  Based on the chiral perturbation theory at the leading order, we show the
presence of a new phase in rapidly rotating QCD matter with two flavors, that
is a domain-wall Skyrmion phase. Based on the chiral Lagrangian with a
Wess-Zumino-Witten (WZW) term responsible for the chiral anomaly and chiral
vortical effect, it was shown that the ground state is a chiral soliton
lattice(CSL) consisting of a stack of $\eta$-solitons in a high density region
under rapid rotation. In a large parameter region, a single $\eta$-soliton
decays into a pair of non-Abelian solitons, each of which carries ${\rm
SU}(2)_{\rm V}/{\rm U}(1) \simeq {\mathbb C}P^1 \simeq S^2$ moduli as a
consequence of the spontaneously broken vector symmetry ${\rm SU}(2)_{\rm V}$.
In such a non-Abelian CSL, we construct the effective world-volume theory of a
single non-Abelian soliton to obtain a $d=2+1$ dimensional ${\mathbb C}P^1$
model with a topological term originated from the WZW term. We show that when
the chemical potential is larger than a critical value, a topological lump
supported by the second homotopy group $\pi_2(S^2) \simeq {\mathbb Z}$ has
negative energy and is spontaneously created, implying the domain-wall Skyrmion
phase. This lump corresponds in the bulk to a Skyrmion supported by the third
homotopy group $\pi_3[ {\rm SU}(2)] \simeq {\mathbb Z}$ carrying a baryon
number. This composite state is called a domain-wall Skyrmion, and is stable
even in the absence of the Skyrme term. An analytic formula for the effective
nucleon mass in this medium is obtained as $4\sqrt{2}\pi f_{\pi}f_\eta/m_{\pi}
\sim 1.21$ GeV with the decay constants $f_{\pi}$ and $f_\eta$ of the pions and
$\eta$ meson, respectively, and the pion mass $m_{\pi}$, which is surprisingly
close to the nucleon mass in the QCD vacuum.
