Observation of the Dirac fluid and the breakdown of the Wiedemann-Franz law in graphene

Crossno, Jesse; Shi, Jing; Wang, Ke; Liu, Xiaomeng; Harzheim, Achim; Lucas, Andrew; Sachdev, Subir; Kim, Philip; Taniguchi, Takashi; Watanabe, Kenji; Ohki, Thomas A.; Fong, Kin Chung

doi:10.1126/science.aad0343

Cited by 626 publications

(737 citation statements)

References 64 publications

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“…Examples include transport near relativistic quantum critical points [12], in graphene [13,14] and in Weyl semi-metals [15]. For conducting matter, MHD is a natural extension of such hydrodynamic models.…”

Section: Jhep05(2017)001mentioning

confidence: 99%

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Relativistic magnetohydrodynamics

Hernandez

Kovtun

2017

J. High Energ. Phys.

135

313

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Abstract:We present the equations of relativistic hydrodynamics coupled to dynamical electromagnetic fields, including the effects of polarization, electric fields, and the derivative expansion. We enumerate the transport coefficients at leading order in derivatives, including electrical conductivities, viscosities, and thermodynamic coefficients. We find the constraints on transport coefficients due to the positivity of entropy production, and derive the corresponding Kubo formulas. For the neutral state in a magnetic field, small fluctuations include Alfvén waves, magnetosonic waves, and the dissipative modes. For the state with a non-zero dynamical charge density in a magnetic field, plasma oscillations gap out all propagating modes, except for Alfvén-like waves with a quadratic dispersion relation. We relate the transport coefficients in the "conventional" magnetohydrodynamics (formulated using Maxwell's equations in matter) to those in the "dual" version of magnetohydrodynamics (formulated using the conserved magnetic flux).

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Section: Jhep05(2017)001mentioning

confidence: 99%

“…At non-zero B 0 , the three gapless modes all have quadratic dispersion relation at small momenta. There are two propagating waves with real frequencies 13) JHEP05 (2017)001 where θ is the angle between k and B 0 , and one diffusive mode. For B 2 0 M Ω,µ 0 + p 0 , the diffusive frequency is…”

Section: Jhep05(2017)001mentioning

confidence: 99%

Relativistic magnetohydrodynamics

Hernandez

Kovtun

2017

J. High Energ. Phys.

135

313

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“…Then (2.45) implies that DðkÞ will have a negative eigenvalue, for small k, and hence, from (2.44) we deduce that there will be a diffusion pole in the upper half plane leading to a dynamical instability. 4 …”

Section: ð2:35þmentioning

confidence: 99%

“…However, motivated by recent experimental progress [3][4][5], there has been considerable theoretical work using hydrodynamics to study thermoelectric transport [2,[6][7][8][9][10][11][12][13][14][15][16][17][18] and it is therefore of interest to see how our general results on diffusion manifest themselves in this particular context. More specifically, we will study this within the context of relativistic hydrodynamics, describing the hydrodynamic limit of a relativistic quantum field theory.…”

Section: Introductionmentioning

confidence: 99%

Diffusion in inhomogeneous media

2017

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The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. We consider the transport of conserved charges in spatially inhomogeneous quantum systems with a discrete lattice symmetry. We analyze the retarded two-point functions involving the charges and the associated currents at long wavelengths, compared to the scale of the lattice, and, when the dc conductivities are finite, extract the hydrodynamic modes associated with diffusion of the charges. We show that the dispersion relations of these modes are related to the eigenvalues of a specific matrix constructed from the dc conductivities and certain thermodynamic susceptibilities, thus obtaining generalized Einstein relations. We illustrate these general results in the specific context of relativistic hydrodynamics where translation invariance is broken using spatially inhomogeneous and periodic deformations of the stress tensor and the conserved Uð1Þ currents. Equivalently, this corresponds to considering hydrodynamics on a curved manifold, with a spatially periodic metric and chemical potential, and we obtain the dispersion relations for the heat and charge diffusive modes.

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“…The need to develop models that allow to address the question of real-time transport in strongly interacting quantum fluids has arisen from experiments in completely different areas of physics: in the quark gluon plasma generated in heavy ion collisions, the collective behavior of ultra-cold atoms, the strange metal phase of the high-T c superconductors and most recently the hydrodynamic electronic flow observed in Graphene and similar materials [2][3][4][5].…”

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confidence: 99%

Odd Viscosity in the Quantum Critical Region of a Holographic Weyl Semimetal

2016

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We study odd viscosity in a holographic model of a Weyl semimetal. The model is characterised by a quantum phase transition from a topological semimetal to a trivial semimetal state. Since the model is axisymmetric in three spatial dimensions there are two independent odd viscosities. Both odd viscosity coefficients are non-vanishing in the quantum critical region and non-zero only due to the mixed axial gravitational anomaly. It is therefore a novel example in which the mixed axial gravitational anomaly gives rise to a transport coefficient at first order in derivatives at finite temperature. We also compute anisotropic shear viscosities and show that one of them violates the KSS bound. In the quantum critical region, the physics of viscosities as well as conductivities is governed by the quantum critical point. Introduction.-One of the most surprising outcomes of string theory is the application of the AdS/CFT correspondence to the physics of strongly interacting quantum many-body systems [1]. The need to develop models that allow to address the question of real-time transport in strongly interacting quantum fluids has arisen from experiments in completely different areas of physics: in the quark gluon plasma generated in heavy ion collisions, the collective behavior of ultra-cold atoms, the strange metal phase of the high-T c superconductors and most recently the hydrodynamic electronic flow observed in Graphene and similar materials [2][3][4][5].

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Observation of the Dirac fluid and the breakdown of the Wiedemann-Franz law in graphene

Cited by 626 publications

References 64 publications

Relativistic magnetohydrodynamics

Relativistic magnetohydrodynamics

Diffusion in inhomogeneous media

Odd Viscosity in the Quantum Critical Region of a Holographic Weyl Semimetal

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