Twisted bilayer transition metal dichalcogenides, such as ${\mathrm{MoTe}}_2$, provide a versatile platform for exploring correlated topological phases. This work investigates the interplay between perpendicular magnetic and electric fields in tuning the electronic structure and emergent topological orders of twisted bilayer ${\mathrm{MoTe}}_2$ (t-${\mathrm{MoTe}}_2$) across two distinct regimes: a low-twist-angle phase ($\theta \approx 2.1^{\circ }$) hosting multiple Chern bands of identical Chern numbers per valley, and a higher-angle phase ($\theta \approx 3.{89}^{\circ }$) featuring Haldane-like bands with opposite Chern numbers. Using a continuum model incorporating moiré potentials up to second harmonics, we compute the Hofstadter fractal spectra under applied fields, revealing Landau fan structures and magnetic-flux-dependent band topology. These fractal spectra are useful in studying emergent topological orders in terms of the composite fermion picture, where the statistical Chern-Simons flux is approximated as a uniform gauge field. We demonstrate that the system hosts both Jain-sequence fractional Chern insulators (FCIs) and non-Jain “fractal FCIs” with higher Chern numbers. The electric field suppresses composite fermion gaps and induces topological quantum phase transitions. Furthermore, our analysis extends to valley-contrasting flux attachment, proposing pathways to describe fractional quantum spin Hall states.

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• Anyons
• Chern insulators
• Chern-Simons gauge theory
• Composite fermions
• Fractionalization
• Lattice gauge theory
• Quantum phase transitions
• Transition metal dichalcogenides
• Twisted heterostructures