Quantitative measure of topological protection in Floquet systems through the spectral localizer
Center for Integrated Nanotechnologies, Sandia National Laboratories（桑迪亚国家实验室集成纳米技术研究中心）；Department of Mathematics, University of Colorado, Colorado Springs（科罗拉多大学科罗拉多斯普林斯分校数学系）
The standard understanding of topological protection from band theory is that a system's topology cannot change without first closing the bulk band gap. However, in Floquet systems, this typical definition of topological protection is one step removed from the experimentally accessible system parameters, as the relationship between the disorder in a system's instantaneous Hamiltonian and its Floquet Hamiltonian that defines its topology is not straightforward. Here, we demonstrate that the spectral localizer framework for classifying material topology can be applied to Floquet systems and prove that its associated measure of topological protection can be understood in terms of the integrated disorder across the system's instantaneous Hamiltonians. As such, we have derived a quantitative bound on a Floquet system's topological protection in terms of the instantaneous system. Moreover, we show the utility of these bounds in both ordinary an anomalous Floquet Chern insulators.
Time-resolved topology of aperiodically driven systems
University of Colorado, Colorado Springs（科罗拉多大学科罗拉多斯普林斯分校）；RPTU University Kaiserslautern-Landau（凯泽斯劳滕-兰道理工科技大学）；University of New Mexico（新墨西哥大学）；Sandia National Laboratories（桑迪亚国家实验室）
Robust Unidirectional Edge States in the Continuum in non-Topological Floquet Photonic Crystals
School of Physics, Beijing Institute of Technology（北京理工大学物理学院）；MOE & Guangxi Key Laboratory of Processing for Non-Ferrous Metals and Featured Materials, School of Physical Science and Technology, Guangxi University（广西大学物理科学与技术学院、有色金属及特色材料加工教育部与广西重点实验室）
Efficient local classification of parity-based material topology
Center for Integrated Nanotechnologies, Sandia National Laboratories（桑迪亚国家实验室集成纳米技术研究中心）；Center for Computing Research, Sandia National Laboratories（桑迪亚国家实验室计算研究中心）；Computational Mathematics Group, Scientific Computing Department, Rutherford Appleton Laboratory（拉瑟福德·阿普尔顿实验室科学计算部计算数学组）；Department of Mathematics and Statistics, University of New Mexico（新墨西哥大学数学与统计系）
