Semiconductor moiré superlattices provide a highly tunable platform to study the interplay between electron correlation and band topology. For example, the generalized Kane-Mele-Hubbard model can be simulated by topological moiré flat bands in twisted transition metal dichalcogenide homobilayers. In this system, we obtain the filling factor, twist angle, and electric field-dependent quantum phase diagrams with a plethora of phases, including the quantum spin Hall insulator, the in-plane antiferromagnetic state, the out-of-plane antiferromagnetic Chern insulator, the spin-polarized Chern insulator, the in-plane ferromagnetic state, and the ${120}^{\circ }$ antiferromagnetic state. We predict that a gate-defined junction formed between the quantum spin Hall insulator phase with proximitized superconductivity and the magnetic phases with in-plane magnetization (either ferromagnetism or antiferromagnetism) can realize a one-dimensional topological superconductor with Majorana zero modes. Our proposal introduces semiconductor moiré homobilayers as an electrically tunable Majorana platform with no need for an external magnetic field.

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• Kane-Mele model
• Magnetic order
• Majorana bound states
• Phase diagrams
• Quantum anomalous Hall effect
• Quantum spin Hall effect
• Topological superconductors
• Transition metal dichalcogenides
• Twisted heterostructures