Anomalous spontaneous induction of magnetic and electric fields in dense quark matter

In this paper, we will demonstrate that a dense quark-matter system in the dual chiral density wave (DCDW) phase behaves as a ferromagnet in the sense that its magnetic-field dependent magnetization remains different from zero even at B → 0 . The corresponding permanent magnetization is a function of the baryonic chemical potential μ , decreasing up to zero as μ increases in the range of intermediate densities ( 312 MeV ⩽ μ ⩽ 342 MeV ) and then increasing from zero in the higher density interval 490 MeV ⩽ μ ⩽ 550 MeV . We will show that this system’s ability to generate permanent magnetization, together with the existence of the axial anomaly, open up the possibility of spontaneously generating a magnetic field coupled to a collinear electric field. The generated magnetic field can reach values up to 10 16 G , depending on μ , and the electric field will be 3 orders smaller. The fact that the DCDW phase is able to induce a magnetic field can be seen as its spontaneous tendency to remove the so called Landau-Peierls instability that is present in this single-modulated phase in the absence of a magnetic field. The spontaneous induction of a strong magnetic field at intermediate to high densities can be of interest for the astrophysics of compact stellar objects exhibiting strong magnetic fields as magnetars.