论文标题
通用拓扑标记
Universal topological marker
论文作者
论文摘要
我们阐述的是，对于狄拉克模型在任何维度和对称类别中描述的拓扑绝缘体和拓扑超导体，拓扑顺序可以通过通用拓扑标记将其映射到晶格位置。从最近发现的动量空间通用拓扑不变的衍生出来，我们介绍了一个拓扑操作员，该拓扑操作员由交替的投影仪组成，以填充和空的晶格特征状态和位置运算符，乘以汉密尔顿省省略的DIRAC矩阵。投影到晶格站点的拓扑操作员产生了拓扑标记，其形式是针对从1D到3D的每个拓扑非平凡的对称类别构建的。拓扑操作员的外元素元素产生一个非局部拓扑标记，其相关长度在拓扑相转变时差异，代表了Wannier状态相关函数。 Various prototype examples, including Su-Schrieffer-Heeger model, Majorana chain, Chern insulators, Bernevig-Hughes-Zhang model, 2D chiral and helical $p$-wave superconductors, lattice model of $^{3}$He B-phase, and 3D time-reversal symmetric topological insulators, etc, are employed to demonstrate the ubiquity of our formalism.
We elaborate that for topological insulators and topological superconductors described by Dirac models in any dimension and symmetry class, the topological order can be mapped to lattice sites by a universal topological marker. Deriving from a recently discovered momentum-space universal topological invariant, we introduce a topological operator that consists of alternating projectors to filled and empty lattice eigenstates and the position operators, multiplied by the Dirac matrices that are omitted in the Hamiltonian. The topological operator projected to lattice sites yields the topological marker, whose form is explicitly constructed for every topologically nontrivial symmetry class from 1D to 3D. The off-diagonal elements of the topological operator yields a nonlocal topological marker, which decays with a correlation length that diverges at topological phase transitions, and represents a Wannier state correlation function. Various prototype examples, including Su-Schrieffer-Heeger model, Majorana chain, Chern insulators, Bernevig-Hughes-Zhang model, 2D chiral and helical $p$-wave superconductors, lattice model of $^{3}$He B-phase, and 3D time-reversal symmetric topological insulators, etc, are employed to demonstrate the ubiquity of our formalism.
