Hydrodynamic and diffusive vortices near obstacles in a two-dimensional electron fluid subject to a strong magnetic field

We study current flow near a radially symmetric density perturbation in graphene in the presence of a magnetic field. In both diffusive and hydrodynamic regimes, for strong fields, the current forms spirals around the perturbation. We show that the scaling of the spiral size as a function of magnetic field is different in the two regimes. We discuss how these phenomena can be probed using scanning imaging techniques, including tunneling, potentiometry, magnetometry, and photocurrent measurements.