Another highly pursued topic is searching for intrinsic magnetic topological insulators (TI) where topology meets magnetism. A robust excitonic insulator has been observed in 1L/2L WSe2/WS2 moiré superlattice with the population of correlated electron-hole pairs in different WSe2 layers. We further explore correlated electronic states and moiré exciton in the TMD moiré system with layer degree of freedom. Our results demonstrate MIM as a powerful tool towards exploring emergent quantum states in such semiconducting moiré superlattices. In this thesis, I will summary our efforts in studying moiré physics using microwave impedance microscopy (MIM), including direct visualization of the moiré pattern in graphene-based heterostructures and observation of correlated insulating states at fractional carrier fillings in a WSe2/WS2 moiré superlattice. Flat electronic bands can form in these twisted 2D samples, which can give birth to various interesting quantum phenomena, for example, superconductivity, Mott insulators, ferromagnetism, and quantum anomalous hall effect. A rising research field, moiré physics, has emerged as a platform for quantum simulation. These emergent materials offer better tunability compared with their bulk relatives, such as carrier density tuning, band structure and topology engineering.One seminal work is the observation of unexpected strong correlation effect and superconductivity in ~1.1° twisted bilayer graphene in 2018. This offers researchers novel control over materials to create novel quantum states which do not exist in their bulk parent. Recently, with the rapid development in device fabrication, artificial superlattices can be created using building blocks of 2D materials. Since then, various electronic properties, such as semi-metal, semiconductor, insulator, superconductor, and magnet, have been discovered with materials in the 2D form. The discovery of one-atom thick graphene layer has marked the starting era of two-dimensional (2D) van der Waals (vdW) materials.
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