Hydrodynamic electron flow in high-mobility wires

Coulomb drag induced non-local resistance in double graphene layers

We study the effect of Coulomb drag between graphene layers in presence of viscosity term. To do this, we use the simple model of Stokes equations for drift velocities in active and passive layers, known as Pogrebinskii's approach. The solution to these equations allows us to find the potential distribution, and thus the non-local drag resistance of passive layer. It is shown that in viscous regime the non-local resistance may take negative values, in contrast, the ohmic regime results in positive non-local resistance for all drag strengths. Additionally, we discuss the influence of magnetic field on the non-local drag magnetoresistance.

Viscous terahertz photoconductivity of hydrodynamic electrons in graphene

Light incident upon materials can induce changes in their electrical conductivity, a phenomenon referred to as photoresistance. In semiconductors, the photoresistance is negative, as light-induced promotion of electrons across the bandgap enhances the number of charge carriers participating in transport. In superconductors and normal metals, the photoresistance is positive because of the destruction of the superconducting state and enhanced momentum-relaxing scattering, respectively. Here we report a qualitative deviation from the standard behaviour in doped metallic graphene. We show that Dirac electrons exposed to continuous-wave terahertz (THz) radiation can be thermally decoupled from the lattice, which activates hydrodynamic electron transport. In this regime, the resistance of graphene constrictions experiences a decrease caused by the THz-driven superballistic flow of correlated electrons. We analyse the dependencies of the negative photoresistance on the carrier density, and the radiation power, and show that our superballistic devices operate as sensitive phonon-cooled bolometers and can thus offer, in principle, a picosecond-scale response time. Beyond their fundamental implications, our findings underscore the practicality of electron hydrodynamics in designing ultra-fast THz sensors and electron thermometers.

Experimental signatures of the transition from acoustic plasmon to electronic sound in graphene

Fermi liquids respond differently to perturbations depending on whether their frequency is higher (collisionless regime) or lower (hydrodynamic regime) than the interparticle collision rate. This results in a different phase velocity between the collisionless zero sound and the hydrodynamic first sound. We performed terahertz photocurrent nanoscopy measurements on graphene devices, with a metallic gate close to the graphene layer, to probe the dispersion of propagating acoustic plasmons, the counterpart of sound modes in electronic Fermi liquids. We report the observation of a change in the plasmon phase velocity when the excitation frequency approaches the electron-electron collision rate that is compatible with the transition between the zero and the first sound mode.

Anomalous electronic transport in high-mobility Corbino rings

We report low-temperature electronic transport measurements performed in two multi-terminal Corbino samples formed in GaAs/Al-GaAs two-dimensional electron gases (2DEG) with both ultra-high electron mobility ( ≳ 20 × 10⁶ cm²/ Vs) and with distinct electron density of 1.7 and 3.6 × 10¹¹ cm^-2. In both Corbino samples, a non-monotonic behavior is observed in the temperature dependence of the resistance below 1 K. Surprisingly, a sharp decrease in resistance is observed with increasing temperature in the sample with lower electron density, whereas an opposite behavior is observed in the sample with higher density. To investigate further, transport measurements were performed in large van der Pauw samples having identical heterostructures, and as expected they exhibit resistivity that is monotonic with temperature. Finally, we discuss the results in terms of various lengthscales leading to ballistic and hydrodynamic electronic transport, as well as a possible Gurzhi effect.

Anomalous High-Temperature Magnetoresistance in a Dilute 2D Hole System

We report an unusual magnetoresistance that strengthens with the temperature in a dilute two-dimensional (2D) hole system in GaAs/AlGaAs quantum wells with densities p=1.98-0.99×10^{10}/cm^{2} where r_{s}, the ratio between Coulomb energy and Fermi energy, is as large as 20-30. We show that, while the system exhibits a negative parabolic magnetoresistance at low temperatures (≲0.4  K) characteristic of an interacting Fermi liquid, a positive magnetoresistance emerges unexpectedly at higher temperatures, and grows with increasing temperature even in the regime T∼E_{F}, close to the Fermi energy. This unusual positive magnetoresistance at high temperatures can be attributed to the viscous transport of 2D hole fluid in the hydrodynamic regime where holes scatter frequently with each other. These findings give insight into the collective transport of strongly interacting carriers in the r_{s}≫1 regime and new routes toward magnetoresistance at high temperatures.

Current Noise of Hydrodynamic Electrons

A resistor at finite temperature produces white noise fluctuations of the current called Johnson-Nyquist noise. Measuring the amplitude of this noise provides a powerful primary thermometry technique to access the electron temperature. In practical situations, however, one needs to generalize the Johnson-Nyquist theorem to handle spatially inhomogeneous temperature profiles. Recent work provided such a generalization for Ohmic devices obeying the Wiedemann-Franz law, but there is a need to provide a similar generalization for hydrodynamic electron systems, since hydrodynamic electrons provide unusual sensitivity for Johnson noise thermometry but they do not admit a local conductivity nor obey the Wiedemann-Franz law. Here we address this need by considering low-frequency Johnson noise in the hydrodynamic setting for a rectangular geometry. Unlike in the Ohmic setting, we find that the Johnson noise is geometry dependent due to nonlocal viscous gradients. Nonetheless, ignoring the geometric correction only leads to an error of at most 40% as compared to naively using the Ohmic result.

