Probing quantum geometry through quantum oscillations

Résumé :

Since the observation of Shubnikov-de Haas and de Hass-Van Alphen quantum oscillations (QO) in 1930 on Bismuth, QO have become a standard experimental tool to map out the Fermi surface of metals 1. Decades later, following the discovery of the quantum Hall effect, the topological and geometric extensions of band theory were developed. The understanding then came that a band is not just represented by its dispersion, but also by its topology and underlying quantum geometry. One can then wonder if QO can also be used to obtain the topology and quantum geometry of a given band. Although the Berry phase is known to shift the phase of the oscillations, it is not known if the quantum metric can be measured in QO. Such a measurement is of high scientific interest, as the quantum metric is known is to affect an array of transport quantities 2. In this work, we establish the effect of the quantum metric through Weiss oscillations, where a sinusoidal electric field is applied to the material. We derive the associated equations of motion as well as a general semiclassical theory of Weiss oscillations, showing precisely how the quantum metric appears. We compare the semiclassical results with a quantum calculation in the case of Rombohedral graphene. We then discuss how the quantum metric affects the commensurability relations associated to the Weiss oscillations. 1 Shoenberg, D. (2009). Magnetic oscillations in metals. Cambridge University Press. 2 Gao, A., Nagaosa, N., Ni, N., & Xu, S.-Y. (2026) Reviews of Modern Physics, 98(3)

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Contact : cecile.repellin@lpmmc.cnrs.fr