  We study the phase diagram of strongly interacting matter including the
inhomogeneous phase of Chiral Density Waves (CDW) within the Polyakov loop
extended Nambu-Jona-Lasinio (PNJL) model. We discuss the phase structure taking
into account density and flavour dependence of the Polyakov loop potential
parameter and temperature dependence of the four-point coupling constant of the
NJL model. It is shown that the CDW phase exists and that can be interpreted as
a special realisation of quarkyonic matter. This fact is of particular interest
because the existence of homogeneous quarkyonic matter is strongly constrained.
This also indicates that the study of inhomogeneous phases at finite
temperatures and baryon densities are of special importance.
