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 len
gthscales exceeding the electron-electron scattering mean free path $ell_{rm ee}$. Here we predict that in two-dimensional electron gases the collective free flows actually occur at the distances much smaller than $ell_{rm ee}$, in a nominally ballistic regime. The sub-$ell_{rm ee}$ free flows arise due to retroreflected holes originating from head-on electron electron collisions, which 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. Screened potential is described by a fractional power law $r^{-5/3}$ over a wide range of $r$ values, from macroscales down to deep sub-$ell_{rm ee}$ scales, and a distinct non-Fermi-liquid temperature dependence.
Momentum-conserving quasiparticle collisions in two-dimensional Fermi gases give rise to a large family of exceptionally long-lived excitation modes. The lifetimes of these modes exceed by a factor $(T_F/T)^2gg 1$ the conventional Landau Fermi-liquid
lifetimes $tausim T_F/T^2$. The long-lived modes have a distinct angular structure, taking the form of $cos mtheta$ and $sin mtheta$ with odd $m$ values for a circular Fermi surface, with relaxation rate dependence on $m$ of the form $m^4log m$, valid at not-too-large $m$. In contrast, the even-$m$ harmonics feature conventional lifetimes with a weak $m$ dependence. The long-time dynamics, governed by the long-lived modes, takes the form of angular (super)diffusion over the Fermi surface. Altogether, this leads to unusual long-time memory effects, defining an intriguing transport regime that lies between the conventional ballistic and hydrodynamic regimes.
Electron interactions are usually probed indirectly, through their impact on transport coefficients. Here we describe a direct scheme that, in principle, gives access to the full angle dependence of carrier scattering in 2D Fermi gases. The latter is
particularly interesting, because, due to the dominant role of head-on collisions, carrier scattering generates tightly focused fermionic jets. We predict a jet-dominated signal for the magnetic steering geometry, that appears at classically weak $B$-fields, much lower than the free-particle focusing fields. The effect is anti-Lorentz in sign, producing a peak at the field polarity for which the free-particle focusing does not occur. The steering signal measured vs. $B$ yields detailed information on the angular structure of fermionic jets.
Fermi gases in two dimensions display a surprising collective behavior originating from the head-on carrier collisions. The head-on processes dominate angular relaxation at not-too-high temperatures $Tll T_F$ owing to the interplay of Pauli blocking
and momentum conservation. As a result, a large family of excitations emerges, associated with the odd-parity harmonics of momentum distribution and having exceptionally long lifetimes. This leads to tomographic dynamics: fast 1D spatial diffusion along the unchanging velocity direction accompanied by a slow angular dynamics that gradually randomizes velocity orientation. The tomographic regime features an unusual hierarchy of time scales and scale-dependent transport coefficients with nontrivial fractional scaling dimensions, leading to fractional-power current flow profiles and unusual conductance scaling vs. sample width.
