Negative local resistance caused by viscous electron backflow in graphene

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Science  11 Feb 2016:
DOI: 10.1126/science.aad0201

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  • RE: "negative voltage needs no backflow" by Falkovich and Levitov
    • Marco Polini, Senior Scientist, Istituto Italiano di Tecnologia

    We agree with the thoughtful comment by Falkovich and Levitov that a viscous electron flow can cause a negative resistance drop even without current backflow. Our Report dealt with a particular experimental geometry referred to as 'vicinity'. It was employed to distinguish the negative resistance due to electron viscosity from spurious ballistic effects. In the vicinity geometry, the negative voltage is inherently accompanied by current whirlpools as illustrated by the numerical simulations presented in our Report and analytical calculations in Phys. Rev. B 92, 165433 (2015). Our further work ( elucidates a subtle relation between negative resistance and current backflow for various geometries.

    Competing Interests: None declared.
  • negative voltage needs no backflow
    • Gregory Falkovich, Professor of Physics, Weizmann Institute of Science
    • Other Contributors:
      • Leonid Levitov, Professor of Physics, MIT

    We wish to comment on an interesting issue raised by this excellent experimental work and also to clear a possible misunderstanding. Namely, the title, abstract and Fig 1b may create an impression that a negative voltage response (like that discovered in this experiment) always signals the presence of a backflow and vortices i.e. streamline loops. This can be easily shown not to be the case e.g. by inspecting the analytic solution for the viscous current flow from a point source in a half-plane geometry. In this simple and instructive example there are neither vortices nor backflow (unlike the sketch in Fig 1b). Indeed the stream function and potential take on a really simple form (obtained e.g. by taking an appropriate limit of Eqs.(5,7) of our recently published paper ). Namely, for the no-slip boundary condition, the stream function behaves as 2theta-sin(2theta) with theta the azimuthal angle measured from the boundary. This describes an outward and vortex-free flow. At the same time, the potential values at the boundary are negative, varying as inverse square of the distance from contact, in strong resemblance to experiment. The potential distribution within the bulk alternates in sign, exhibiting nodal lines at theta equal 45 and 135 degrees. The origin of this behavior can be understood by noting that for angles b...

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    Competing Interests: None declared.