  Aims: We present a new microscopic hadron-quark hybrid equation of state
model for astrophysical applications, from which compact hybrid star
configurations are constructed. These are composed of a quark core and a
hadronic shell with a first-order phase transition at their interface. The
resulting mass-radius relations are in accordance with the latest astrophysical
constraints. Methods: The quark matter description is based on a quantum
chromodynamics (QCD) motivated chiral approach with higher-order quark
interactions in the Dirac scalar and vector coupling channels. For hadronic
matter we select a relativistic mean-field equation of state with
density-dependent couplings. Since the nucleons are treated in the
quasi-particle framework, an excluded volume correction has been included for
the nuclear equation of state at suprasaturation density which takes into
account the finite size of the nucleons. Results: These novel aspects, excluded
volume in the hadronic phase and the higher-order repulsive interactions in the
quark phase, lead to a strong first-order phase transition with large latent
heat, i.e. the energy-density jump at the phase transition, which fulfils a
criterion for a disconnected third-family branch of compact stars in the
mass-radius relationship. These twin stars appear at high masses ($\sim$ 2
M$_\odot$) that are relevant for current observations of high-mass pulsars.
Conclusions: This analysis offers a unique possibility by radius observations
of compact stars to probe the QCD phase diagram at zero temperature and large
chemical potential and even to support the existence of a critical point in the
QCD phase diagram.