Para-hydrodynamics from weak surface scattering in ultraclean thin flakes

Electron hydrodynamics typically emerges in electron fluids with a high electron-electron collision rate. However, new experiments with thin flakes of WTe2 have revealed that other momentum-conserving scattering processes can replace the role of the electron-electron interaction, thereby leading to a novel, so-called para-hydrodynamic regime. Here, we develop the kinetic theory for para-hydrodynamic transport. To this end, we consider a ballistic electron gas in a thin three-dimensional sheet where the momentum-relaxing (lmr) and momentum-conserving (lmc) mean free paths are decreased due to boundary scattering from a rough surface. The resulting effective mean free path of the in-plane components of the electronic flow is then expressed in terms of microscopic parameters of the sheet boundaries, predicting that a para-hydrodynamic regime with lmr ≫ lmc emerges generically in ultraclean three-dimensional materials. Using our approach, we recover the transport properties of WTe2 in the para-hydrodynamic regime in good agreement with existing experiments.

Hydrodynamics of dipole-conserving fluids

Dipole-conserving fluids serve as examples of kinematically constrained systems that can be understood on the basis of symmetry. They are known to display various exotic features including glassylike dynamics, subdiffusive transport, and immobile excitations' dubbed fractons. Unfortunately, such systems have so far escaped a complete macroscopic formulation as viscous fluids. In this work, we construct a consistent hydrodynamic description for fluids invariant under translation, rotation, and dipole shift symmetry. We use symmetry principles to formulate a thermodynamic theory for dipole-conserving systems at equilibrium and apply irreversible thermodynamics in order to elucidate dissipative effects. Remarkably, we find that the inclusion of the energy conservation not only renders the longitudinal modes diffusive rather than subdiffusive but also diffusion is present even at the lowest order in the derivative expansion. This work paves the way towards an effective description of many-body systems with constrained dynamics such as ensembles of topological defects, fracton phases of matter, and certain models of glasses.

Imaging the breaking of electrostatic dams in graphene for ballistic and viscous fluids

The charge carriers in a material can, under special circumstances, behave as a viscous fluid. In this work, we investigated such behavior by using scanning tunneling potentiometry to probe the nanometer-scale flow of electron fluids in graphene as they pass through channels defined by smooth and tunable in-plane p-n junction barriers. We observed that as the sample temperature and channel widths are increased, the electron fluid flow undergoes a Knudsen-to-Gurzhi transition from the ballistic to the viscous regime characterized by a channel conductance that exceeds the ballistic limit, as well as suppressed charge accumulation against the barriers. Our results are well modeled by finite element simulations of two-dimensional viscous current flow, and they illustrate how Fermi liquid flow evolves with carrier density, channel width, and temperature.

How Electron Hydrodynamics Can Eliminate the Landauer-Sharvin Resistance

It has long been realized that even a perfectly clean electronic system harbors a Landauer-Sharvin resistance, inversely proportional to the number of its conduction channels. This resistance is usually associated with voltage drops on the system's contacts to an external circuit. Recent theories have shown that hydrodynamic effects can reduce this resistance, raising the question of the lower bound of resistance of hydrodynamic electrons. Here, we show that by a proper choice of device geometry, it is possible to spread the Landauer-Sharvin resistance throughout the bulk of the system, allowing its complete elimination by electron hydrodynamics. We trace the effect to the dynamics of electrons flowing in channels that terminate within the sample. For ballistic systems this termination leads to back-reflection of the electrons and creates resistance. Hydrodynamically, the scattering of these electrons off other electrons allows them to transfer to transmitted channels and avoid the resistance. Counterintuitively, we find that in contrast to the ohmic regime, for hydrodynamic electrons the resistance of a device with a given width can decrease with its length, suggesting that a long enough device may have an arbitrarily small total resistance.

Imaging the Breakdown of Ohmic Transport in Graphene

Ohm's law describes the proportionality of the current density and electric field. In solid-state conductors, Ohm's law emerges due to electron scattering processes that relax the electrical current. Here, we use nitrogen-vacancy center magnetometry to directly image the local breakdown of Ohm's law in a narrow constriction fabricated in a high mobility graphene monolayer. Ohmic flow is visible at room temperature as current concentration on the constriction edges, with flow profiles entirely determined by sample geometry. However, as the temperature is lowered below 200 K, the current concentrates near the constriction center. The change in the flow pattern is consistent with a crossover from diffusive to viscous electron transport dominated by electron-electron scattering processes that do not relax current.

