Spontaneous CP violation in the 2HDM: physical conditions and the   alignment limit
  For the general Two-Higgs-Doublet model, we present conditions for having spontaneous CP violation, in terms of physical masses and couplings. These relations involve the charged-Higgs mass, its cubic couplings with neutral scalars and quartic coupling, and become particularly simple in the alignment limit. In the simplified model with softly broken $Z_2$ symmetry, some deviation from alignment is required for spontaneous CP violation to be present. 
B. Grzadkowski, O. M. Ogreid, P. Osland
hep-ph