Perfect Fluid Behavior in Graphene

Markus Müller, Jörg Schmalian and Lars Fritz Phys. Rev. Lett.103, 025301 (2009)

Graphene, a single-atom thick sheet of graphite, is a material that combines deep intellectual challenges to our understanding electron-dynamics in low dimensional systems with great promise for applications in nano-electronics devices[1]. Based on our earlier work[2], the paper determines the hydro-dynamics of the electron fluid of clean graphene, by evaluating the electron shear viscosity. It addresses the following open questions:

  • What is the nature of the electron flow in clean graphene, laminar or turbulent?
  • What determines the typical device size, gate voltage and driving currents where  electron turbulence may emerge? 

The paper finds that the shear viscosity of graphene is exceptionally small. This permits low dissipation for electron motion, in particular for small multi-terminal devices (see Fig.1). In addition, this finding is of fundamental importance as it establishes deep and direct connections to other branches of physics. It places graphene along with the quark gluon plasma and cold atom gasses,  in the family of almost perfect liquids.  Such liquids are the most strongly coupled systems in the sense that the mean carrier distance and the mean free path are similar.  Recent developments that relate strongly interacting quantum many body theories to weakly coupled gravity theories with black holes helped to establish general bounds for the shear viscosity[3]. Graphene turns out be  closest to the lowest possible viscosity values allowed. Our results for the electron transport in nano-electronics graphene-devices reveal this material can also help to understand particle dynamics in strongly coupled atomic physics and nuclear physics systems alike.                         

[1] K. S. Novoselov, et al.  Nature 438, 197 (2005); H. Castro Neto, et al. Rev. Mod. Phys.  81, 109 (2009)                                                                          

[2] D. E. Sheehy and J. Schmalian, Phys. Rev. Lett. 99, 226803 (2007). L. Fritz, J. Schmalian, M. Muller, and S. Sachdev, Phys. Rev. B 78, 085416 (2008).                                                                                                                 

[3] P. Kovtun et al, Phys. Rev. Lett.94, 111601 (2005).

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