Octahedral Tilt Instability of ReO_3-type Crystals

The octahedron tilt transitions of ABX_3 perovskite-structure materials lead to an anti-polar (or antiferroelectric) arrangement of dipoles, with the low temperature structure having six sublattices polarized along various crystallographic directions. It is shown that an important mechanism driving the transition is long range dipole-dipole forces acting on both displacive and induced parts of the anion dipole. This acts in concert with short range repulsion, allowing a gain of electrostatic (Madelung) energy, both dipole-dipole and charge-charge, because the unit cell shrinks when the hard ionic spheres of the rigid octahedron tilt out of linear alignment.Comment: 4 page with 3 figures included; new version updates references and clarifies the argument

Magnetism in Dense Quark Matter

We review the mechanisms via which an external magnetic field can affect the ground state of cold and dense quark matter. In the absence of a magnetic field, at asymptotically high densities, cold quark matter is in the Color-Flavor-Locked (CFL) phase of color superconductivity characterized by three scales: the superconducting gap, the gluon Meissner mass, and the baryonic chemical potential. When an applied magnetic field becomes comparable with each of these scales, new phases and/or condensates may emerge. They include the magnetic CFL (MCFL) phase that becomes relevant for fields of the order of the gap scale; the paramagnetic CFL, important when the field is of the order of the Meissner mass, and a spin-one condensate associated to the magnetic moment of the Cooper pairs, significant at fields of the order of the chemical potential. We discuss the equation of state (EoS) of MCFL matter for a large range of field values and consider possible applications of the magnetic effects on dense quark matter to the astrophysics of compact stars.Comment: To appear in Lect. Notes Phys. "Strongly interacting matter in magnetic fields" (Springer), edited by D. Kharzeev, K. Landsteiner, A. Schmitt, H.-U. Ye