In a strong magnetic field, electrons in a thin metal film move along circular orbits. When the film thickness is comparable to the size of such an orbit, the resistance starts to oscillate: these are Sondheimer oscillations, known since the mid-20th century as a purely geometric effect. New research shows that quantum corrections tied to the topology of electron bands change the frequency of these oscillations.

The authors developed a general quantum theory for thin conductors in the high-magnetic-field limit. Unlike Shubnikov–de Haas oscillations, where topology enters only through the phase, here it shifts the frequency itself. This allows direct reconstruction of the full Landau level spectrum, the allowed energies of an electron in a magnetic field, without complex fitting.

A model with tunable Berry phase demonstrates how topology shows up in experimentally accessible magnetoresistance spectra. The damping of oscillations due to surface roughness, an important factor for real samples, is also considered.