Optimal geometries for low-resistance viscous electron flow

This work explores the impact of geometry on viscous electron flow in graphene channels. We demonstrate that structural modifications of the material edges distinctly influence its electrical resistance. As a general trend, we observe that softening the edges reduces the resistance in both the hydrodynamic and the ballistic regimes. Our simulations are based on a two-dimensional hydrodynamic model, which is compared with those obtained by the Boltzmann transport equation in some representative cases. In both formalisms, the scattering length due to electron-electron collisions and due to momentum-relaxing collisions of electrons with impurities and phonons are taken into account. A minimization algorithm was employed to optimize the channel geometry of the minimal resistance. Our findings emphasize the critical role of the channel geometry in graphene, presenting significant implications for the design of advanced electronic devices based on two-dimensional materials.