Quantum Critical Ballistic Transport in Two-Dimensional Fermi Liquids

TL;DR

This paper reveals that ballistic transport in two-dimensional Fermi liquids at a quantum critical point exhibits universal, scale-invariant features such as vortices and nonlocal relations, bridging the gap between Ohmic and hydrodynamic regimes.

Contribution

It introduces a quantum critical point characterized by a conformal field theory that governs ballistic transport, with novel universal dissipation and vortex phenomena in 2D Fermi liquids.

Findings

Ballistic regime is a quantum critical point with conformal symmetry.

Device geometries show intrinsic universal dissipation and nonlocal relations.

Vortices appear at all scales, demonstrating collective effects from Pauli exclusion.

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.