Ferroelectric and ferroelastic domain walls are 2D topological defects with thicknesses approaching the unit cell level. When this spatial confinement is combined with observations of emergent functional properties, such as polarity in non-polar systems or electrical conductivity in otherwise insulating materials, it becomes clear that domain walls represent new and exciting objects in matter. In this Review, we discuss the exotic polarization profiles that can arise at domain walls with multiple order parameters and the different mechanisms that lead to domain-wall polarity in non-polar ferroelastic materials. The emergence of energetically degenerate variants of the domain walls themselves suggests the existence of interesting quasi-1D topological defects within such walls. We also provide an overview of the general notions that have been postulated as fundamental mechanisms responsible for domain-wall conduction in ferroelectrics. We then discuss the prospect of combining domain walls with transition regions observed at phase boundaries, homo- and heterointerfaces, and other quasi-2D objects, enabling emergent properties beyond those available in today’s topological systems.

铁电和铁弹性畴壁是二维拓扑缺陷，其厚度接近单位晶胞水平。当将这种空间限制与新兴功能特性（例如非极性系统中的极性或绝缘材料中的电导率）的观察结果结合起来时，很明显畴壁代表了物质中新的令人兴奋的对象。在这篇综述中，我们讨论了在具有多个阶数参数的畴壁处可能会出现的奇异极化轮廓，以及导致非极性铁弹性材料中畴壁极性的不同机制。畴壁本身的能量简并变体的出现表明在这种壁中存在有趣的准1D拓扑缺陷。我们还提供了一般概念的概述，这些概念被假定为负责铁电体中畴壁传导的基本机制。然后，我们讨论将畴壁与在相界，均质和异质界面以及其他准2D对象处观察到的过渡区域结合在一起的前景，从而使超出当前拓扑系统中可用范围的新兴属性成为可能。