  The invisible variant axion model is very attractive as it is free from the
domain wall problem. This model requires two Higgs doublets at the electroweak
scale where one Higgs doublet carries a nonzero Peccei-Quinn (PQ) charge and
the other is neutral under the PQ $\text U(1)$ symmetry. We consider the most
interesting and less constrained scenario of the variant axion model, where
only the right-handed top quark is charged under the PQ symmetry and couples
with the PQ-charged Higgs doublet. As a result, the top quark can decay to the
observed standard-model-like Higgs boson $h$ and the charm or up quark, $t\to
h~ c/u$, which is testable soon at the LHC Run-II. Moreover, we propose a
method to probe the chiral nature of the Higgs flavor-changing interaction
using the angular distribution of $t \to ch$ decays if a sufficient number of
such events are observed. We also show that our model has the capacity to
explain the $h\to\tau\mu$ decay reported by the CMS Collaboration, if the
right-handed tau lepton also carries a PQ charge and couples to the PQ-charged
Higgs boson.
