论文标题
Benalcazar-Bernevig-Hughes型号的混合阶拓扑
Mixed-order topology of Benalcazar-Bernevig-Hughes models
论文作者
论文摘要
Benalcazar-Bernevig-Hughes（BBH）型号（以$ d $ d的简单立方晶格定义）是用于研究$ d $ d $ th订单拓扑和角度定位的中间隙状态的范式玩具模型。在周期性的边界条件下，已经有人说，BBH模型的非亚洲浆果连接的威尔逊环路已被认为显示出间隙的光谱，该光谱预测在开放边界条件下的表面群体。在这项工作中，我们确定了1D，2D和3D拓扑的不变性，以表征高阶拓扑绝缘子。此外，我们证明了BBBH模型布里鲁因区域的身体对角线方向的威尔逊环和表面状态的立方对称性，无间隙光谱的存在。我们显示了无间隙的表面状态由$ 2^{d-1} $ - 零件，无质量的狄拉克费米子描述。因此，根据外部施加的边界条件的细节，BBH模型可以表现出第一和$ d $ thorder阶拓扑的签名。
Benalcazar-Bernevig-Hughes (BBH) models, defined on $D$-dimensional simple cubic lattice, are paradigmatic toy models for studying $D$-th order topology and corner-localized, mid-gap states. Under periodic boundary conditions, the Wilson loops of non-Abelian Berry connection of BBH models along all high-symmetry axes have been argued to exhibit gapped spectra, which predict gapped surface-states under open boundary conditions. In this work, we identify 1D, 2D, and 3D topological invariants for characterizing higher order topological insulators. Further, we demonstrate the existence of cubic-symmetry-protected, gapless spectra of Wilson loops and surface-states along the body diagonal directions of the Brillouin zone of BBH models. We show the gapless surface-states are described by $2^{D-1}$-component, massless Dirac fermions. Thus, BBH models can exhibit the signatures of first and $D$-th order topological insulators, depending on the details of externally imposed boundary conditions.
