Pion Condensation in Baryonic Matter: from Sarma Phase to Larkin-Ovchinnikov-Fudde-Ferrell Phase

We investigated two pion condensed phases in the frame of the two flavor Nambu–Jona-Lasinio model at finite baryon density: the homogeneous and isotropic Sarma phase and inhomogeneous and anisotropic Larkin-Ovchinnikov-Fudde-Ferrell(LOFF) phase. At small isospin chemical potential ${\mu }_I$, the Sarma state is free from the Sarma instability and magnetic instability due to the strong coupling and large enough effective quark mass. At large ${\mu }_I$, while the Sarma instability can be cured via fixing baryon density $n_B$ to be nonzero, its magnetic instability implies that the LOFF state is more favored than the Sarma state. In the intermediate ${\mu }_I$ region, the stable ground state is the Sarma state at higher $n_B$ and LOFF state at lower $n_B$.