Direct observation of vortices in an electron fluid

Vortices are the hallmarks of hydrodynamic flow. Strongly interacting electrons in ultrapure conductors can display signatures of hydrodynamic behaviour, including negative non-local resistance^1-4, higher-than-ballistic conduction^5-7, Poiseuille flow in narrow channels^8-10 and violation of the Wiedemann-Franz law¹¹. Here we provide a visualization of whirlpools in an electron fluid. By using a nanoscale scanning superconducting quantum interference device on a tip¹², we image the current distribution in a circular chamber connected through a small aperture to a current-carrying strip in the high-purity type II Weyl semimetal WTe₂. In this geometry, the Gurzhi momentum diffusion length and the size of the aperture determine the vortex stability phase diagram. We find that vortices are present for only small apertures, whereas the flow is laminar (non-vortical) for larger apertures. Near the vortical-to-laminar transition, we observe the single vortex in the chamber splitting into two vortices; this behaviour is expected only in the hydrodynamic regime and is not anticipated for ballistic transport. These findings suggest a new mechanism of hydrodynamic flow in thin pure crystals such that the spatial diffusion of electron momenta is enabled by small-angle scattering at the surfaces instead of the routinely invoked electron-electron scattering, which becomes extremely weak at low temperatures. This surface-induced para-hydrodynamics, which mimics many aspects of conventional hydrodynamics including vortices, opens new possibilities for exploring and using electron fluidics in high-mobility electron systems.

Asymmetrically Engineered Nanoscale Transistors for On-Demand Sourcing of Terahertz Plasmons

Terahertz (THz) plasma oscillations represent a potential path to implement ultrafast electronic devices and circuits. Here, we present an approach to generate on-chip THz signals that relies on plasma-wave stabilization in nanoscale transistors with specific structural asymmetry. A hydrodynamic treatment shows how the transistor asymmetry supports plasma-wave amplification, giving rise to pronounced negative differential conductance (NDC). A demonstration of these behaviors is provided in InGaAs high-mobility transistors, which exhibit NDC in accordance with their designed asymmetry. The NDC onsets once the drift velocity in the channel reaches a threshold value, triggering the initial plasma instability. We also show how this feature can be made to persist beyond room temperature (to at least 75 °C), when the gating is configured to facilitate a transition between the hydrodynamic and ballistic regimes (of electron-electron transport). Our findings represent a significant step forward for efforts to develop active components for THz electronics.

Diffusion of Photoexcited Holes in a Viscous Electron Fluid

The diffusion of photogenerated holes is studied in a high-mobility mesoscopic GaAs channel where electrons exhibit hydrodynamic properties. It is shown that the injection of holes into such an electron system leads to the formation of a hydrodynamic three-component mixture consisting of electrons and photogenerated heavy and light holes. The obtained results are analyzed within the framework of ambipolar diffusion, which reveals characteristics of a viscous flow. Both hole types exhibit similar hydrodynamic characteristics. In such a way the diffusion lengths, ambipolar diffusion coefficient, and the effective viscosity of the electron-hole system are determined.

Skin effect as a probe of transport regimes in Weyl semimetals

SignificanceWeyl semimetals are a class of three-dimensional materials, whose low-energy excitations mimic massless fermions. In consequence they exhibit various unusual transport properties related to the presence of chiral anomalies, a subtle quantum phenomenon that denotes the breaking of the classical chiral symmetry by quantum fluctuations. In this work we present a universal description of transport in weakly disordered Weyl semimetals with several scattering mechanisms taken into account. Our work predicts the existence of a new anomaly-induced transport regime in these materials and gives a crisp experimental signature of a chiral anomaly in optical conductivity measurements. Finally, by also capturing the hydrodynamic regime of quasiparticles, our construction bridges the gap between developments in electronic fluid mechanics and three-dimensional semimetals.

Evidence for Local Spots of Viscous Electron Flow in Graphene at Moderate Mobility

Dominating electron-electron scattering enables viscous electron flow exhibiting hydrodynamic current density patterns, such as Poiseuille profiles or vortices. The viscous regime has recently been observed in graphene by nonlocal transport experiments and mapping of the Poiseuille profile. Herein, we probe the current-induced surface potential maps of graphene field-effect transistors with moderate mobility using scanning probe microscopy at room temperature. We discover micrometer-sized large areas appearing close to charge neutrality that show current-induced electric fields opposing the externally applied field. By estimating the local scattering lengths from the gate dependence of local in-plane electric fields, we find that electron-electron scattering dominates in these areas as expected for viscous flow. Moreover, we suppress the inverted fields by artificially decreasing the electron-disorder scattering length via mild ion bombardment. These results imply that viscous electron flow is omnipresent in graphene devices, even at moderate mobility.

