标题： 一个例外曲面及其拓扑 显示英文标题

标题： An exceptional surface and its topology

摘要： 非厄米（NH）系统可以表现出没有厄米对应物的特殊拓扑缺陷，例如在NH二维系统中的特殊环。然而，与高维拓扑缺陷相关的特殊拓扑特征仍未被探索。我们在这里研究了NH三维系统中的奇点拓扑。我们发现参数空间中的三阶奇点形成一个特殊表面（ES），在该表面上所有三个本征态和本征能级都合并。这样的ES对应于点状合成张量单极子的二维扩展。我们通过Dixmier-Douady不变量量化其拓扑，该不变量测量与合成张量场相关的量子通量。我们进一步提出了一种实验上可行的方案来构建这样的NH模型。我们的结果为研究与多维拓扑缺陷相关的特殊拓扑提供了途径。 显示英文摘要

摘要： Non-Hermitian (NH) systems can display exceptional topological defects without Hermitian counterparts, exemplified by exceptional rings in NH two-dimensional systems. However, exceptional topological features associated with higher-dimension topological defects remain unexplored yet. We here investigate the topology for the singularities in an NH three-dimensional system. We find that the three-order singularities in the parameter space form an exceptional surface (ES), on which all the three eigenstates and eigenenergies coalesce. Such an ES corresponds to a two-dimensional extension of a point-like synthetic tensor monopole. We quantify its topology with the Dixmier-Douady invariant, which measures the quantized flux associated with the synthetic tensor field. We further propose an experimentally feasible scheme for engineering such an NH model. Our results pave the way for investigations of exceptional topology associated with topological defects with more than one dimension.