Higher-order topological phases emerging from Su-Schrieffer-Heeger stacking
Higher-order topological phases emerging from Su-Schrieffer-Heeger stacking
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DOI：
10.1103/physrevb.107.045118
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发表时间：
2022-02
影响因子：
3.7
通讯作者：
Xun-Jiang Luo;Xiaoguang Pan;Chaoxing Liu;Xin Liu
中科院分区：
文献类型：
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作者：
Xun-Jiang Luo;Xiaoguang Pan;Chaoxing Liu;Xin Liu
在这项工作中，我们开发了一种系统的方法来构造和分类具有角零能态的二维（2D）高阶拓扑相（CZESs）的模型哈密顿量。我们的方法是基于在一系列二维系统中直接构建CZESs的解析解，这些系统沿着两个正交方向堆叠1D扩展Su-Schrieffer-Heeger （SSH）模型，即原始SSH模型的两个副本。令人着迷的是，我们的方法不仅给出了著名的benalcazar - bernevigg - hughes和2D SSH模型，而且还揭示了一个新的模型，我们将其称为交叉2D SSH模型。虽然这三种模型具有完全不同的体拓扑结构，但由于其统一的哈密顿构造形式和边缘拓扑结构，我们发现CZESs在一维边缘状态下可以普遍地用边缘圈数来表征。值得注意的是，我们的原理可以很容易地推广到任意维和超导系统。因此，我们的工作揭示了对高阶拓扑相的理论认识，并为寻找高阶拓扑绝缘体和超导体铺平了道路。
In this work, we develop a systematical approach of constructing and classifying the model Hamiltonians for two-dimensional (2D) higher-order topological phase with corner zero energy states (CZESs). Our approach is based on the direct construction of analytical solution of the CZESs in a series of 2D systems that stack the 1D extended Su-Schrieffer-Heeger (SSH) model, two copies of the original SSH model, along two orthogonal directions. Fascinatingly, our approach not only gives the celebrated Benalcazar-Bernevig-Hughes and 2D SSH models but also reveals a novel model and we refer it to crossed 2D SSH model. Although these three models exhibit completely different bulk topology, we find that the CZESs can be universally characterized by edge winding number for 1D edge states, attributing to their unified Hamiltonian construction form and edge topology. Remarkably, our principle of obtaining CZESs can be readily generalized to arbitrary dimension and superconducting systems. Thus, our work sheds new light on the theoretical understanding of the higher-order topological phase and paves the way to looking for higher-order topological insulators and superconductors.