Nonlocal transport and the hydrodynamic shear viscosity in graphene

Torre, Iacopo; Tomadin, Andrea; Geǐm, A. K.; Polini, Marco

doi:10.1103/physrevb.92.165433

Cited by 246 publications

(309 citation statements)

References 59 publications

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“…Previous studies of the electron hydrodynamics in graphene were carried out using the vicinity geometry and Hall bar devices of a uniform width. Anomalous (negative) voltages were observed, indicating a highly viscous flow, more viscous than that of honey 12,22,23 . In this report, we employ a narrow constriction geometry (Fig.…”

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confidence: 98%

Superballistic flow of viscous electron fluid through graphene constrictions

et al. 2017

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Electron-electron (e-e) collisions can impact transport in a variety of surprising and sometimes counterintuitive ways 1-6 . Despite strong interest, experiments on the subject proved challenging because of the simultaneous presence of di erent scattering mechanisms that suppress or obscure consequences of e-e scattering 7-11 . Only recently, su ciently clean electron systems with transport dominated by e-e collisions have become available, showing behaviour characteristic of highly viscous fluids 12-14 . 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 15 . Notably, the measured conductance exceeds the maximum conductance possible for free electrons 16,17 . This anomalous behaviour is attributed to collective movement of interacting electrons, which 'shields' individual carriers from momentum loss at sample boundaries 18,19 . 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 e ects can facilitate high-mobility transport at elevated temperatures, a potentially useful behaviour for designing graphene-based devices.Graphene hosts a high-quality electron system with weak phonon coupling 20,21 such that e-e collisions can become the dominant scattering process at elevated temperatures, T . In addition, the electronic structure of graphene inhibits Umklapp processes 15 , which ensures that e-e scattering is momentum conserving. These features lead to a fluid-like behaviour of charge carriers, with the momentum taking on the role of a collective variable that governs local equilibrium. Previous studies of the electron hydrodynamics in graphene were carried out using the vicinity geometry and Hall bar devices of a uniform width. Anomalous (negative) voltages were observed, indicating a highly viscous flow, more viscous than that of honey 12,22,23 . In this report, we employ a narrow constriction geometry (Fig. 1a) which offers unique insight into the behaviour of viscous electron fluids. In particular, the hydrodynamic conductance through such constrictions becomes

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confidence: 98%

Superballistic flow of viscous electron fluid through graphene constrictions

et al. 2017

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“…Spatially resolved measurements of the voltage allow determination of the viscosity. Torre, Tomadin, Geim, and Polini [77] considered the electron liquid in graphene in the hydrodynamic regime and showed that the shear viscosity could be determined from measurements of nonlocal resistances in multiterminal Hall bar devices. Although these proposals are promising for the two-dimensional electron fluids in graphene and semiconductor heterostructures fabrication of the relevant micron-scale devices may be particularly challenging for bad metals such as cuprates and organic charge-transfer salts.…”

Section: Experimental Determination Of η In Electronic Systemsmentioning

confidence: 99%

Shear viscosity of strongly interacting fermionic quantum fluids

Pakhira

McKenzie

2015

Phys. Rev. B

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Eighty years ago, Eyring proposed that the shear viscosity of a liquid η has a quantum limit η n where n is the density of the fluid. Using holographic duality and the anti-de Sitter/conformal field theory correspondence in string theory, Kovtun, Son, and Starinets (KSS) conjectured a universal bound η s 4πk B for the ratio between the shear viscosity and the entropy density s. Using dynamical mean-field theory, we calculate the shear viscosity and entropy density for a fermionic fluid described by a single-band Hubbard model at half-filling. Our calculated shear viscosity as a function of temperature is compared with experimental data for liquid 3 He. At low temperature, the shear viscosity is found to be well above the quantum limit and is proportional to the characteristic Fermi liquid 1/T 2 dependence, where T is the temperature. With increasing temperature and interaction strength U , there is significant deviation from the Fermi liquid form. Also, the shear viscosity violates the quantum limit near the crossover from coherent quasiparticle-based transport to incoherent transport (the bad metal regime). Finally, the ratio of the shear viscosity to the entropy density is found to be comparable to the KSS bound for parameters appropriate to liquid 3 He. However, this bound is found to be strongly violated in the bad metal regime for parameters appropriate to lattice electronic systems such as organic charge-transfer salts.

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“…IV E, elastic disorder at the edges is not able to change the clean-limit picture. Negative values of R 21,34 (which occur only at sufficiently large temperatures) have been attributed to hydrodynamic viscous flow [4,5].…”

Section: Detailed Analysis Of the Numerical Resultsmentioning

confidence: 99%

“…The ability to fabricate ultraclean graphene sheets by encapsulation in hexagonal boron nitride crystals [1][2][3][4] allows the investigation of ballistic transport in a large range of temperatures up to the hydrodynamic temperature scale [4,5] T hydro . At T T hydro , the mean-free path for electron-electron collisions ee becomes shorter than the mean-free path for momentum nonconserving scattering and inelastic electronelectron collisions need to be taken into account in any theoretical description of transport.…”

Section: Introductionmentioning

confidence: 99%

Scaling approach to tight-binding transport in realistic graphene devices: The case of transverse magnetic focusing

et al. 2016

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Ultraclean graphene sheets encapsulated between hexagonal boron nitride crystals host two-dimensional electron systems in which low-temperature transport is solely limited by the sample size. We revisit the theoretical problem of carrying out microscopic calculations of nonlocal ballistic transport in such micron-scale devices. By employing the Landauer-Büttiker scattering theory, we propose a scaling approach to tight-binding nonlocal transport in realistic graphene devices. We test our numerical method against experimental data on transverse magnetic focusing (TMF), a textbook example of nonlocal ballistic transport in the presence of a transverse magnetic field. This comparison enables a clear physical interpretation of all the observed features of the TMF signal, including its oscillating sign.

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Nonlocal transport and the hydrodynamic shear viscosity in graphene

Cited by 246 publications

References 59 publications

Superballistic flow of viscous electron fluid through graphene constrictions

Superballistic flow of viscous electron fluid through graphene constrictions

Shear viscosity of strongly interacting fermionic quantum fluids

Scaling approach to tight-binding transport in realistic graphene devices: The case of transverse magnetic focusing

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