Fluidity onset in graphene

Bandurin, Denis; Shytov, A. V.; Levitov, L. S.; Kumar, Roshan Krishna; Berdyugin, A. I.; Shalom, M. Ben; Grigorieva, I. V.; Geǐm, A. K.; Falkovich, Gregory

doi:10.1038/s41467-018-07004-4

Cited by 195 publications

(182 citation statements)

References 44 publications

(88 reference statements)

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“…93 is used to parametrize phonon-electron scattering as a friction term, with τ D the single scattering time. Albeit very simple, this parametrization has proven successful in describing experiments in the linear-response regime [102][103][104]. 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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“…The implications of a dominant viscous force on electronic flow have been studied in wide range of theoretical works [5][6][7][8][9][10] . While initial efforts were primarily based on linearized Navier-Stokes equations, which describe electron hydrodynamics in the context of diffusive transport [11][12][13] , there is now a developing understanding that a central part of the physical picture is the emergence of hydrodynamics from ballistic flow [14][15][16][17][18][19][20][21][22] . Reaching the hydrodynamic regime in experiment requires materials of such high purity that the influence of ohmic, transport can be minimized, which is now possible in a growing number of high-mobility systems.…”

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Visualizing Poiseuille flow of hydrodynamic electrons

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Ella

Rozen

et al. 2019

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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 image the Hall voltage of electronic flow through channels of high-mobility graphene. We find that the profile of the Hall field across the channel is a key physical quantity for distinguishing ballistic from hydrodynamic flow. We image the transition from flat, ballistic field profiles at low temperature into parabolic field profiles at elevated temperatures, which is the hallmark of Poiseuille flow. The curvature of the imaged profiles is qualitatively reproduced by Boltzmann calculations, which allow us to create a 'phase diagram' that characterizes the electron flow regimes. Our results provide long-sought, direct confirmation of Poiseuille flow in the solid state, and enable a new approach for exploring the rich physics of interacting electrons in real space.

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“…Transport in metals is usually dominated by MR scattering which results in a diffusive Ohmic regime. A novel hydrodynamic regime with collective fluid-like behavior, found in graphene [24][25][26][27], (Ga,Al)As [28][29][30] and other select materials [31][32][33][34], can arise when MR scattering is weak and MC scattering is strong. We show that the transition from an Ohmic to a hydrodynamic regime can be readily tuned to occur through the fluctuation-dominated ballistic regime, realizing a QCP-mediated nonequilibrium transition.…”

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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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Fluidity onset in graphene

Cited by 195 publications

References 44 publications

Relativistic lattice Boltzmann methods: Theory and applications

Relativistic lattice Boltzmann methods: Theory and applications

Visualizing Poiseuille flow of hydrodynamic electrons

Hydrodynamic and ballistic AC transport in two-dimensional Fermi liquids

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