In highly viscous electron systems [1-3] such as high-quality graphene above liquid nitrogen temperature, a linear response to applied electric current becomes essentially nonlocal, which can give rise to a number of new and counterintuitive phenomena including negative nonlocal resistance and current whirlpools. It has also been shown that, although both effects originate from high electron viscosity, a negative voltage drop does not principally require current backflow.
We study the role of geometry on viscous flow and show that confinement effects and relative positions of injector and collector contacts play a pivotal role in the occurrence of whirlpools. Certain geometries may exhibit backflow at arbitrarily small values of the electron viscosity, whereas others require a specific threshold value for whirlpools to emerge .
In the same setups we study similarly the hydrodynamic electronic transport in presence of a perpendicular magnetic field.
An additional component of the electron fluid stress tensor is enabled by the lacking of time reversal symmetry induced by the magnetic field. This component is proportional to a new transport coefficient known as Hall viscosity .
We find a particular highly symmetric geometry which allows us to measure the non dissipative Hall viscosity using DC transport measurements.
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