Superballistic boundary conductance and hydrodynamic transport in microstructures

Abstract

It is shown that the ideal boundary between a perfectly conducting electrode and electron liquid state acts as a contact whose conductance per unit area is higher than the fundamental Sharvin conductance by a numerical coefficient $2\ensuremath{\alpha}$, where $\ensuremath{\alpha}$ is slightly smaller than unity and depends on the dimensionality of the system. If the boundary has a finite curvature, an additional correction to the boundary conductance appears, which is parametrically small as a product of the curvature by the electron-electron mean free path length. The relation of the normal current density to the voltage between the electrode and electron liquid represents itself a hydrodynamic boundary condition for current-penetrable boundary. Calculations of the conductance and potential distribution in microstructures by means of numerical solution of the Boltzmann equation show that the concept of boundary conductance works very good when the hydrodynamic transport regime is reached. The superballistic transport, when the device conductance is higher than the Sharvin conductance, can be realized in Corbino disk devices not only in the hydrodynamic regime, although requires that the electron-electron scattering rate must be higher than the momentum-relaxing scattering rate. The theoretical results for Corbino disks are consistent with recent experimental findings.