Topological Vortex Domains in Quantum Materials

Engineering of domains and domain boundaries is quintessential for technological exploitation of numerous functional materials. However, it has only recently realized that the configuration of these domains/⁠domain boundaries can have non-⁠trivial topology. We will discuss a new topological classification scheme of domain/⁠domain boundary configurations with Ising-⁠type or two-⁠dimensional order parameters: Zm×Zn domains (m directional variants and n translational antiphases) and Zl vortices (where l number of domains and that of domain boundaries merge). This classification, with the concept of topological protection and topological charge conservation, has been applied to a wide range of materials such as improper ferroelectric R(Mn,Fe)O3, antipolar In(Mn,Ga)O3, hybrid improper ferroelectric (Ca,Sr)3Ti2O7, chiral (and ferromagnetic) Fe1/⁠3TaS2, and magnetic-⁠superconducting Sr2VO3FeAs. We will also discuss the emergent physical properties of domain boundaries, distinct from those of domains. The presented topological consideration provides a basis in understanding the formation, kinetics, manipulation and property optimization of domains/⁠domain boundaries in quantum materials.