Abstract
We study twisted bilayer MoTe₂ systems at fractional fillings of the lowest hole band under an applied out-of-plane displacement field. By employing exact diagonalization in finite-size systems, we systematically map out the ground state quantum phase diagram for two filling fractions, ν=1/3 and 2/3, and provide a detailed characterization of each phase. We identify the phase transition between a fractional Chern insulator (FCI) and a layer-polarized charge density wave (CDW) at a filling fraction of ν=1/3, denoted as CDW-1. Additionally, we demonstrate that the competition between the displacement field and twist angle leads to another phase transition from a layer-polarized CDW-1 to a layer-hybridized CDW-2, identified as a first-order phase transition. Furthermore, at ν=2/3 filling of the lowest hole band, we observe that the FCI remains stable against the displacement field until it approaches proximity to a transition in single-particle band topology at a smaller twist angle.