Magnetic hallmarks of viscous electron flow in graphene

TL;DR

This paper predicts magnetic field patterns generated by viscous electron flow in graphene, providing a method to identify hydrodynamic behavior and boundary conditions using advanced magnetometry techniques.

Contribution

It introduces a protocol to detect viscous electron flow signatures in graphene through magnetic field profiles, linking flow features to boundary conditions and whirlpool formations.

Findings

Magnetic field profiles reveal whirlpools and backflow in viscous electron flow.

Profiles can determine boundary conditions at sample edges.

Predictions are experimentally accessible with NV-center magnetometry.

Abstract

We propose a protocol to identify spatial hallmarks of viscous electron flow in graphene and other two-dimensional viscous electron fluids. We predict that the profile of the magnetic field generated by hydrodynamic electron currents flowing in confined geometries displays unambiguous features linked to whirlpools and backflow near current injectors. We also show that the same profile sheds light on the nature of the boundary conditions describing friction exerted on the electron fluid by the edges of the sample. Our predictions are within reach of vector magnetometry based on nitrogen-vacancy centers embedded in a diamond slab mounted onto a graphene layer.