Tyner Alexander C, Juričić Vladimir
Nordita, KTH Royal Institute of Technology and Stockholm University, Hannes Alfvéns väg 12, 106 91, Stockholm, Sweden.
Department of Physics, University of Connecticut, Storrs, CT, 06269, USA.
Sci Rep. 2024 Feb 21;14(1):4288. doi: 10.1038/s41598-024-54821-3.
In recent decades, the Altland-Zirnabuer (AZ) table has proven incredibly powerful in delineating constraints for topological classification of a given band-insulator based on dimension and (nonspatial) symmetry class, and has also been expanded by considering additional crystalline symmetries. Nevertheless, realizing a three-dimensional (3D), time-reversal symmetric (class AII) topological insulator (TI) in the absence of reflection symmetries, with a classification beyond the [Formula: see text] paradigm remains an open problem. In this work we present a general procedure for constructing such systems within the framework of projected topological branes (PTBs). In particular, a 3D projected brane from a "parent" four-dimensional topological insulator exhibits a [Formula: see text] topological classification, corroborated through its response to the inserted bulk monopole loop. More generally, PTBs have been demonstrated to be an effective route to performing dimensional reduction and embedding the topology of a [Formula: see text]-dimensional "parent" Hamiltonian in d dimensions, yielding lower-dimensional topological phases beyond the AZ classification without additional symmetries. Our findings should be relevant for the metamaterial platforms, such as photonic and phononic crystals, topolectric circuits, and designer systems.
近几十年来，阿尔特兰 - 齐尔纳布尔（AZ）表已被证明在基于维度和（非空间）对称类来描绘给定带绝缘体拓扑分类的约束条件方面极其强大，并且通过考虑额外的晶体对称性也得到了扩展。然而，在不存在反射对称性的情况下实现三维（3D）、时间反演对称（AII类）拓扑绝缘体（TI），且其分类超出[公式：见原文]范式仍然是一个未解决的问题。在这项工作中，我们提出了一种在投影拓扑膜（PTB）框架内构建此类系统的通用程序。特别地，来自“母体”四维拓扑绝缘体的三维投影膜表现出[公式：见原文]拓扑分类，这通过其对插入的体单极子环的响应得到了证实。更一般地，PTB已被证明是执行降维以及将[公式：见原文]维“母体”哈密顿量的拓扑嵌入到d维的有效途径，从而产生超出AZ分类且无额外对称性的低维拓扑相。我们的发现应该与超材料平台相关，例如光子晶体和声子晶体、拓扑电电路以及定制系统。
