Stray magnetic field and stability of time-dependent viscous electron flow

A hydrodynamic flow of electrons driven by an oscillating electric field in Dirac and Weyl semimetals is investigated. It is found that a double-peak profile of the electric current appears and is manifested in a stray magnetic field with peaks in one of the field components. The nontrivial current profile originates from the interplay of viscous and inertial properties of the electron fluid as well as the boundary conditions. Analytical results are supported by numerical calculations in samples of different geometries such as straight channels, nozzles, and cavities. The double-peak profile of the current is found to be qualitatively insensitive to a specific form of the time dependence of the oscillating electric field and is stable with respect to the sample geometry. A phase diagram and criteria for observing the double-peak structure are determined. In addition, it is shown that nozzles and cavities provide an efficient means to locally enhance or reduce the fluid velocity.