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Quantum oscillations originating from the quantization of electron cyclotron orbits provide sensitive diagnostics of electron bands and interactions. We report on nanoscale imaging of the thermodynamic magnetization oscillations caused by the de Haas-van Alphen effect in moiré graphene. Scanning by means of superconducting quantum interference device (SQUID)-on-tip in Bernal bilayer graphene crystal axis-aligned to hexagonal boron nitride reveals large magnetization oscillations with amplitudes reaching 500 Bohr magneton per electron in weak magnetic fields, unexpectedly low frequencies, and high sensitivity to superlattice filling fraction. The oscillations allow us to reconstruct the complex band structure, revealing narrow moiré bands with multiple overlapping Fermi surfaces separated by unusually small momentum gaps. We identified sets of oscillations that violate the textbook Onsager Fermi surface sum rule, signaling formation of broad-band particle-hole superposition states induced by coherent magnetic breakdown.

Attaining viable thermoelectric cooling at cryogenic temperatures is of considerable fundamental and technological interest for electronics and quantum materials applications. In-device temperature control can provide more efficient and precise thermal environment management compared with conventional global cooling. The application of a current and perpendicular magnetic field gives rise to cooling by generating electron-hole pairs on one side of the sample and to heating due to their recombination on the opposite side, which is known as the Ettingshausen effect. Here we develop nanoscale cryogenic imaging of the magneto-thermoelectric effect and demonstrate absolute cooling and an Ettingshausen effect in exfoliated WTe 2 Weyl semimetal flakes at liquid He temperatures. In contrast to bulk materials, the cooling is non-monotonic with respect to the magnetic field and device size. Our model of magneto-thermoelectricity in mesoscopic semimetal devices shows that the cooling efficiency and the induced temperature profiles are governed by the interplay between sample geometry, electron-hole recombination length, magnetic field, and flake and substrate heat conductivities. The observations open the way for the direct integration of microscopic thermoelectric cooling and for temperature landscape engineering in van der Waals devices., Competing Interests: Competing interestsThe authors declare no competing interests., (© The Author(s) 2024.)

The exceptional control of the electronic energy bands in atomically thin quantum materials has led to the discovery of several emergent phenomena 1 . However, at present there is no versatile method for mapping the local band structure in advanced two-dimensional materials devices in which the active layer is commonly embedded in the insulating layers and metallic gates. Using a scanning superconducting quantum interference device, here we image the de Haas-van Alphen quantum oscillations in a model system, the Bernal-stacked trilayer graphene with dual gates, which shows several highly tunable bands 2-4 . By resolving thermodynamic quantum oscillations spanning more than 100 Landau levels in low magnetic fields, we reconstruct the band structure and its evolution with the displacement field with excellent precision and nanoscale spatial resolution. Moreover, by developing Landau-level interferometry, we show shear-strain-induced pseudomagnetic fields and map their spatial dependence. In contrast to artificially induced large strain, which leads to pseudomagnetic fields of hundreds of tesla 5-7 , we detect naturally occurring pseudomagnetic fields as low as 1 mT corresponding to graphene twisting by 1 millidegree, two orders of magnitude lower than the typical angle disorder in twisted bilayer graphene 8-11 . This ability to resolve the local band structure and strain at the nanoscale level enables the characterization and use of tunable band engineering in practical van der Waals devices., (© 2023. The Author(s), under exclusive licence to Springer Nature Limited.)

The scanning superconducting quantum interference device (SQUID) fabricated on the tip of a sharp quartz pipette (SQUID-on-tip) has emerged as a versatile tool for the nanoscale imaging of magnetic, thermal, and transport properties of microscopic devices of quantum materials. We present the design and performance of a scanning SQUID-on-tip microscope in a top-loading probe of a cryogen-free dilution refrigerator. The microscope is enclosed in a custom-made vacuum-tight cell mounted at the bottom of the probe and is suspended by springs to suppress vibrations caused by the pulse tube cryocooler. Two capillaries allow for the in situ control of helium exchange gas pressure in the cell that is required for thermal imaging. A nanoscale heater is used to create local temperature gradients in the sample, which enables quantitative characterization of relative vibrations between the tip and the sample. The spectrum of the vibrations shows distinct resonant peaks with a maximal power density of about 27 nm/Hz1/2 in the in-plane direction. The performance of the SQUID-on-tip microscope is demonstrated by magnetic imaging of the MnBi2Te4 magnetic topological insulator, magnetization and current distribution imaging in a SrRuO3 ferromagnetic oxide thin film, and thermal imaging of dissipation in graphene., (© 2023 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).)