Xu, XiaodongCai, Jiaqi2024-10-162024-10-162024-10-162024Cai_washington_0250E_27378.pdfhttps://hdl.handle.net/1773/52602Thesis (Ph.D.)--University of Washington, 2024New developments in van der Waals materials and fabrication techniques bring new oppor- tunities for investigating emergent quantum phases of matter in two dimensions. Chern insulator is a notable example, characterized by the Chern number C. The Chern insulator is remarked as the lattice version of quantum Hall effect, and has vanishing longitudinal resistance and quantized Hall resistance of h/Ce2, where h is the Planck constant and e is the electron charge. This thesis investigates novel Chern insulators enriched by magnetism, pseudospin degrees of freedom, and translational symmetry. The discovery is enabled by new materials that incorporate intrinsic magnetism into topological insulators, or new con- trol knobs such as the twist angle between layers that can lead to strong interaction and spontaneous magnetism. The interplay between topology and the above ingredients deep- ens our understanding of the topological phase of matter and also seeks device applications. Another family of novel Chern insulators, the fractional Chern insulator, is a strongly cor- related phase that has fractionally charged excitations, anyons. It is characterized by a non-integer rational many-body Chern number (C ∈ Q/Z). This lattice analogy of frac- tional quantum Hall states can exist at elevated temperatures and in zero magnetic field and could facilitate anyonic research into a more experimentally accessible regime. This state of matter, and the associated fractional quantum anomalous Hall effect, is discovered in the twisted molybdenum ditelluride (MoTe2) moir ́e superlattice and will be another central topic of this thesis.application/pdfen-USnonecondensed matter physicsopticstopological insulatortransporttwo dimensional materialPhysicsPhysicsThesis