论文标题
方形拓扑绝缘子和超导体的系统构造
Systematic construction of square-root topological insulators and superconductors
论文作者
论文摘要
我们提出了一个一般方案，以构造Hamiltonian $ h _ {\ text {root}} $，描述了基于图理论的原始汉密尔顿$ h _ {\ text {artional}} $的平方根。 Square-root Hamiltonian在$ h _ {\ text {onsimal}} $的原始图的细分图上定义，其中通过将一个顶点放在原始图中的每个链接上获得了细分图。当$ h _ {\ text {oinartial}} $描述一个拓扑系统时，在$ h _ {\ text {root}} $的频谱中以非零能量出现了间隙边缘状态，这是$ h _ _ _ {\ text fext {\ firmita ofference in topolical Edge Station in Zero Engial in Zero Engial in of totogical Edge States的本质。在这种情况下，$ h _ {\ text {root}} $描述了方形拓扑绝缘子或超导体。典型的例子是Su-Schrieffer-Heeger（SSH）模型，Kitaev拓扑超导体模型和Haldane模型的平方根。我们的方案也适用于非霍米特拓扑系统，在该系统中，我们研究了一个非近代非官方SSH模型的示例。
We propose a general scheme to construct a Hamiltonian $H_{\text{root}}$ describing a square root of an original Hamiltonian $H_{\text{original}}$ based on the graph theory. The square-root Hamiltonian is defined on the subdivided graph of the original graph of $H_{\text{original}}$, where the subdivided graph is obtained by putting one vertex on each link in the original graph. When $H_{\text{original}}$ describes a topological system, there emerge in-gap edge states at non-zero energy in the spectrum of $H_{\text{root}}$, which are the inherence of the topological edge states at zero energy in $H_{\text{original}}$. In this case, $H_{\text{root}}$ describes a square-root topological insulator or superconductor. Typical examples are square roots of the Su-Schrieffer-Heeger (SSH) model, the Kitaev topological superconductor model and the Haldane model. Our scheme is also applicable to non-Hermitian topological systems, where we study an example of a nonreciprocal non-Hermitian SSH model.
