  Inhomogeneous chiral-symmetry breaking phases at non-vanishing chemical
potential and temperature are studied within a two-flavor quark-meson model in
the chiral limit. The analysis is performed beyond the standard mean-field
approximation by taking into account the Dirac-sea contributions of the quarks.
Compared with the case where the Dirac sea is neglected, we find that the
inhomogeneous phase shrinks, but in general does not disappear. It is shown
within a Ginzburg-Landau analysis that the Lifshitz point of the inhomogeneous
phase coincides with the tricritical point if the ratio between sigma-meson and
constituent quark mass in vacuum is chosen to be $m_\sigma/M = 2$,
corresponding to the fixed mass ratio in the Nambu--Jona-Lasinio model. In the
present model, however, this ratio can be varied, offering the possibility to
separate the two points. This is confirmed by our numerical calculations, which
demonstrate a strong sensitivity of the size of the inhomogeneous phase on
$m_\sigma$. Finally, we uncover a general instability of the model with respect
to large wave numbers of the chiral modulations, which calls for further
improvements beyond the present approximation.
