Imaging de Haas–van Alphen quantum oscillations in moiré graphene

Quantum oscillations originating from the quantization of the electron cyclotron orbits in presence of magnetic fields provide fundamental information about the band structure and interactions in novel materials. While the Shubnikov-de Haas resistivity oscillations are widely used for characterizing 2D electron systems including graphene, the thermodynamic magnetization oscillations due to the de Haas-van Alphen effect have evaded so far direct experimental observation in graphene structures. Here we report on scanning SQUID-on-tip imaging of the de Haas-van Alphen quantum oscillations in narrow electronic bands formed in AB-bilayer graphene/hBN superlattices. The local nanoscale measurements reveal very large magnetization oscillations vs. carrier density with amplitudes in excess of 500 Bohr magneton per electron in weak magnetic fields. The oscillations are position dependent and are highly sensitive to the superlattice filling fraction, appearing at elevated carrier densities where moiré bands overlap. We ascribe these observations to the formation of multiple Fermi surfaces, with the large, low-frequency oscillations originating from carriers occupying small Fermi pockets. The findings offer a unique tool for nanoscale mapping of the local band structure in a wide range of van der Waals structures with complex Fermi surfaces and strong electron interactions.