Mixed-order topology of Benalcazar-Bernevig-Hughes models
Shouvik Sur, Alexander C. Tyner, Pallab Goswami
备注：
13 pages; 7 figures. (v2) added discussions on 3D invariant, observables, and non-BBH class models; new figures; updated reference list; abstract updated accordingly
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.
Comment to "Quantum Spin Hall Effect and Topological Phase Transition in HGTe Quantum Wells" by B. Andrei Bernevig, Taylor L. Hughes and Shou-Cheng Zhang Science 314, 1757 (2006)
本文是对B. M.“HGTe量子阱中的量子自旋霍尔效应和拓扑相变”一文的评论。作者：Andrei Bernevig，Taylor L. Hughes and Shou-Cheng Zhang Science 314，1757（2006）.本文证明了这些作者所认为的碲化汞阱内表面态的量子态在物理上是不正确的。态的动能为负。状态不能被识别为希尔伯特空间中的本征函数（向量）。因此，该状态可以用作拓扑状态理论的入门，在以下出版物中开发。
Tunable cornerlike states in topological type-II hyperbolic lattices
Hubei University（湖北大学）；Hubei University of Automotive Technology（湖北汽车工业学院）；Wuchang Shouyi University（武昌首义学院）；Hubei University of Science and Technology（湖北科技学院）；Wuhan University（武汉大学）；Wuhan Institute of Quantum Technology（武汉量子技术研究院）
Hidden topology and strong quantum metric bounds in trivial systems
Hefei National Laboratory（合肥国家实验室）；University of Science and Technology of China（中国科学技术大学）；Fudan University（复旦大学）；Westlake University（西湖大学）；Great Bay University（大湾区大学）
Manipulation of Topological Corner States via Subchiral Symmetry
National University of Singapore（新加坡国立大学）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；MajuLab, CNRS-UNS-NUS-NTU International Joint Research Unit（中法新南洋联合实验室）；Agency for Science, Technology and Research (A*STAR)（科学技术研究局）；Bioinformatics Institute, Agency for Science, Technology and Research (A*STAR)（新加坡科技研究局生物信息学研究所）；Institute of High Performance Computing (IHPC), Agency for Science, Technology and Research (A*STAR)（新加坡科技研究局高性能计算研究所）；National Institute of Education, Nanyang Technological University（南洋理工大学国立教育学院）；Quantum Science and Engineering Centre (QSec), Nanyang Technological University（南洋理工大学量子科学与工程中心）；Department of Physics, National University of Singapore（新加坡国立大学物理系）
Dissipation driven boundary localization in higher order topological insulators
Center for Advanced Quantum Studies, School of Physics and Astronomy, Beijing Normal University（北京师范大学物理与天文学院量子前沿研究中心）；Key Laboratory of Multiscale Spin Physics (Ministry of Education), Beijing Normal University（北京师范大学多尺度自旋物理教育部重点实验室）
Higher-Order Topological Systems and Their Sub-Symmetry-Protected Topology
Hanyang University（汉阳大学）；Institute for Basic Science (IBS)（基础科学研究院）；Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau（莱茵兰-普法尔茨技术大学凯泽斯劳滕-兰道）
