Bending space to create a geometric analogue of the classical Hall effect without magnetic field*

We show that it is possible to determine the sign and density of the charge carriers in a material without using magnetism. Instead of a magnetic field, we use the geometry of the wire carrying the current to measure these properties. If the wire is curved, the charge carriers must experience a centripetal force to follow the wire. The centripetal force arises from surface charges along the wire, which create a component of the electric field perpendicular to the drift velocity. This transverse electric field produces a potential difference between the sides of the wire which depends on the sign and density of the charge carriers.

We perform measurements on devices made from graphene to find experimental evidence for this effect. We measure a signal from our curved wires which is consistent with positive carriers at zero back-gate voltage, as expected in CVD graphene. However, we also find a background signal that occurs even in straight graphene wires. We investigate other possible sources of small potentials, such as the Seebeck effect, to determine the origin of this background. Our measurements provide evidence of a new classical effect, similar to the Hall effect, where geometry replaces the magnetic field as a tool for characterizing a material’s charge carriers.