Geometry induced domain-walls of dipole lattices on curved structures

We investigate the ground state (GS) properties of rectangular dipole lattices on curved surfaces. The curved geometry can 'distort' the lattice and lead to dipole equilibrium configurations that strongly depend on the local geometry of the surface. We find that the system's GS can exhibit domain-walls separating domains with different dipole configurations. Furthermore, we show how, regardless of the surface geometry, the domain-walls (DWs) locate along the lattice sites for which the (Euclidean) distances to nearest and next-nearest neighbors are equal. We analyze the response of the DWs to an external electric field and observe displacements and splittings thereof below and above a critical electric field, respectively. We further show that the DW acts as a boundary that traps low-energy excitations within a domain.