Exotic phases may exist in neutron stars with increasing densities.
We study the hadron-quark mixed phase, which may occur in the interior of neutron stars.
The relativistic mean-field model is employed to describe the hadronic phase, while the
Nambu-Jona-Lasinio model with vector interactions is used for the quark phase. We study the
finite-size effects, like the surface and Coulomb energies, on the hadron-quark mixed
phase in neutron stars. We show that a massive star may contain a mixed phase core
and its size depends on the surface tension of the hadron-quark interface and the
vector coupling between quarks. The isovector-vector meson (ρ) plays an important role
to control the symmetry energy. The symmetry energy in nuclear matter has been studied
intensively and is known to affect the neutron star properties such as radii, it should be
important in the hadron-quark coexistence. As a result, the hadron-quark mixed phase shrinks with
isovector-vector coupling in quark matter.
