufficiently strong momentum-conserving scattering. In this letter, we formulate a theory of electron hydrodynamics with broken inversion symmetry under magnetic fields and find that novel terms emerge in hydrodynamic equations which play a crucial role for the realization of the nonreciprocal responses. Specifically, we clarify that there exist a novel type of nonreciprocal collective modes dubbed nonreciprocal surface magnetoplasmons arising …
We develop an analytically solvable model for interacting two-dimensional Fermi liquids with separate collisional relaxation rates for parity-odd and parity-even Fermi surface deformations. Such a disparity of collisional lifetimes exists whenever scattering is restricted to inversion-symmetric Fermi surfaces, and should thus be a generic feature of two-dimensional Fermi liquids. It implies an additional unanticipated "tomographic" transport regime (in between the standard collisionless and hydrodynamic regimes) in which even-parity modes are overdamped while odd-parity modes are collisionless…
