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We report the implementation of a dilution refrigerator-based scanning microwave impedance microscope with a base temperature of ∼100 mK. The vibration noise of our apparatus with tuning-fork feedback control is as low as 1 nm. Using this setup, we have demonstrated the imaging of quantum anomalous Hall states in magnetically (Cr and V) doped (Bi, Sb)2Te3 thin films grown on mica substrates. Both the conductive edge modes and topological phase transitions near the coercive fields of Cr- and V-doped layers are visualized in the field-dependent results. Our study establishes the experimental platform for investigating nanoscale quantum phenomena at ultralow temperatures. 

Abstract Electrostatic gating of two-dimensional (2D) materials with ionic liquids (ILs), leading to the accumulation of high surface charge carrier densities, has been often exploited in 2D devices. However, the intrinsic liquid nature of ILs, their sensitivity to humidity, and the stress induced in frozen liquids inhibit ILs from constituting an ideal platform for electrostatic gating. Here we report a lithium-ion solid electrolyte substrate, demonstrating its application in high-performance back-gated n-type MoS₂and p-type WSe₂transistors with sub-threshold values approaching the ideal limit of 60 mV/dec and complementary inverter amplifier gain of 34, the highest among comparable amplifiers. Remarkably, these outstanding values were obtained under 1 V power supply. Microscopic studies of the transistor channel using microwave impedance microscopy reveal a homogeneous channel formation, indicative of a smooth interface between the TMD and underlying electrolytic substrate. These results establish lithium-ion substrates as a promising alternative to ILs for advanced thin-film devices.