  In a class of new physics models, an extended Higgs sector and new
CP-violating sources are simultaneously present in order to explain the baryon
asymmetry in the Universe. The aim of this work is to study the implications of
beyond the Standard Model (SM) CP violation for the searches of heavy scalars
at the LHC. In particular, we focus on the diphoton channel searches in the
CP-violating two-Higgs-doublet model (CPV 2HDM). To have a sizable CPV in the
scalar sector, the two heavy neutral scalars in 2HDM tend to be nearly
degenerate. The theoretical constraints of unitarity, perturbativity and vacuum
stability are considered, which requires that the heavy scalars $M_H \lesssim
1$ TeV in a large region of the parameter space. The experimental limits are
also taken into account, including the direct searches of heavy neutral scalars
in the final state of the SM $h$, $W$ and $Z$ bosons, the differential
$t\bar{t}$ data, those from the charged scalar sector which is implied by the
oblique $T$ parameter, as well as the precise measurements of the electric
dipole moments of electron and mercury. The quantum interference effects
between the resonances and the SM background are crucially important for the
diphoton signals, and the CPV mixing of the quasi-degenerate heavy scalars
could enhance significantly the resonance peak. With an integrated luminosity
of 3000 fb$^{-1}$ at the LHC, almost the whole parameter space of CPV 2HDM
could be probed in the diphoton channel, and the CPV could also be directly
detected via the diphoton spectrum.
