  Inhomogeneous chiral phase is discussed in the presence of the magnetic
field. A topological aspect is pointed out for the complex order parameter, in
relation to the spectral asymmetry of the Dirac operator. It induces an
anomalous baryon number and extremely extends the region of the inhomogeneous
chiral phase in the QCD phase diagram. It is also shown that the novel
tricritical point appears at zero chemical potential, which should be examined
by the lattice QCD simulation.
