We present a symmetry-based scheme to create zero-dimensional (0D) second-order topological modes in continuous two-dimensional (2D) systems. We show that a metamaterial with a $p6m$-symmetric pattern exhibits two Dirac cones, which can be gapped in two distinct ways by deforming the pattern. Combining the deformations in a single system then emulates the 2D Jackiw-Rossi model of a topological vortex, where 0D in-gap bound modes are guaranteed to exist. We exemplify our approach with the simple hexagonal, kagome, and honeycomb lattices. We furthermore formulate a quantitative method to extract the topological properties from finite-element simulations, which facilitates further optimization of the bound mode characteristics. Our scheme enables the realization of second-order topology in a wide range of experimental systems.

中文翻译：

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二维连续介质中的二阶拓扑模式

我们提出了一种基于对称性的方案，以在连续二维 (2D) 系统中创建零维 (0D) 二阶拓扑模式。我们展示了一种具有$磷6米$- 对称图案表现出两个狄拉克锥体，可以通过使图案变形以两种不同的方式将其分开。结合单个系统中的变形，然后模拟拓扑涡旋的二维 Jackiw-Rossi 模型，其中保证存在 0D 间隙边界模式。我们用简单的六边形、kagome 和蜂窝​​格子来举例说明我们的方法。我们进一步制定了一种定量方法来从有限元模拟中提取拓扑特性，这有助于进一步优化边界模式特性。我们的方案能够在广泛的实验系统中实现二阶拓扑。