  In this work we continue our efforts to study the existence of a phase with
an inhomogeneous, i.e., spatially varying, chiral condensate in QCD. To this
end we employ a previously established method of stability analysis of the
two-particle irreducible effective action in a truncation that corresponds to a
rainbow-ladder approximation of the quark-gluon interaction of QCD. If the
analysis is restricted to homogeneous phases, the phase diagram features a
first-order chiral transition in the lower-temperature regime. Performing the
stability analysis along the lower-chemical-potential border of the
corresponding spinodal region, we find that below a certain temperature the
homogeneous chirally symmetric solution is unstable against inhomogeneous
condensation. We argue that this instability may persist to chemical potentials
above the homogeneous first-order phase boundary, in which case it signals the
existence of an inhomogeneous ground state. Our methodology is also applicable
for more sophisticated truncations of the QCD effective action.
