  We systematically apply density functional theory to determine the kind of
inhomogeneities that spontaneously develop in a homogeneous gapless phase of
neutral two-flavor superfluid quark matter. We consider inhomogeneities in the
quark and electron densities and in the phases and amplitude of the order
parameter. These inhomogeneities are expected to lead the gapless phase to a
BCS-normal coexisting phase, a Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) state
with phase oscillations alone, and a LOFF state with amplitude oscillations. We
find that which of them the homogeneous system tends towards depends
sensitively on the chemical potential separation between up and down quarks and
the gradient energies.
