  Semiconductor moir\'e 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 the
topological moir\'e flat bands in twisted transition metal dichalcogenides
homobilayers. For 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
magnetic phases with in-plane magnetization (either ferromagnetic or
antiferromagnetic) can realize one-dimensional topological superconductor with
Majorana zero modes. Our proposal introduces semiconductor moir\'e homobilayers
as an electrically tunable Majorana platform with no need of an external
magnetic field.
