Graphene - a nearly perfect fluid

TL;DR

The ratio eta/s of the shear viscosity eta to the entropy density s is determined in clean undoped graphene using a quantum kinetic theory and comes close to a lower bound conjectured in the context of the quark gluon plasma.

Abstract

Hydrodynamics and collision dominated transport are crucial to understand the slow dynamics of many correlated quantum liquids. The ratio η/s of the shear viscosity ηto the entropy density s is uniquely suited to determine how strongly the excitations in a quantum fluid interact. We determine η/s in clean undoped graphene using a quantum kinetic theory. As a result of the quantum criticality of this system the ratio is smaller than in many other correlated quantum liquids and, interestingly, comes close to a lower bound conjectured in the context of the quark gluon plasma. We discuss possible consequences of the low viscosity, including pre-turbulent current flow.

Figures (2)

• Figure 1: (a) Velocity profile $\mathbf{u}$ and associated Stokes force density $\mathbf{f^s}=\eta \nabla^2 \mathbf{u}$ counteracting the current flow. (b) Inhomogeneous current flow expected in a four-contact geometry with split source and drain contacts held at voltage $\pm V/2$. In the absence of viscous and other nonlocal effects, the current would be proportional to the applied voltage $V$, independent of the distance $L$ between the contacts. Viscous effects diminish the current as $L$ decreases.
• Figure 2: Ratio $\eta /s$ in graphene as a function of $T$. The UV cut-off was taken to be $T_{\Lambda }=8.34\cdot 10^{4}\mathrm{K}$ following Sheehy07. In the undoped, quantum critical system $\eta /s$ is very small in a large temperature window where the coupling $\alpha (T)$ remains of order $O(1)$. The value $1/4\pi$ obtained for some strongly coupled critical theories is shown for comparison. As shown in the inset, away from zero doping and quantum criticality ($T<|\mu |$), the viscosity assumes the behavior of a degenerate Fermi liquid, $\eta /s\sim (|\mu |/T)^{3}$.