Superscreening by a retroreflected hole backflow in tomographic electron fluids

Electron hydrodynamics gives rise to surprising correlated behaviors in which electrons cooperate to quench dissipation and reduce the electric fields needed to sustain the flow. Such collective free flows are usually expected at the hydrodynamic length scales exceeding the electron-electron scattering mean free path ${\ensuremath{\ell}}_{\mathrm{ee}}$. Here we predict that in two-dimensional electron gases, the collective free flows actually occur at distances much smaller than ${\ensuremath{\ell}}_{\mathrm{ee}}$, in a nominally ballistic regime. The sub-${\ensuremath{\ell}}_{\mathrm{ee}}$ free flows arise due to retroreflected holes originating from head-on quasiparticle collisions; the holes retrace the paths of impinging electrons and cancel out their potential. An exact solution, obtained in Corbino geometry, predicts potential strongly screened by the hole backflow. The screened potential is described by a fractional power law ${r}^{\ensuremath{-}5/3}$ over a wide range of $r$ values, from macroscales down to deep sub-${\ensuremath{\ell}}_{\mathrm{ee}}$ scales, and distinct non-Fermi-liquid temperature dependence.