标题： 高阶拓扑偶性异常和高维合成晶格中的半整数量子霍尔效应 显示英文标题

标题： Higher-order Topological Parity Anomaly and Half-integer Hall Effect in High-dimensional Synthetic Lattices

摘要： 近期在构建合成维度方面的进展提供了一种强大的工具，用于探索高维物质的奇异拓扑态。 这里我们报告，在2$j$+1（时空）维度中，单个或奇数个狄拉克锥的存在下，由奇数性异常和相关的\textit{半整数}量子化霍尔电导率可以由（2$j$+$n$）维合成晶格中的第$n$阶拓扑绝缘体的边界态实现。 我们通过将“嵌套”威尔逊环理论与时间反演极化相结合，建立了普遍的体-边界对应关系，在高度对称的动量点上，提取出一组$Z_2$拓扑不变量，这些不变量决定了更高阶边界狄拉克锥的数量及其位置。 我们开发了一种支持这种更高阶拓扑奇数性异常的哈密顿量的一般构造程序。 此外，我们提出了一种基于光子合成维度的实验实施方案，并提供了一种通过传输谱探测相关半整数量子霍尔电导的方法。 我们的工作提供了对一般高维更高阶拓扑绝缘体中奇数性异常的实现和表征，并为探索由操控狄拉克锥所开启的基本物理现象和可能的器件应用开辟了途径。 显示英文摘要

摘要： Recent advances in constructing synthetic dimension provide a powerful tool for exploring exotic topological states of matter in high dimensions. Here we report that the parity anomaly and associated \textit{half-integer} quantized Hall conductance, arising in 2$j$+1 (space-time) dimensions with a single or odd number of Dirac cones, can be realized by the boundary states of $n$-th order topological insulators in (2$j$+$n$)-dimensional synthetic lattices. We establish a general bulk-boundary correspondence by integrating the ``nested" Wilson loop theory with the time-reversal polarization at highly-symmetric momenta, a set of $Z_2$ topological invariants are extracted which determines the number of higher-order-boundary Dirac cones and their locations. We develop a general construction procedure for Hamiltonians supporting such higher-order topological parity anomaly. Moreover, we propose an experimental implementation scheme based on photonic synthetic dimensions and provide a method for probing the associated half-integer Hall conductance by the transmission spectra. Our work offers the realization and characterization of parity anomaly in general high-dimensional higher-order topological insulators and opens an avenue for exploring fundamental physics and possible device applications enabled by manipulating Dirac cones.