The Hall effect, minus the magnetic field

Every introductory-physics student learns that for an object to move along a curved path, it must experience a centripetal force. Electrons are subject to the same rule, so when current flows through a curved wire, something must provide that force. Logically, the force comes from a radial electric field, which would require a transverse charge separation in the wire, as illustrated in the first image. But that charge configuration looks tantalizingly like the Hall effect, in which a magnetic field diverts moving charges to one side of a current-carrying wire. The situation raises the following question: Can a conductor develop a Hall voltage in the absence of a magnetic field?

The answer, it turns out, is yes. Nicholas Schade , David Schuster , and Sidney Nagel at the University of Chicago have now shown that a transverse voltage can indeed stem from purely geometric origins. The researchers measured the voltage between the inner and outer edges of curved graphene wires mounted on doped silicon substrates; one wire with two probes is shown in the second image. The transverse voltage had a quadratic dependence on current, as predicted for a geometrical effect, rather than linear, as in the traditional Hall effect. And the effect was appreciable: The largest current through the wire generated a transverse voltage of 0.5 mV.

Like its traditional counterpart, the geometric Hall voltage should indicate the sign of the charge carrier. Graphene is well suited for demonstrating that correspondence because it’s easy to tune the charge-carrier sign; it’s negative when the Fermi level is above the Dirac point and positive when they’re reversed. By applying an external voltage, the researchers continuously varied the Fermi level and confirmed that the transverse voltage switched its sign.

As another check on the voltage’s geometric origin, the researchers simultaneously measured the transverse voltage for a straight section of wire adjacent to the curve. Surprisingly, they found that although the straight segment’s voltage was consistently smaller than that in the curved section, it was also nonzero. The unexpected voltage was caused by the conduction electrons’ tortuous paths. Even though the wire doesn’t change its direction, the electrons navigate complex paths of least resistance that are generated by local variations in graphene’s conductivity. That meandering also explains the larger-than-predicted transverse voltage that the researchers measured along the curved wire segment.

The geometric Hall effect could help researchers more easily measure the effective masses of charge carriers in graphene. Also, because it doesn’t rely on a magnetic field, the effect could be used to characterize charge carriers in bulk superconductors. (N. B. Schade, D. I. Schuster, S. R. Nagel, Proc. Natl. Acad. Sci. USA 116, 24475, 2019 .)