Geometric control of universal hydrodynamic flow in a two dimensional electron fluid

Electron transport in most solid state systems is dominated by extrinsic factors, such as sample geometry and scattering from impurities, and is essentially independent of the intrinsic properties of the electron system. An exception is the hydrodynamic regime, in which Coulomb interactions transform electron kinematics from independent particles to the collective motion of a viscous “electron fluid”. The viscosity is a universal and intrinsic property of the electron system, independent of the sample details. Experimental signatures of hydrodynamic flow of the electron fluid are revealed through the interaction with the sample boundaries, just as water flow in a pipe is affected by wide the pipe is and how rough the walls are. In contrast to the universal nature of the viscosity, this roughness is specific to each experiment, introducing an arbitrary and unknown fitting parameter when trying to quantitatively compare experiments with theoretical models.

Here we introduce a new approach to studying hydrodynamic flow. We demonstrate this technique with 2D electrons in a GaAs/AlGaAs heterostructure device with smooth sidewalls to eliminate all unknown sample boundary conditions and other extrinsic factors, and then controllably re-introduce viscous dissipation by deliberately engineering the shape of the sample boundaries. This allows the viscosity and electron-electron scattering length to be measured without any fitting parameters. We observe a clear transition from ballistic to hydrodynamic electron motion driven by both temperature and also by magnetic field. We observe an unexpected deviation of the e-e scattering length from existing theoretical models based on the Random Phase and Hubbard Approximations.

This boundary engineering technique provides a new quantitative approach to measure the electron quasiparticle lifetime, a fundamental concept in Fermi liquid theory, over a much wider range of $T$ and $B$ than has previously been possible.