  We investigate the properties of hybrid stars with the hadron-quark phase
transition by using a quasiparticle model. Results from our study indicate that
the coupling constant $g$ can stiffen the EOS of hybrid star matter and thus
increase the hybrid star maximum mass and its tidal deformability, whereas it
also decreases the mass and radius of the pure quark core. In addition, we find
that a step change of the sound velocity occurs in the hadron-quark mixed
phase, and it is restored with the decrease of nucleon and lepton degrees of
freedom in the high density quark phase. The approximate rule that the
polytropic index $\gamma \leq 1.75$ can also be used as a criterion for
separating hadronic from quark matter in our work. The hypothesis of absolutely
stable SQM (or "Witten hypothesis") suggests that a hybrid star containing a
sufficient amount of SQM in its core will rapidly convert into a strange quark
star. The SQM in hybrid stars therefore should break the absolutely stable
condition, and the energy per nucleon ($E/A$) of both $ud$QM and SQM must
exceed the lowest energy per nucleon 930 MeV. As a result, we provide the
maximum mass, minimum radius $R_{1.4}$ and minimum tidal deformation
$\Lambda_{1.4}$ of the hybrid stars as well as the maximum mass and radius of
the quark matter core with different $g$ values within the allowable regions
($E/A>930$ MeV) on the $g-B^{1/4}$ plane. Using the constraints from
astrophysical observations and heavy-ion experiments for comparison, our
results indicate that the recently discovered massive neutron stars be well
described as hybrid stars in the quasiparticle model, and confirm that the
sizable quark-matter cores ($R_{QC}>6.5$ km) containing the mixed phase can
appear in $2M_{\odot}$ massive stars.
