Baryonic Vortex Phase and Magnetic Field Generation in QCD with Isospin and Baryon Chemical Potentials

We propose a novel baryonic vortex phase in low energy dense QCD with finite baryon and isospin chemical potentials. It is known that the homogeneous charged pion condensate emerges as a ground state at finite isospin chemical potential, and therein arises the Abrikosov vortex lattice with an applied magnetic field. We first demonstrate that a vortex with the same quantized magnetic flux as the conventional Abrikosov vortex, carries a baryon number captured by the third homotopy group of Skyrmions, once we take into account a modulation of the neutral pion inside the vortex core. Such a vortex-Skyrmion state is therefore dubbed the baryonic vortex. We further reveal that when the baryon chemical potential is above a critical value, the baryonic vortex has negative tension measured from the charged pion condensation. It implies that the phase, in which such vortices emerge spontaneously without an external magnetic field, would take over the ground state at high baryon density. Such a new phase contributes to the comprehension of QCD phase diagram and relates to the generation of magnetic fields inside neutron stars.