Quantum-critical conductivity of the Dirac fluid in graphene

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Graphene is expected to behave like a quantum-critical, relativistic plasma known as “Dirac fluid” near charge neutrality in which massless electrons and holes rapidly collide. In a recent study now published in Science, Patrick Gallagher and co-workers at the departments of physics and materials science in the U.S., Taiwan, China and Japan used on-chip terahertz spectroscopy and measured the frequency-dependent optical conductivity of graphene between 77 K and 300 K electron temperatures for the first time. Additionally, the scientists observed the quantum-critical scattering rate characteristic of the Dirac fluid. At higher doping, Gallagher et al. uncovered two distinct current-carrying modes with zero and nonzero total momenta as a manifestation of relativistic hydrodynamics.

The work revealed the quantum criticality of the material in which each site is in a quantum superposition of order and disorder (similar to Schrödinger’s hypothetical cat in a quantum superposition of ‘dead’ and ‘alive’) and the unusual dynamic excitation in graphene near charge neutrality. Physicists consider quantum relativistic effects in the experimental systems influencing condensed matter to be too minute for accurate description by the non-relativistic Schrödinger’s equation. As a result, previous studies have reported on experimental condensed matter systems such as graphene (a single atomic layer of carbon) in which electron transport was governed by Dirac’s (relativistic) equation.

Landau’s theory of the Fermi liquid defines electron interactions of a typical metal as an ideal gas of non-interacting quasiparticles. In monolayer graphene, this description does not apply due to its structure of linearly dispersing bands and minimally screened Coulomb interactions. Near charge neutrality, graphene is thus expected to host a “Dirac fluid,” which is a quantum-critical plasma of electrons and holes that are governed by relativistic hydrodynamics. In lightly doped graphene, a surprising consequence of relativistic hydrodynamics is that current can be carried by two distinct modes; with zero and non-zero total momenta, also referred to as “energy waves” and “plasmons” in some studies.

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