2D Fermi Liquids

In clean, two-dimensional materials, the electrons can reach a hydrodynamic transport regime, flowing around obstacles like water. However, the kinematics of electrons in 2D are heavily constrained by the scattering phase space set by the Fermi surface. By expanding Fermi surface deformations into angular harmonics, one may classify that even-parity deformations can decay through head-on collisions, leading to a standard Fermi liquid decay rate $\gamma_{\text{even}} \sim T^2/T_F$. Odd-parity deformations instead have to rely on repeated small-angle scattering events assited by the thermal broadening, leading to a thermally supressed decay rate $\gamma_{\text{odd}} \sim T^4/T_F^3$.

That odd and even Fermi surface deformations relax on parametrically different timescales hints at the existence of a novel transport regime in between ballistic and hydrodynamic flow: a “tomographic” regime, consisting of hydrodynamic modes, in addition to the long-lived odd-parity modes.