  We present a novel relativistic density-functional approach to modeling quark
matter with a mechanism to mimic confinement. The quasiparticle treatment of
quarks provides their suppression due to large quark selfenergy already at the
mean-field level. We demonstrate that our approach is equivalent to a chiral
quark model with medium-dependent couplings. The dynamical restoration of the
chiral symmetry is ensured by construction of the density functional. Beyond
the mean field, quark correlations in the pseudoscalar channel are described
within the Gaussian approximation. This explicitly introduces pionic states
into the model. Their contribution to the thermodynamics potential is analyzed
within the Beth-Uhlenbeck framework. The modification of the meson mass
spectrum in the vicinity of thee (de)confinement transition is interpreted as
the Mott transition. Supplemented with the vector repulsion and diquark pairing
the model is applied to construct a hybrid quark-hadron EoS of cold
compact-star matter. We study the connection of such a hybrid EoS with the
stellar mass-radius relation and tidal deformability. The model results are
compared to various observational constraints including the NICER radius
measurement of PSR J0740+6620 and the tidal deformability constraint from
GW170817. The model is shown to be consistent with the constraints, still
allowing for further improvement by adjusting the vector repulsion and diquark
pairing couplings.
