Intrinsic Properties of Large CP Violation in the Complex Two-Higgs-Doublet Model

We investigate the parameter space supporting large CP violation (CPV) in the complex two-Higgs-doublet model with softly broken $Z_2$ symmetry, where the 125~GeV Higgs boson is identified as the lightest neutral Higgs boson $H_1$. Through a comprehensive global scan of Type-I and Type-II models under theoretical, collider, and eEDM constraints, we identify distinct structures that facilitate large CPV. In Type-I, gauge-sector CPV is maximized when the 125~GeV Higgs boson is nearly degenerate with a second neutral scalar. For the ensemble of physically viable points, the predicted eEDM values typically exceed ${10}^{-31}e\cdot \mathrm{c}\mathrm{m}$, placing the model largely within the sensitivity of next-generation experiments. Conversely, Type-II models strongly suppress gauge-sector CPV while allowing for nearly maximal CPV in the Yukawa sector. Destructive interference among various contributions allows for $\mathrm{\mid }{d}_e\mathrm{\mid }$ values as low as $O({10}^{-35})e\cdot \mathrm{c}\mathrm{m}$, resulting in no phenomenologically relevant lower bound. Finally, we uncover the phenomenon of ``hidden CPV’’ in the near-alignment limit, characterized by CP-violating mixing between the heavy neutral Higgs bosons governed by the angle ${\alpha }_3$. We demonstrate that this hidden CPV can be experimentally probed at future colliders via CP-violating Yukawa interactions of $H_2$ and $H_3$, as well as the robust $H_2$-$H_3$-$Z$ coupling.