论文标题
教程：高阶拓扑绝缘子的狄拉克方程观点
Tutorial: Dirac Equation Perspective on Higher-Order Topological Insulators
论文作者
论文摘要
在本教程中，我们以教学的方式回顾了物质非相互作用的费米子阶段领域的最新发展，重点是在迪拉克方程方面的高阶拓扑绝缘子的低能量描述。我们的目标是给予大多数独立的治疗方法。在引入了拓扑结晶条带结构的狄拉克近似之后，我们使用它来得出一个和两个空间维度的第一和高阶拓扑绝缘子的异常端和角状态。特别是，我们根据晶体对称性重塑了Su-Schrieffer-Heeger（SSH）链的域壁结合状态的经典推导。然后可以将二维高阶拓扑绝缘子的边缘视为单一晶体对称性保护的SSH链，其域壁结合成为角状态。我们从来没有明确地解决二维系统的完整对称边界，而是通过绝热的连续性来争论。我们的方法捕获了高阶拓扑的所有显着特征，同时还可以在分析上进行分析。
In this tutorial, we pedagogically review recent developments in the field of non-interacting fermionic phases of matter, focussing on the low energy description of higher-order topological insulators in terms of the Dirac equation. Our aim is to give a mostly self-contained treatment. After introducing the Dirac approximation of topological crystalline band structures, we use it to derive the anomalous end and corner states of first- and higher-order topological insulators in one and two spatial dimensions. In particular, we recast the classical derivation of domain wall bound states of the Su-Schrieffer-Heeger (SSH) chain in terms of crystalline symmetry. The edge of a two-dimensional higher-order topological insulators can then be viewed as a single crystalline symmetry-protected SSH chain, whose domain wall bound states become the corner states. We never explicitly solve for the full symmetric boundary of the two-dimensional system, but instead argue by adiabatic continuity. Our approach captures all salient features of higher-order topology while remaining analytically tractable.