Viscometry of Electron Fluids from Symmetry

When electrons flow as a viscous fluid in anisotropic metals, the reduced symmetry can lead to exotic viscosity tensors with many additional, nonstandard components. We present a viscometry technique that can, in principle, measure the multiple dissipative viscosities allowed in isotropic and anisotropic fluids alike. By applying representation theory to exploit the intrinsic symmetry of the fluid, our viscometry is also exceptionally robust to both boundary complications and ballistic effects. We present the technique via the illustrative example of dihedral symmetry, relevant in this context as the point symmetry of 2D crystals. Finally, we propose a present-day realizable experiment for detecting, in a metal, a novel hydrodynamic phenomenon: the presence of rotational dissipation in an otherwise isotropic fluid.

Entropy Wave Instability in Dirac and Weyl Semimetals

Hydrodynamic instabilities driven by a direct current are analyzed in 2D and 3D relativisticlike systems with the Dyakonov-Shur boundary conditions supplemented by a boundary condition for temperature. Besides the conventional Dyakonov-Shur instability for plasmons, we find an entropy wave instability in both 2D and 3D systems. The entropy wave instability is a manifestation of the relativisticlike nature of electron quasiparticles and a nontrivial role of the energy current in such systems. These two instabilities occur for the opposite directions of fluid flow. While the Dyakonov-Shur instability is characterized by the plasma frequency in 3D and the system size in 2D, the frequency of the entropy wave instability is tunable by the system size and the flow velocity.

Precision measurement of electron-electron scattering in GaAs/AlGaAs using transverse magnetic focusing

Electron-electron (e-e) interactions assume a cardinal role in solid-state physics. Quantifying the e-e scattering length is hence critical. In this paper we show that the mesoscopic phenomenon of transverse magnetic focusing (TMF) in two-dimensional electron systems forms a precise and sensitive technique to measure this length scale. Conversely we quantitatively demonstrate that e-e scattering is the predominant effect limiting TMF amplitudes in high-mobility materials. Using high-resolution kinetic simulations, we show that the TMF amplitude at a maximum decays exponentially as a function of the e-e scattering length, which leads to a ready approach to extract this length from the measured TMF amplitudes. The approach is applied to measure the temperature-dependent e-e scattering length in high-mobility GaAs/AlGaAs heterostructures. The simulations further reveal current vortices that accompany the cyclotron orbits - a collective phenomenon counterintuitive to the ballistic transport underlying a TMF setting.

Electron-electron scattering plays a crucial role in many solid state phenomena; however, the direct measurement of electron-electron scattering length is challenging. Here, the authors use transverse magnetic focusing to measure this quantity in high-mobility GaAs/AlGaAs heterostructures.

Anomalous Hydrodynamics in a One-Dimensional Electronic Fluid

We construct multimode viscous hydrodynamics for one-dimensional spinless electrons. Depending on the scale, the fluid has six (shortest lengths), four (intermediate, exponentially broad regime), or three (asymptotically long scales) hydrodynamic modes. Interaction between hydrodynamic modes leads to anomalous scaling of physical observables and waves propagating in the fluid. In the four-mode regime, all modes are ballistic and acquire Kardar-Parisi-Zhang (KPZ)-like broadening with asymmetric power-law tails. "Heads" and "tails" of the waves contribute equally to thermal conductivity, leading to ω^{-1/3} scaling of its real part. In the three-mode regime, the system is in the universality class of a classical viscous fluid [O. Narayan and S. Ramaswamy, Anomalous Heat Conduction in One-Dimensional Momentum-Conserving Systems, Phys. Rev. Lett. 89, 200601 (2002).PRLTAO0031-900710.1103/PhysRevLett.89.200601, H. Spohn, Nonlinear fluctuating hydrodynamics for anharmonic chains, J. Stat. Phys. 154, 1191 (2014).JSTPBS0022-471510.1007/s10955-014-0933-y]. Self-interaction of the sound modes results in a KPZ-like shape, while the interaction with the heat mode results in asymmetric tails. The heat mode is governed by Levy flight distribution, whose power-law tails give rise to ω^{-1/3} scaling of heat conductivity.

Electron-Hole Scattering Limited Transport of Dirac Fermions in a Topological Insulator

We have experimentally investigated the effect of electron temperature on transport in the two-dimensional Dirac surface states of the three-dimensional topological insulator HgTe. We have found that around the minimal conductivity point, where both electrons and holes are present, heating the carriers with a DC current results in a nonmonotonic differential resistance of narrow channels. We have shown that the observed initial increase in resistance can be attributed to electron-hole scattering, while the decrease follows naturally from the change in Fermi energy of the charge carriers. Both effects are governed dominantly by a van Hove singularity in the bulk valence band. The results demonstrate the importance of interband electron-hole scattering in the transport properties of topological insulators.

