Transfer of planar orders onto a sphere: formation and properties of complex topological defects

Abstract

General topological principles how to transfer the planar orders onto a sphere are considered. Formation of extended topological defects (ETDs), which have a reconstructed inner structure surrounded by perfect initial order, is discussed. Topological charge of the ETD can be determined from the shape of a characteristic polygon bounding the defect. Relation between the total topological charge of all defects in the spherical structure and the type of initial planar order is found. It is also demonstrated that in the spherical hexagonal crystal a dislocation located in the ETD area is actually absorbed by it, because the order outside the defect doesn't display existence of dislocation in any way. For the case of singly connected spherical hexagonal order arising from mutual repulsion of N particles (N < 1000) only triangulation of the order inside the ETD regions recovers the linear scars which represent a narrow parts of wider ETD areas.