# Geometry induced domain-walls of dipole lattices on curved structures

## TL;DR

This paper studies how curved surfaces influence dipole lattice configurations, revealing the formation and behavior of domain-walls that depend on local geometry and respond to external electric fields.

## Contribution

It introduces the concept of geometry-induced domain-walls in dipole lattices on curved surfaces and analyzes their properties and responses to external stimuli.

## Key findings

- Domain-walls form along specific lattice sites determined by local geometry.
- External electric fields cause domain-wall displacements and splittings.
- Domain-walls trap low-energy excitations within domains.

## Abstract

We investigate the ground state 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 ground state can exhibit domain-walls separating domains with different dipole configurations. Furthermore, we show how, regardless of the surface geometry, the domain-walls locate along the lattice sites for which the (Euclidean) distances to nearest and next-nearest neighbors are equal. We analyze the response of the domain-walls to an external electric field and observe displacements and splittings thereof below and above a critical electric field, respectively. We further show that the domain-wall acts as a boundary that traps low-energy excitations within a domain.