Universality in quantum critical flow of charge and heat in ultra-clean graphene

Abstract

Close to the Dirac point, graphene is expected to exist in quantum critical Dirac fluid state, where the flow of both charge and heat can be described with a dc electrical conductivity ${\sigma }_{\mathrm{Q}}$, and thermodynamic variables such as the entropy and enthalpy densities. Although the fluid-like viscous flow of charge is frequently reported in state-of-the-art graphene devices, the value of ${\sigma }_{\mathrm{Q}}$, predicted to be quantized and determined only by the universality class of the critical point, has not been established experimentally so far. Here we have discerned the quantum critical universality in graphene transport by combining the electrical ($\sigma$) and thermal (${\kappa }_{\mathrm{e}}$) conductivities in very high-quality devices close to the Dirac point. We find that $\sigma$ and ${\kappa }_{\mathrm{e}}$ are inversely related, as expected from relativistic hydrodynamics, and ${\sigma }_{\mathrm{Q}}$ converges to $\approx (4\pm 1)\times e^2/h$ for multiple devices, where $e$ and $h$ are the electronic charge and the Planck's constant, respectively. We also observe, (1) a giant violation of the Wiedemann-Franz law where the effective Lorentz number exceeds the semiclassical value by more than 200 times close to the Dirac point at low temperatures, and (2) the effective dynamic viscosity (${\eta }_{\mathrm{th}}$) in the thermal regime approaches the holographic limit ${\eta }_{\mathrm{th}}/s_{\mathrm{th}}\to \hslash /4\pi k_{\mathrm{B}}$ within a factor of four in the cleanest devices close to the room temperature, where $s_{\mathrm{th}}$ and $k_{\mathrm{B}}$ are the thermal entropy density and the Boltzmann constant, respectively. Our experiment addresses the missing piece in the potential of high-quality graphene as a testing bed for some of the unifying concepts in physics.

6 pages, 10 figures

References in corpus (17)

• The Raman Fingerprint of Graphene
• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• A self-consistent theory for graphene transport
• Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes
• Quantum critical transport in clean graphene
• Quantum critical point in graphene approached in the limit of infinitely strong Coulomb interaction
• Quantum-critical relativistic magnetotransport in graphene
• Hot electron cooling by acoustic phonons in graphene
• Electron hydrodynamics dilemma: whirlpools or no whirlpools
• Giant magnetoresistance of Dirac plasma in high-mobility graphene
• Imaging Hydrodynamic Electrons Flowing Without Landauer-Sharvin Resistance
• Observation of giant and tuneable thermal diffusivity of Dirac fluid at room temperature
• Wiedemann-Franz law in graphene
• Extreme electron-hole drag and negative mobility in the Dirac plasma of graphene
• Hydrodynamic electron transport in graphene Hall-bar devices
• Viscosity Enhancement by Electron-Hole Collisions in Dirac Electron Fluid
• Non-monotonic temperature dependence of electron viscosity and crossover to high-temperature universal viscous fluid in monolayer and bilayer graphene

Cited by in corpus (6)

• Hydrodynamics of the electronic Fermi liquid: a pedagogical overview
• Extreme disorder in crystalline perovskite oxide: a new paradigm in quantum materials research
• Electron viscosity and device-dependent variability in four-probe electrical transport in ultra-clean graphene field-effect transistors
• Spectroscopy of Heat Transport and Violation of the Wiedemann--Franz Law in a GaAs Hydrodynamic Mesoscopic Channel
• Analysis of Spin-1/2 Particle Scattering in a Spinning Cosmic String Spacetime with Torsion, Curvature, and a Coulomb Potential
• Microwave radiometry of a quantum-critical, hybrid Josephson array