Magnetic response of a two-dimensional viscous electron fluid

It has been established that the Coulomb interactions can transform the electron gas into a viscous fluid. This fluid is realized in a number of platforms, including graphene and two-dimensional semiconductor heterostructures. The defining characteristic of the electron fluid is the formation of layers of charge carriers that are in local thermodynamic equilibrium, as in classical fluids. In the presence of nonuniformities, whirlpools and nontrivial flow profiles are formed, which have been directly imaged in recent experiments. In this paper, we theoretically study the response of the electron fluid to localized magnetic fields. We find that the electric current is suppressed by viscous vortices in regions where magnetic field is sharply varying, causing strong transport signatures. Experimentally, our considerations are relevant since local magnetic fields can be applied to the system through implanting adatoms or embedding micromagnets in the top-gate. Our theory is essential for the characterization and future applications of electron fluids in hydrodynamic spin transport.