Magnetic Dual Chiral Density Wave: A Candidate Quark Matter Phase for the Interior of Neutron Stars

In this review, we discuss the physical characteristics of the magnetic dual chiral density wave (MDCDW) phase of dense quark matter and argued why it is a promising candidate for the interior matter phase of neutron stars. The MDCDW condensate occurs in the presence of a magnetic field. It is a single-modulated chiral density wave characterized by two dynamically generated parameters: the fermion quasiparticle mass $m$ and the condensate spatial modulation $q$. The lowest Landau level quasiparticle modes in the MDCDW system are asymmetric about the zero energy, a fact that leads to the topological properties and anomalous electric transport exhibited by this phase. The topology makes the MDCDW phase robust against thermal phonon fluctuations, and as such, it does not display the Landau-Peierls instability, a stapled feature of single-modulated inhomogeneous chiral condensates in three dimensions. The topology is also reflected in the presence of the electromagnetic chiral anomaly in the effective action and in the formation of hybridized propagating modes known as an axion-polaritons. Taking into account that one of the axion-polaritons of this quark phase is gapped, we argued how incident $\gamma$-ray photons can be converted into gapped axion-polaritons in the interior of a magnetar star in the MDCDW phase leading the star to collapse, a phenomenon that can serve to explain the so-called missing pulsar problem in the galactic center.