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Abstract In this paper it is reviewed the topological properties and possible astrophysical consequences of a spatially inhomogeneous phase of quark matter, known as the Magnetic Dual Chiral Density Wave (MDCDW) phase, that can exist at intermediate baryon density in the presence of a magnetic field. Going beyond mean-field approximation, it is shown how linearly polarized electromagnetic waves penetrating the MDCDW medium can mix with the phonon fluctuations to give rise to two hybridized modes of propagation called as axion polaritons because of their similarity with certain modes found in condensed matter for topological magnetic insulators. The formation of axion polaritons in the MDCDW core of a neutron star can serve as a mechanism for the collapse of a neutron star under the bombardment of the gamma rays produced during gamma ray bursts. This mechanism can provide a possible solution to the missing pulsar problem in the galactic center. 

Abstract In this paper we discuss in some detail how the pressures determined from semi-classical statistical averaging of the energy momentum tensor in the presence of a uniform background magnetic field are anisotropic with different pressures arising along and perpendicular to the magnetic field direction. Hence, we analyze how this result can affect two important characteristics of dense magnetized systems: (i) The hadron-quark phase transition in the presence of a magnetic field, (ii) The behavior of the speed of sound in dense magnetized systems. Taking into account that large magnetic fields are expected to be present in the interior of neutron stars, we will stress the role the pressure anisotropy plays in the physics of these compact astronomical objects. 

Abstract The correct description of strongly interacting matter at low temperatures and moderately high densities—in particular the conditions realized inside neutron stars—is still unknown. We review some recent results on the magnetic dual chiral density wave (MDCDW) phase, a candidate phase of quark matter for this region of the QCD phase diagram. We highlight the effects of magnetic fields and temperature on the condensate, which can be explored using a high-order Ginzburg-Landau (GL) expansion. We also explain how the condensate’s nontrivial topology, which arises due to the asymmetry in the lowest Landau level modes, affects its physical properties. Finally, we comment on the possible relevance of these results to neutron star applications. Over a wide range of densities and magnetic field strengths, MDCDW is preferred over the chirally symmetric ground state at temperatures consistent with typical cold neutron stars, and in some cases, even hot ones. 

We study the phase transitions at finite temperature and density of the magnetic dual chiral density wave (MDCDW) phase. This spatially inhomogeneous phase emerges in cold, dense QCD in the presence of a strong magnetic field. Starting from the generalized Ginzburg-Landau (GL) expansion of the free energy, we derive several analytical formulas that enable fast numerical computation of the expansion coefficients to arbitrary order, allowing high levels of precision in the determination of the physical dynamical parameters, as well as in the transition curves in the temperature vs chemical potential plane at different magnetic fields. At magnetic fields and temperatures compatible with neutron star (NS) conditions, the MDCDW remains favored over the symmetric ground state at all densities. The phase’s “resilience” manifests in (1) a region of small but nonzero remnant mass and significant modulation at intermediate densities, originating in part from the nontrivial topology of the lowest Landau level, and (2) a region of increasing condensate parameters at high densities. Our analysis suggests the MDCDW condensate remains energetically favored at densities and temperatures much higher than previously considered, opening the possibility for this phase to be a viable candidate for the matter structure of even young neutron stars produced by binary neutron star (BNS) mergers. 

We investigate the hadron-quark phase transition at nite density in the presence of a magnetic eld taking into account the anisotropy created by a uniform magnetic eld in the system's equations of state.We find a new anisotropic equilibrium condition that will drive the first-order phase transition along the boundary between the two phases. Fixing the magnetic eld in the hadronic phase, the phase transition is realized by increasing the baryonic chemical potential at zero-temperature. It is shown that the magnetic eld is mildly boosted after the system transitions from the hadronic to the quark phase. The magnetic-eld discontinuity between the two phases is supported by a surface density of magnetic monopoles, which accumulate at the boundary separating the two phases. The mechanism responsible for the monopole charge density generation is discussed. Each phase is found to be paramagnetic with higher magnetic susceptibility in the quark phase. The connection with the physics of neutron stars is highlighted throughout the paper. 

We investigate the hadron-quark phase transition at finite density in the presence of a magnetic field taking into account the anisotropy created by a uniform magnetic field in the system’s equations of state. We find a new anisotropic equilibrium condition that will drive the first-order phase transition along the boundary between the two phases. Fixing the magnetic field in the hadronic phase, the phase transition is realized by increasing the baryonic chemical potential at zero-temperature. It is shown that the magnetic field is mildly boosted after the system transitions from the hadronic to the quark phase. The magnetic-field discontinuity between the two phases is supported by a surface density of magnetic monopoles, which accumulate at the boundary separating the two phases. The mechanism responsible for the monopole charge density generation is discussed. Each phase is found to be paramagnetic with higher magnetic susceptibility in the quark phase. The connection with the physics of neutron stars is highlighted throughout the paper. 

Several anomalous electromagnetic effects that can take place in quark matter at low temperatures and intermediate densities will be discussed. The anomalous transport properties of the spatially inhomogeneous phase of quark matter known as the Magnetic Dual Chiral Density Wave (MDCDW) phase will be reviewed. Going beyond mean-field approximation, it will be shown how linearly polarized electromagnetic waves that penetrate the MDCDW medium mix with the phonon fluctuations to give rise to two hybridized modes of propagation called axion polaritons. Finally, some possible implications of these results for the astrophysics of neutron stars will be indicated. 

In this review, we discuss the physical characteristics of the magnetic dual chiral density wave (MDCDW) phase of dense quark matter and argue 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 staple 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 axion-polaritons. Taking into account that one of the axion-polaritons of this quark phase is gapped, we argue how incident g-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.