Para-hydrodynamics from weak surface scattering in ultraclean thin flakes

Abstract: Electron hydrodynamics typically emerges in electron fluids with a high electron-electron collision rate. However, new experiments with thin flakes of WTe$2$ have revealed that other momentum-conserving scattering processes can replace the role of the electron-electron interaction, thereby leading to a novel, so-called para-hydrodynamic regime. Here, we develop the kinetic theory for para-hydrodynamic transport. To this end, we consider a ballistic electron gas in a thin 3-dimensional sheet where the momentum-relaxing ($\ell{mr}$) and momentum-conserving ($\ell_{mc}$) mean free paths are decreased due to boundary scattering from a rough surface. The resulting effective mean free path of the electronic flow is then expressed in terms of microscopic parameters of the sheet boundaries, predicting that a para-hydrodynamic regime with $\ell_{mr}\gg \ell_{mc}$ emerges generically in ultraclean three-dimensional materials. Using our approach, we recover the transport properties of WTe$_2$ in the para-hydrodynamic regime in good agreement with existing experiments.