  We explore the inhomogeneous QCD phases at finite density and temperature
using a (3+1)-dimensional Nambu-Jona-Lasinio (NJL) model in the large Nc limit
with an additional attractive tensor-tensor interaction channel. For single
modulated solutions, the problem reduces to solving the gap equation of a
Chiral Gross-Neveu (NJL2) theory, whose minimum solution is a periodic array of
chirally twisted kinks. At zero temperature, the minimum solution reduces to
the quarkyonic chiral spiral found in quarkyonic matter. The connection between
the quarkyonic matter and our (3+1)-dimensional NJL model is rooted on the fact
that the first reduces to (1+1)-dimensional QCD and the second to the NJL2
theory, both of which have continuous chiral symmetry and asymptotic freedom.
Our findings can be useful to obtain a reliable qualitative picture of the QCD
phase diagram and the location of the QCD critical point in the technically
challenging region of intermediate densities and temperatures.
