Phases with Regular Arrays of Defects or Solitons

This chapter provides a perspective on phases with regular arrays of defects or solitons, arguing that these structures are generally caused by frustration. The frustration may arise from an incompatibility between two physical mechanisms, such as between chirality and applied magnetic field. Alternatively, it may arise from an incompatibility between a single physical mechanism and the geometry of space, as in the packing of pentagons, or in a director field with favored splay. Based on this perspective, the chapter discusses several examples of phases with defects or solitons, including lattices of skyrmions or half-skyrmions, blue phases, Abrikosov vortex lattices in superconductors, and twist-grain-boundary (TGB) phases.