Topological Quantum Materials from the Viewpoint of Chemistry

Topology, a mathematical concept, has recently become a popular and truly transdisciplinary topic encompassing condensed matter physics, solid state chemistry, and materials science. Since there is a direct connection between real space, namely atoms, valence electrons, bonds, and orbitals, and reciprocal space, namely bands and Fermi surfaces, via symmetry and topology, classifying topological materials within a single-particle picture is possible. Currently, most materials are classified as trivial insulators, semimetals, and metals or as topological insulators, Dirac and Weyl nodal-line semimetals, and topological metals. The key ingredients for topology are certain symmetries, the inert pair effect of the outer electrons leading to inversion of the conduction and valence bands, and spin-orbit coupling. This review presents the topological concepts related to solids from the viewpoint of a solid-state chemist, summarizes techniques for growing single crystals, and describes basic physical property measurement techniques to characterize topological materials beyond their structure and provide examples of such materials. Finally, a brief outlook on the impact of topology in other areas of chemistry is provided at the end of the article.

Hydrodynamic and Ballistic Transport over Large Length Scales in GaAs/AlGaAs

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 demarcate various transport regimes.

Thermal resistivity and hydrodynamics of the degenerate electron fluid in antimony

Detecting hydrodynamic fingerprints in the flow of electrons in solids constitutes a dynamic field of investigation in contemporary condensed matter physics. Most attention has been focused on the regime near the degeneracy temperature when the thermal velocity can present a spatially modulated profile. Here, we report on the observation of a hydrodynamic feature in the flow of quasi-ballistic degenerate electrons in bulk antimony. By scrutinizing the temperature dependence of thermal and electric resistivities, we detect a size-dependent departure from the Wiedemann-Franz law, unexpected in the momentum-relaxing picture of transport. This observation finds a natural explanation in the hydrodynamic picture, where upon warming, momentum-conserving collisions reduce quadratically in temperature both viscosity and thermal diffusivity. This effect has been established theoretically and experimentally in normal-state liquid ³He. The comparison of electrons in antimony and fermions in ³He paves the way to a quantification of momentum-conserving fermion-fermion collision rate in different Fermi liquids.

Viscous fermionic flow appears in liquid helium but rarely appears in metallic solid. Here, Jaoui et al. report a T-square thermal resistivity due to momentum conserving electronic scattering in semi-metallic antimony, which is in agreement with the hydrodynamic scenario.

Thermal transport of helium-3 in a strongly confining channel

The investigation of transport properties in normal liquid helium-3 and its topological superfluid phases provides insights into related phenomena in electron fluids, topological materials, and putative topological superconductors. It relies on the measurement of mass, heat, and spin currents, due to system neutrality. Of particular interest is transport in strongly confining channels of height approaching the superfluid coherence length, to enhance the relative contribution of surface excitations, and suppress hydrodynamic counterflow. Here we report on the thermal conduction of helium-3 in a 1.1 μm high channel. In the normal state we observe a diffusive thermal conductivity that is approximately temperature independent, consistent with interference of bulk and boundary scattering. In the superfluid, the thermal conductivity is only weakly temperature dependent, requiring detailed theoretical analysis. An anomalous thermal response is detected in the superfluid which we propose arises from the emission of a flux of surface excitations from the channel.

Electron hydrodynamics in anisotropic materials

Rotational invariance strongly constrains the viscosity tensor of classical fluids. When this symmetry is broken in anisotropic materials a wide array of novel phenomena become possible. We explore electron fluid behaviors arising from the most general viscosity tensors in two and three dimensions, constrained only thermodynamics and crystal symmetries. We find nontrivial behaviors in both two- and three-dimensional materials, including imprints of the crystal symmetry on the large-scale flow pattern. Breaking time-reversal symmetry introduces a non-dissipative Hall component to the viscosity tensor, and while this vanishes for 3D isotropic systems we show it need not for anisotropic materials. Further, for such systems we find that the electronic fluid stress can couple to the vorticity without breaking time-reversal symmetry. Our work demonstrates the anomalous landscape for electron hydrodynamics in systems beyond graphene, and presents experimental geometries to quantify the effects of electronic viscosity.

Heat vortex in hydrodynamic phonon transport of two-dimensional materials

We study hydrodynamic phonon heat transport in two-dimensional (2D) materials. Starting from the Peierls-Boltzmann equation with the Callaway model approximation, we derive a 2D Guyer-Krumhansl-like equation describing hydrodynamic phonon transport, taking into account the quadratic dispersion of flexural phonons. In addition to Poiseuille flow, second sound propagation, the equation predicts heat current vortices and negative non-local thermal conductance in 2D materials, which are common in classical fluids but have not yet been considered in phonon transport. Our results also illustrate the universal transport behaviors of hydrodynamics, independent of the type of quasi-particles and their microscopic interactions.

Stokes flow around an obstacle in viscous two-dimensional electron liquid

The electronic analog of the Poiseuille flow is the transport in a narrow channel with disordered edges that scatter electrons in a diffuse way. In the hydrodynamic regime, the resistivity decreases with temperature, referred to as the Gurzhi effect, distinct from conventional Ohmic behaviour. We studied experimentally an electronic analog of the Stokes flow around a disc immersed in a two-dimensional viscous liquid. The circle obstacle results in an additive contribution to resistivity. If specular boundary conditions apply, it is no longer possible to detect Poiseuille type flow and the Gurzhi effect. However, in flow through a channel with a circular obstacle, the resistivity decreases with temperature. By tuning the temperature, we observed the transport signatures of the ballistic and hydrodynamic regimes on the length scale of disc size. Our experimental results confirm theoretical predictions.

