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A hydrodynamic flow of electrons driven by an oscillating electric field is investigated. It is found that a double-peak profile of the electric current can appear. Such a profile originates from the interplay of viscous and inertial properties of the electron fluid as well as the boundary conditions. The nontrivial profile of the current results in a characteristic stray magnetic field where peaks could also occur in one of the field components. Analytical results are supported by numerical calculations in samples of different geometries such as straight channel, nozzle, and cavity and are found to be qualitatively insensitive to a specific form of the oscillating electric field. In addition, it is shown that nozzle and cavity provide an efficient means to locally enhance or reduce the fluid velocity.
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Electron-electron (e-e) collisions can impact transport in a variety of surprising and sometimes counterintuitive ways. Despite strong interest, experiments on the subject proved challenging because of the simultaneous presence of different scattering mechanisms that suppress or obscure consequences of e-e scattering. Only recently, sufficiently clean electron systems with transport dominated by e-e collisions have become available, showing behavior characteristic of highly viscous fluids. Here we study electron transport through graphene constrictions and show that their conductance below 150 K increases with increasing temperature, in stark contrast to the metallic character of doped graphene. Notably, the measured conductance exceeds the maximum conductance possible for free electrons. This anomalous behavior is attributed to collective movement of interacting electrons, which shields individual carriers from momentum loss at sample boundaries. The measurements allow us to identify the conductance contribution arising due to electron viscosity and determine its temperature dependence. Besides fundamental interest, our work shows that viscous effects can facilitate high-mobility transport at elevated temperatures, a potentially useful behavior for designing graphene-based devices.
We investigate the impact of geometric constriction on the viscous flow of electron liquid through quantum point contacts. We provide analysis on the electric potential distribution given the setup of a slit configuration and use the method of conformal mapping to obtain analytical results. The potential profile can be tested and contrasted experimentally with the scanning tunneling potentiometry technique. We discuss intricate physics that underlies the Gurzhi effect, i.e. the enhancement of conductivity in the viscous flow, and calculate the temperature dependence of the momentum relaxation time as a result of impurity assisted quasi-ballistic interference effects. We caution that spatially inhomogeneous profiles of current in the Gurzhi crossover between Ohmic and Stokes flows might also appear in the non-hydrodynamic regime where non-locality plays an important role.
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.
We develop a theory of magnetoresistance of two-dimensional electron systems in a smooth disorder potential in the hydrodynamic regime. Our theory applies to two-dimensional semiconductor structures with strongly correlated carriers when the mean free path due to electron-electron collisions is sufficiently short. The dominant contribution to magnetoresistance arises from the modification of the flow pattern by the Lorentz force, rather than the magnetic field dependence of the kinetic coefficients of the electron liquid. The resulting magnetoresistance is positive and quadratic at weak fields. Although the resistivity is governed by both viscosity and thermal conductivity of the electron fluid, the magnetoresistance is controlled by the viscosity only. This enables extraction of viscosity of the electron liquid from magnetotransport measurements.
The electron-hole plasma in charge-neutral graphene is predicted to realize a quantum critical system whose transport features a universal hydrodynamic description, even at room temperature. This quantum critical Dirac fluid is expected to have a shear viscosity close to a minimum bound, with an inter-particle scattering rate saturating at the Planckian time $hbar/(k_B T)$. While electrical transport measurements at finite carrier density are consistent with hydrodynamic electron flow in graphene, a smoking gun of viscous behavior remains elusive. In this work, we directly image viscous Dirac fluid flow in graphene at room temperature via measurement of the associated stray magnetic field. Nanoscale magnetic imaging is performed using quantum spin magnetometers realized with nitrogen vacancy (NV) centers in diamond. Scanning single-spin and wide-field magnetometry reveals a parabolic Poiseuille profile for electron flow in a graphene channel near the charge neutrality point, establishing the viscous transport of the Dirac fluid. This measurement is in contrast to the conventional uniform flow profile imaged in an Ohmic conductor. Via combined imaging-transport measurements, we obtain viscosity and scattering rates, and observe that these quantities are comparable to the universal values expected at quantum criticality. This finding establishes a nearly-ideal electron fluid in neutral graphene at room temperature. Our results pave the way to study hydrodynamic transport in quantum critical fluids relevant to strongly-correlated electrons in high-$T_c$ superconductors. This work also highlights the capability of quantum spin magnetometers to probe correlated-electronic phenomena at the nanoscale.
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