Chiral hedgehog textures in two-dimensional $\mathrm{XY}$-like ordered domains

The textures associated with a point defect centered in a circular domain of a thin film with $\mathrm{XY}$-like ordering have been analyzed. The family of equilibrium textures, both stable and metastable, can be classified by a new radial topological number in addition to the winding number of the defect. Chiral textures are supported in an achiral system as a result of spontaneously broken chiral symmetry. Among these chiral textures, our theoretical analysis accurately describes two categories of recently discovered “reversing spiral” textures, ones that are energetically stable and metastable.