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

Quantum Critical Ballistic Transport in Two-Dimensional Fermi Liquids