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We study aspects of the pion condensation in two-flavor neutral quark matterusing the Nambu--Jona-Lasinio model of QCD at finite density. We investigatethe role of electric charge neutrality, and explicit symmetry breaking viaquark mass, both of which control the onset of the charged pion $(\pi^c)$condensation. We show that the equality between the electric chemical potentialand the in-medium pion mass, $\mu_{e}=M_{\pi^-}$, as a threshold, persists evenfor a composite pion system in the medium, provided the transition to the pioncondensed phase is of the second order. Moreover, we find that the pioncondensate in neutral quark matter is extremely fragile to the symmetrybreaking effect via a current quark mass $m$, and is ruled out for $m$ largerthan the order of 10 keV.

The fate of pion condensation in quark matter: from the chiral limit to the physical pion mass