Quantum Critical Ballistic Transport in Two-Dimensional Fermi Liquids

We show that the ballistic regime in two-dimensional Fermi liquids is a quantum critical point (QCP) on the regime boundary separating Ohmic and hydrodynamic transport. The QCP corresponds to a 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 vortices at all spatial scales. 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. We animate the emergence of critical spatial (vimeo.com/365020115) and Fermi surface (vimeo.com/364982637) fluctuations as experimental parameters are tuned to the QCP. The vortices clearly demonstrate that Pauli exclusion alone can produce collective effects, with low-frequency AC transport mediated by vortex dynamics (vimeo.com/366725650).