Classical E&M with a twist: A geometric Hall effect without magnetic field

The classical Hall effect, the traditional means of determining charge-carrier sign and density in a conductor, requires a magnetic field to produce transverse voltages across a current-carrying wire. We demonstrate a fundamentally novel use of geometry to create transverse potentials along curved paths without any magnetic field. These potentials also reflect the charge-carrier sign and density, and they arise because a transverse electric field must accelerate the current radially in order to follow the curve. We demonstrate this effect experimentally in curved graphene wires where the transverse voltages are as large as millivolts. The potentials are consistent with the doping and change polarity as we switch the carrier sign. In straight wires, we measure transverse voltage fluctuations with random polarity demonstrating that the current follows a complex, tortuous path. This geometrically-induced potential offers a sensitive characterization of inhomogeneous current flow in thin films.