Imaging Time-Dependent Electronic Currents through a Graphene-Based Nanojunction

To assist the design of efficient molecular junctions, a precise understanding of the charge transport mechanisms through nanoscaled devices is of prime importance. In the present contribution, we present time- and space-resolved electron transport simulations through a nanojunction under time-dependent potential biases. We use the driven Liouville-von Neumann approach to simulate the time evolution of the one-electron density matrix under nonequilibrium conditions, which allows us to capture the ultrafast scattering dynamics, the electronic relaxation process, and the quasi-stationary current limit from the same simulation. Using local projection techniques, we map the coherent electronic current density, unraveling insightful mechanistic details of the transport on time scales ranging from atto- to picoseconds. Memory effects dominate the early time transport process, and they reveal different current patterns on short time scales in comparison to those in the long-time regime. For nanotransistors with high switching rates, the scattering perspective on electron transport should thus be favored.

Tomographic Dynamics and Scale-Dependent Viscosity in 2D Electron Systems

Fermi gases in two dimensions display collective dynamics originating from head-on collisions, a collinear carrier scattering process that dominates angular relaxation at not-too-high temperatures T≪T_{F}. In this regime, a large family of excitations emerges, with an odd-parity angular structure of momentum distribution and exceptionally long lifetimes. This leads to "tomographic" dynamics: fast 1D spatial diffusion along the unchanging velocity direction accompanied by a slow angular dynamics that gradually randomizes velocity orientation. The tomographic regime features an unusual hierarchy of timescales and scale-dependent transport coefficients with nontrivial fractional scaling dimensions, leading to fractional-power current flow profiles and unusual conductance scaling versus sample width.

Unified Description of the Classical Hall Viscosity

In the 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 the Hall viscosity and the 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 the channel. Ballistic flow, on the other hand, is dominated by boundary effects. In a Corbino geometry, viscous effects arise not from boundary friction but from the circular flow pattern of the Hall current. In this geometry, we introduce a viscous Hall angle that remains well defined throughout the crossover from ballistic to hydrodynamic flow and captures the bulk viscous response of the fluid.

Dissipative and Hall Viscosity of a Disordered 2D Electron Gas

Hydrodynamic charge transport is at the center of recent research efforts. Of particular interest is the nondissipative Hall viscosity, which conveys topological information in clean gapped systems. The prevalence of disorder in the real world calls for a study of its effect on viscosity. Here we address this question, both analytically and numerically, in the context of disordered noninteracting 2D electrons. Analytically, we employ the self-consistent Born approximation, explicitly taking into account the modification of the single-particle density of states and the elastic transport time due to the Landau quantization. The reported results interpolate smoothly between the limiting cases of a weak (strong) magnetic field and strong (weak) disorder. In the regime of a weak magnetic field our results describe the quantum (Shubnikov-de Haas type) oscillations of the dissipative and Hall viscosity. For strong magnetic fields we characterize the effects of the disorder-induced broadening of the Landau levels on the viscosity coefficients. This is supplemented by numerical calculations for a few filled Landau levels. Our results show that the Hall viscosity is surprisingly robust to disorder.

Enhanced Photoenergy Harvesting and Extreme Thomson Effect in Hydrodynamic Electronic Systems

The thermoelectric (TE) properties of a material are dramatically altered when electron-electron interactions become the dominant scattering mechanism. In the degenerate hydrodynamic regime, the thermal conductivity is reduced and becomes a decreasing function of the electronic temperature, due to a violation of the Wiedemann-Franz law. We here show how this peculiar temperature dependence gives rise to new striking TE phenomena. These include an 80-fold increase in TE efficiency compared to the Wiedemann-Franz regime, dramatic qualitative changes in the steady state temperature profile, and an anomalously large Thomson effect. In graphene, which we pay special attention to here, these effects are further amplified due to a doubling of the thermopower.

Measuring Hall viscosity of graphene's electron fluid

An electrical conductor subjected to a magnetic field exhibits the Hall effect in the presence of current flow. Here, we report a qualitative deviation from the standard behavior in electron systems with high viscosity. We found that the viscous electron fluid in graphene responds to nonquantizing magnetic fields by producing an electric field opposite to that generated by the ordinary Hall effect. The viscous contribution is substantial and identified by studying local voltages that arise in the vicinity of current-injecting contacts. We analyzed the anomaly over a wide range of temperatures and carrier densities and extracted the Hall viscosity, a dissipationless transport coefficient that was long identified theoretically but remained elusive in experiments.

