Quantum Critical Ballistic Transport in Two-Dimensional Fermi Liquids

Abstract

Electronic transport in Fermi liquids is usually Ohmic, because of momentum-relaxing scattering due to defects and phonons. These processes can become sufficiently weak in two-dimensional materials, giving rise to either ballistic or hydrodynamic transport, depending on the strength of electron-electron scattering. We show that the ballistic regime is a quantum critical point (QCP) on the regime boundary separating Ohmic and hydrodynamic transport. The QCP corresponds to a \emph{free} conformal field theory (CFT) with a dynamical scaling exponent $z=1$. Its nontrivial aspects emerge in device geometries with shear, wherein the regime has an intrinsic universal dissipation, a nonlocal current-voltage relation, and exhibits the critical scaling of the underlying CFT. The Fermi surface has electron-hole pockets across all angular scales and the current flow has \emph{vortices} at all spatial scales. We image the fluctuations in high-definition and animate their emergence as experimental parameters are tuned to the QCP (movie links in comments). The vortices clearly demonstrate that Pauli exclusion alone can produce collective effects, with low-frequency AC transport mediated by vortex dynamics. The scale-invariant spatial structure is much richer than that of an interaction-dominated hydrodynamic regime, which only has a single vortex at the device scale. Our findings provide a theoretical framework for both interaction-free and interaction-dominated non-Ohmic transport in two-dimensional materials, as seen in several contemporary experiments.

arXiv commentMovies: (1) Spatial fluctuations: https://vimeo.com/365020115 [1 min 19 secs] , (2) Regime transitions and Fermi surface fluctuations: https://vimeo.com/364982637 [1 min 49 secs], (3) Vortex dynamics and frequency crossover in the ballistic regime: https://vimeo.com/366725650 [1 min 48 secs] Main text: 6 pages + 4 figures Methods + supplementary: 4 pages + 6 figures

References in corpus (25)

• Boron nitride substrates for high-quality graphene electronics
• Continuous Quantum Phase Transitions
• Time-dependence of correlation functions following a quantum quench
• Quantum Transport in Semiconductor Nanostructures
• Light-cone-like spreading of correlations in a quantum many-body system
• Quantum criticality in an Ising chain: experimental evidence for emergent E8 symmetry
• Observation of the Dirac fluid and the breakdown of the Wiedemann-Franz law in graphene
• Evidence for hydrodynamic electron flow in PdCoO${}_2$
• On Landau damping
• Superballistic flow of viscous electron fluid through graphene constrictions
• Electron Viscosity, Current Vortices and Negative Nonlocal Resistance in Graphene
• Hydrodynamic electron flow in high-mobility wires
• Electrical and Thermal Transport at the Planckian Bound of Dissipation in the Hydrodynamic Electron Fluid of WP2
• Non-local transport and the hydrodynamic shear viscosity in graphene
• Quantum critical scaling in graphene
• Quantum critical point in graphene approached in the limit of infinitely strong Coulomb interaction
• Hydrodynamic description of transport in strongly correlated electron systems
• Fluidity Onset in Graphene
• Electrically tunable transverse magnetic focusing in graphene
• Transport in inhomogeneous quantum critical fluids and in the Dirac fluid in graphene
• Ballistic miniband conduction in a graphene superlattice
• Bulk and shear viscosities of the 2D electron liquid in a doped graphene sheet
• Electron hydrodynamics dilemma: whirlpools or no whirlpools
• Scanning Gate Microscopy in a Viscous Electron Fluid
• Theory of the plasma-wave photoresponse of a gated graphene sheet