Viscoelastic Resonance in Two-Dimensional Electron Flows with Realistic Boundary Conditions at the Channel Edges

A theory of high-frequency hydrodynamic flows of two-dimensional electrons in nanostructures with a low defect density and edges with various imperfections is developed. It is shown that a resonance in high-frequency viscosity coefficients leads to a dependence of the sample impedance on a magnetic field with a sharp singularity, the character of which depends on the edge type: complete adhesion of the fluid to the edges corresponds to a narrow high resonance, while increasing fluid slip near the edges leads to a strong broadening of the peak and a decrease in its amplitude, followed by its disappearance. Thus, the type of boundary conditions is an important factor determining the shape of high-frequency two-dimensional electron flows. Possible explanations within the developed model for the anomalous magnetophotoresistance observed in ultrapure graphene samples and GaAs quantum wells are discussed.