Stokes flow analogous to viscous electron current in graphene

Electron transport in two-dimensional conducting materials such as graphene, with dominant electron-electron interaction, exhibits unusual vortex flow that leads to a nonlocal current-field relation (negative resistance), distinct from the classical Ohm's law. The transport behavior of these materials is best described by low Reynolds number hydrodynamics, where the constitutive pressure-speed relation is Stoke's law. Here we report evidence of such vortices observed in a viscous flow of Newtonian fluid in a microfluidic device consisting of a rectangular cavity-analogous to the electronic system. We extend our experimental observations to elliptic cavities of different eccentricities, and validate them by numerically solving bi-harmonic equation obtained for the viscous flow with no-slip boundary conditions. We verify the existence of a  predicted threshold at which vortices appear. Strikingly, we find that a two-dimensional theoretical model captures the essential features of three-dimensional Stokes flow in experiments.

Electron aspirator using electron-electron scattering in nanoscale silicon

Current enhancement without increasing the input power is a critical issue to be pursued for electronic circuits. However, drivability of metal-oxide-semiconductor (MOS) transistors is limited by the source-injection current, and electrons that have passed through the source unavoidably waste their momentum to the phonon bath. Here, we propose the Si electron-aspirator, a nanometer-scaled MOS device with a T-shaped branch, to go beyond this limit. The device utilizes the hydrodynamic nature of electrons due to the electron-electron scattering, by which the injected hot electrons transfer their momentum to cold electrons before they relax with the phonon bath. This momentum transfer induces an electron flow from the grounded side terminal without additional power sources. The operation is demonstrated by observing the output-current enhancement by a factor of about 3 at 8 K, which reveals that the electron-electron scattering can govern the electron transport in nanometer-scaled MOS devices, and increase their effective drivability.

Prospects for the Detection of Electronic Preturbulence in Graphene

Based on extensive numerical simulations, accounting for electrostatic interactions and dissipative electron-phonon scattering, we propose experimentally realizable geometries capable of sustaining electronic preturbulence in graphene samples. In particular, preturbulence is predicted to occur at experimentally attainable values of the Reynolds number between 10 and 50, over a broad spectrum of frequencies between 10 and 100 GHz.

Two-Particle Collisional Coordinate Shifts and Hydrodynamic Anomalous Hall Effect in Systems without Lorentz Invariance

We show that electrons undergoing a two-particle collision in a crystal experience a coordinate shift that depends on their single-particle Bloch wave functions and derive a gauge-invariant expression for such a shift, valid for arbitrary band structures and arbitrary two-particle interaction potentials. As an application of the theory, we consider two-particle coordinate shifts for Weyl fermions in space of three spatial dimensions. We demonstrate that such shifts in general contribute to the anomalous Hall conductivity of a clean electron liquid.

Fluidity onset in graphene

Viscous electron fluids have emerged recently as a new paradigm of strongly-correlated electron transport in solids. Here we report on a direct observation of the transition to this long-sought-for state of matter in a high-mobility electron system in graphene. Unexpectedly, the electron flow is found to be interaction-dominated but non-hydrodynamic (quasiballistic) in a wide temperature range, showing signatures of viscous flows only at relatively high temperatures. The transition between the two regimes is characterized by a sharp maximum of negative resistance, probed in proximity to the current injector. The resistance decreases as the system goes deeper into the hydrodynamic regime. In a perfect darkness-before-daybreak manner, the interaction-dominated negative response is strongest at the transition to the quasiballistic regime. Our work provides the first demonstration of how the viscous fluid behavior emerges in an interacting electron system.

Particle Collisions and Negative Nonlocal Response of Ballistic Electrons

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 irrefutable evidence to that of a mere forerunner. Furthermore, we find that negative response is log enhanced in the ballistic regime by the physics related to the seminal Dorfman-Cohen log divergence due to memory effects in the kinetics of dilute gases. The ballistic regime therefore offers a unique setting for exploring these interesting effects due to electron interactions.

Out-of-Bounds Hydrodynamics in Anisotropic Dirac Fluids

We study hydrodynamic transport in two-dimensional, interacting electronic systems with merging Dirac points at charge neutrality. The dispersion along one crystallographic direction is Dirac-like, while it is Newtonian-like in the orthogonal direction. As a result, the electrical conductivity is metallic in one and insulating in the other direction. The shear viscosity tensor contains six independent components, which can be probed by measuring an anisotropic thermal flow. One of the viscosity components vanishes at zero temperature leading to a generalization of the previously conjectured lower bound for the shear viscosity to entropy density ratio.

Universal linear and nonlinear electrodynamics of a Dirac fluid

A general relation is derived between the linear and second-order nonlinear ac conductivities of an electron system in the hydrodynamic regime of frequencies below the interparticle scattering rate. The magnitude and tensorial structure of the hydrodynamic nonlinear conductivity are shown to differ from their counterparts in the more familiar kinetic regime of higher frequencies. Due to universality of the hydrodynamic equations, the obtained formulas are valid for systems with an arbitrary Dirac-like dispersion, ranging from solid-state electron gases to free-space plasmas, either massive or massless, at any temperature, chemical potential, or space dimension. Predictions for photon drag and second-harmonic generation in graphene are presented as one application of this theory.

