  We consider the phase diagram of two-flavor quark matter under neutron star
constraints for two nonlocal, covariant quark models within the mean field
approximation. In the first case (Model I) the nonlocality arises from the
regularization procedure, motivated by the instanton liquid model, whereas in
the second one (Model II) a separable approximation of the one-gluon exchange
interaction is applied. We find that Model II predicts a larger quark mass gap
and a chiral symmetry breaking (CSB) phase transition line which extends 15-20%
further into the phase diagram spanned by temperature (T) and chemical
potential (mu). The corresponding critical temperature at mu=0, T_c(0)~140 MeV,
is in better accordance to recent lattice QCD results than the prediction of
the standard local NJL model, which exceeds 200 MeV. For both Model I and Model
II we have considered various coupling strengths in the scalar diquark channel,
showing that different low-temperature quark matter phases can occur at
intermediate densities: a normal quark matter (NQM) phase, a two-flavor
superconducting (2SC) quark matter phase and a mixed 2SC-NQM phase. Although in
most cases there is also a gapless 2SC phase, this occurs in general in a small
region at nonzero temperatures, thus its effect should be negligible for
compact star applications.
