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Our modern way of thinking about a Fermi liquid is to use the language of renormalization group theory-a theory that extracts the essential physics of many-body systems by zooming out from the microscopic details. Landau’s notion of a Fermi liquid as a system of interacting fermions that, at low energies, effectively behave as noninteracting quasiparticles is the central paradigm of many-body physics. By this criterion graphene comes closer to being a “perfect fluid” than several other quantum systems that have often been labeled as strongly correlated. Such a low viscosity-to-entropy ratio, somewhat paradoxically, means that the electrons in graphene form a quantum liquid that is, in fact, strongly interacting. They find that the value of this ratio in graphene is surprisingly close to its likely lower bound.
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They show that a particularly suitable measure of how strongly the excitations in a given quantum fluid interact is given by the dimensionless ratio between the fluid’s shear viscosity and entropy density. This usual mantra, however, may sometimes be quite misleading, as argued by Markus Müller at the ICTP in Trieste, Italy, Jörg Schmalian at Ames Lab and Iowa State University, US, and Lars Fritz at Harvard University, US, in a paper appearing in Physical Review Letters. The linear dispersion relation also implies a vanishing density of single-particle states at the Fermi level, which should make the effects of the Coulomb interaction between electrons weak. This means that the electrons can be described as “massless” fermions, though with a velocity of about 300 times less than the velocity of light. The popularity of graphene is rooted in the unusual nature of its low-energy excitations: near the Fermi level, the electron energies scale linearly with their momenta. ×Įver since it was shown that graphene-a single layer of carbon atoms-could be isolated from graphite, it has occupied a center stage of condensed matter physics. The density of the arrows increases with the speed of the flow. α parameterizes the ∼ 1 / r tail of the Coulomb interaction, and λ stands collectively for the electron-electron repulsion on the lattice scale. Illustration: Alan Stonebraker Figure 1: The schematic “flow” of the coupling constants describing weak electron-electron interaction with decreasing temperature in graphene.