Kinetic Theory of Electronic Transport in Random Magnetic Fields

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∝T^{2} resistivity in a Fermi liquid may describe low T transport in single-band SrTiO_{3}.

Hydrodynamics of electrons in graphene

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. We derive hydrodynamics, both from a phenomenological perspective and using kinetic theory. We then describe how hydrodynamic electron flow is visible in electronic transport measurements. Although we focus on graphene in this review, the broader framework naturally generalizes to other materials. We assume only basic knowledge of condensed matter physics, and no prior knowledge of hydrodynamics.

Evidence for topological type-II Weyl semimetal WTe2

Recently, a type-II Weyl fermion was theoretically predicted to appear at the contact of electron and hole Fermi surface pockets. A distinguishing feature of the surfaces of type-II Weyl semimetals is the existence of topological surface states, so-called Fermi arcs. Although WTe₂ was the first material suggested as a type-II Weyl semimetal, the direct observation of its tilting Weyl cone and Fermi arc has not yet been successful. Here, we show strong evidence that WTe₂ is a type-II Weyl semimetal by observing two unique transport properties simultaneously in one WTe₂ nanoribbon. The negative magnetoresistance induced by a chiral anomaly is quite anisotropic in WTe₂ nanoribbons, which is present in b-axis ribbon, but is absent in a-axis ribbon. An extra-quantum oscillation, arising from a Weyl orbit formed by the Fermi arc and bulk Landau levels, displays a two dimensional feature and decays as the thickness increases in WTe₂ nanoribbon.

Exotic transport properties of type-II Weyl semimetals have been predicted but are yet to be experimentally evidenced. Here, Li et al. report evidences of an anisotropy of negative magnetoresistance and a quantum oscillation arising from the predicted Weyl orbit in the type-II Weyl semimetal WTe₂.

Resistivity bound for hydrodynamic bad metals

We obtain a rigorous upper bound on the resistivity [Formula: see text] of an electron fluid whose electronic mean free path is short compared with the scale of spatial inhomogeneities. When such a hydrodynamic electron fluid supports a nonthermal diffusion process-such as an imbalance mode between different bands-we show that the resistivity bound becomes [Formula: see text] The coefficient [Formula: see text] is independent of temperature and inhomogeneity lengthscale, and [Formula: see text] is a microscopic momentum-preserving scattering rate. In this way, we obtain a unified mechanism-without umklapp-for [Formula: see text] in a Fermi liquid and the crossover to [Formula: see text] in quantum critical regimes. This behavior is widely observed in transition metal oxides, organic metals, pnictides, and heavy fermion compounds and has presented a long-standing challenge to transport theory. Our hydrodynamic bound allows phonon contributions to diffusion constants, including thermal diffusion, to directly affect the electrical resistivity.

Linking Spatial Distributions of Potential and Current in Viscous Electronics

Viscous electronics is an emerging field dealing with systems in which strongly interacting electrons behave as a fluid. Electron viscous flows are governed by a nonlocal current-field relation which renders the spatial patterns of the current and electric field strikingly dissimilar. Notably, driven by the viscous friction force from adjacent layers, current can flow against the electric field, generating negative resistance, vorticity, and vortices. Moreover, different current flows can result in identical potential distributions. This sets a new situation where inferring the electron flow pattern from the measured potentials presents a nontrivial problem. Using the inherent relation between these patterns through complex analysis, here we propose a method for extracting the current flows from potential distributions measured in the presence of a magnetic field.

Viscous Dissipation in One-Dimensional Quantum Liquids

We develop a theory of viscous dissipation in one-dimensional single-component quantum liquids at low temperatures. Such liquids are characterized by a single viscosity coefficient, the bulk viscosity. We show that for a generic interaction between the constituent particles this viscosity diverges in the zero-temperature limit. In the special case of integrable models, the viscosity is infinite at any temperature, which can be interpreted as a breakdown of the hydrodynamic description. Our consideration is applicable to all single-component Galilean-invariant one-dimensional quantum liquids, regardless of the statistics of the constituent particles and the interaction strength.

Hydrodynamic Electron Flow and Hall Viscosity

In metallic samples of small enough size and sufficiently strong momentum-conserving scattering, the viscosity of the electron gas can become the dominant process governing transport. In this regime, momentum is a long-lived quantity whose evolution is described by an emergent hydrodynamical theory. Furthermore, breaking time-reversal symmetry leads to the appearance of an odd component to the viscosity called the Hall viscosity, which has attracted considerable attention recently due to its quantized nature in gapped systems but still eludes experimental confirmation. Based on microscopic calculations, we discuss how to measure the effects of both the even and odd components of the viscosity using hydrodynamic electronic transport in mesoscopic samples under applied magnetic fields.