  We explore the phase structure of two-color and two-flavor QCD in the space
of the quark chemical potential \mu_q and the isospin chemical potential \mu_I.
Using a mean-field model we calculate the chiral and diquark condensates,
\sigma and \Delta, self-consistently. In weak coupling and in the chiral limit,
we confirm the interval of the isospin chemical potential,
0.71\Delta_0<\mu_I<0.75\Delta_0, in which a single plane-wave
Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase is favored over isotropic
superfluidity and normal quark matter. The LOFF window becomes slightly wider
at high density. For stronger coupling with nonzero quark mass, which is
relevant to currently available numerical simulations in lattice two-color QCD,
the single plane-wave LOFF phase appears only at sufficiently high density. The
prediction obtained for the LOFF region could be tested with lattice since we
can prove that the present system is free from the fermion sign problem. We
draw the energy landscape on which local minima corresponding to the isotropic
superfluid phase and the LOFF phase and a local maximum corresponding to the
gapless phase are manifest. Our results clearly illustrate the path from the
the unstable gapless phase down to the LOFF phase.
