  We propose a class of the two Higgs doublet Standard models (SMs) with a SM
singlet and a class of supersymmetric SMs with two pairs of Higgs doublets,
where the right-handed up/charm quarks and the right-handed top quark have
different quantum numbers under extra discrete symmetries. Thus, the
right-handed up and charm quarks couple to one Higgs doublet field, while the
right-handed top quark couples to another Higgs doublet. The quark CKM mixings
can be generated from the down-type quark sector. As one of phenomenological
consequences in our models, we explore whether one can accommodate the observed
direct CP asymmetry difference in singly Cabibbo-suppressed D decays. We show
that it is possible to explain the measured values of CP violation under
relevant experimental constraints.
