Electron hydrodynamics dilemma: Whirlpools or no whirlpools

Pellegrino, Francesco; Torre, Iacopo; Geǐm, A. K.; Polini, Marco

doi:10.1103/physrevb.94.155414

Cited by 103 publications

(131 citation statements)

References 36 publications

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“…In this section we provide a validation of this numerical approach by simulating steady-state flows in the so-called "vicinity-geometry", which has been subject of several theoretical and experimental studies [98][99][100] to outline phenomena such as negative nonlocal resistance, current whirlpools, and measuring the Hall viscosity of graphene's electrons fluid. The geometrical setup is sketched in Fig.…”

Section: Hydrodynamic Flow Of Electrons In Graphenementioning

confidence: 99%

Relativistic lattice Boltzmann methods: Theory and applications

et al. 2020

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We present a systematic account of recent developments of the relativistic Lattice Boltzmann method (RLBM) for dissipative hydrodynamics. We describe in full detail a unified, compact and dimension-independent procedure to design relativistic LB schemes capable of bridging the gap between the ultra-relativistic regime, k B T mc 2 , and the non-relativistic one, k B T mc 2 . We further develop a systematic derivation of the transport coefficients as a function of the kinetic relaxation time in d = 1, 2, 3 spatial dimensions. The latter step allows to establish a quantitative bridge between the parameters of the kinetic model and the macroscopic transport coefficients. This leads to accurate calibrations of simulation parameters and is also relevant at the theoretical level, as it provides neat numerical evidence of the correctness of the Chapman-Enskog procedure. We present an extended set of validation tests, in which simulation results based on the RLBMs are compared with existing analytic or semi-analytic results in the mildly-relativistic (k B T ∼ mc 2 ) regime for the case of shock propagations in quark-gluon plasmas and laminar electronic flows in ultra-clean graphene samples. It is hoped and expected that the material collected in this paper may allow the interested readers to reproduce the present results and generate new applications of the RLBM scheme.

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Section: Hydrodynamic Flow Of Electrons In Graphenementioning

confidence: 99%

Relativistic lattice Boltzmann methods: Theory and applications

et al. 2020

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“…How do the ballistic vortices compare to vortices in the hydrodynamic regime? To compute the vortical response in the hydrodynamic regime, it is easiest to resort to the fluid momentum conservation equation [54][55][56],…”

Section: B Hydrodynamic Vs Ballistic Vorticesmentioning

confidence: 99%

“…x [54]. We note here that the disorder requirements for vortex formation in the hydrodynamic regime are greatly mollified in AC transport, where they become equal to the ballistic regime [39].…”

Section: B Hydrodynamic Vs Ballistic Vorticesmentioning

confidence: 99%

Hydrodynamic and ballistic AC transport in two-dimensional Fermi liquids

et al. 2019

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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 free conformal field theory (CFT) with a dynamical scaling exponent z = 1. Its nontrivial aspects emerge in device geometries with shear, wherein the regime has an intrinsic universal dissipation, a nonlocal current-voltage relation, and exhibits the critical scaling of the underlying CFT. The Fermi surface has electron-hole pockets across all angular scales and the current flow has vortices at all spatial scales. We image the fluctuations in high-definition and animate their emergence as experimental parameters are tuned to the QCP a . The vortices clearly demonstrate that Pauli exclusion alone can produce collective effects, with low-frequency AC transport mediated by vortex dynamics b . The scale-invariant spatial structure is much richer than that of an interaction-dominated hydrodynamic regime, which only has a single vortex at the device scale. Our findings provide a theoretical framework for both interaction-free and interaction-dominated non-Ohmic transport in two-dimensional materials, as seen in several contemporary experiments. a Spatial fluctuations: https://vimeo.com/365020115 , Fermi surface fluctuations: https://vimeo.com/ 364982637 b Vortex dynamics and frequency crossover: https://vimeo.com/366725650Quantum critical points (QCP) mediate second-order quantum phase transitions (QPT), produced by tuning non-thermal parameters such as doping, magnetic field or pressure. Systems at QCPs obey universal scaling, and are dominated by quantum fluctuations [1]. A prototypical QPT occurs in the 1D quantum Ising model in a transverse magnetic field, realized in CoNb 2 O 6 [2]. As the external field is increased, the ground state changes from an ordered phase set by exchange interaction to a field-aligned quantum paramagnet. The transition occurs through a QCP with a dynamical scaling exponent z = 1, which connects the correlation length ξ and time τ via τ ∝ ξ z . Remarkably, the ubiquitous Fermi liquid hosts exactly such a QCP in the form of free fermions; a Fermi gas. Absent all interactions, gapless quasiparticles on the Fermi surface obey a relativistic free-field conformal field theory (CFT), with the speed of light set by the Fermi velocity v F [3]. This simple CFT exhibits critical scaling with z = 1. Microscopic interactions are indeed irrelevant, as expected at criticality, because there are none.Although a Fermi gas obeys critical scaling [4], it is never pictured as a QCP. The singleparticle Green's function has a simple pole, not a branch cut characteristic of interacting QCPs [5]; it is unclear how and where critical fluctuatio...

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“…In this geometry one expects positive vicinity voltages for diffusive and ballistic electron motion in the channel, and negative values if electron-electron interaction is dominant [4,9,13]. In the latter case back-flow currents are proposed [11] as indicated by the schematic flow pattern in Fig. 1(a).…”

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confidence: 95%

Scanning gate microscopy in a viscous electron fluid

et al. 2018

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We measure transport through a Ga [Al]As heterostructure at temperatures between 32 mK and 30 K. Increasing the temperature enhances the electron-electron scattering rate and viscous effects in the two-dimensional electron gas arise. To probe this regime we measure so-called vicinity voltages and use a voltage-biased scanning tip to induce a movable local perturbation. We find that the scanning gate images differentiate reliably between the different regimes of electron transport. Our data are in good agreement with recent theories for interacting electron liquids in the ballistic and viscous regimes stimulated by measurements in graphene. However, the range of temperatures and densities where viscous effects are observable in Ga [Al]As are very distinct from the graphene material system. arXiv:1807.03177v3 [cond-mat.mes-hall]

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Electron hydrodynamics dilemma: Whirlpools or no whirlpools

Cited by 103 publications

References 36 publications

Relativistic lattice Boltzmann methods: Theory and applications

Relativistic lattice Boltzmann methods: Theory and applications

Hydrodynamic and ballistic AC transport in two-dimensional Fermi liquids

Scanning gate microscopy in a viscous electron fluid

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