  By considering baryons as clusters of three quarks, we extend the
Nambu-Jona-Lasinio (NJL) model to describe baryonic matter, quark matter, and
their transitions in a unified manner, where the Dirac sea and spontaneous
chiral symmetry breaking are considered. In particular, a density-dependent
structural function $\alpha_S$ is introduced to modulate the four(six)-point
interaction strengths to reproduce the baryon masses in vacuum and medium.
Vector interactions are considered with the exchange of $\omega$ and $\rho$
mesons, where the density-dependent coupling constants are fixed by reproducing
nuclear matter properties as well as the $\Lambda$-hyperon potential depth in
nuclear medium. As density increases, quarks will emerge as quasi-free
particles and coexist with baryons. This phase is interpreted as quarkyonic
matter, where quarks are restricted to the lowest energy states in the presence
of baryons, i.e., quarks are still confined. Similar to the treatment of
$\alpha$ clustering in nuclear medium, a Pauli blocking term is added to baryon
masses so that baryons eventually become unbound in the presence of a quark
Fermi Sea. Then at large enough densities baryons vanish and a Mott transition
takes place, we consider such a transition as deconfinement phase transition.
Depending on the strengths of Pauli blocking term and quark-vector meson
couplings, both first-order and continues phase transitions are observed for
quarkyonic, chiral, and deconfinement phase transitions. The corresponding
compact star structures are then investigated and confronted with various
astrophysical constraints.
