非平凡节点环在含自旋的Rice-Mele链中出现
Exceptional nodal rings emerging in spinful Rice-Mele chains
AI总结：
研究发现含自旋的Rice-Mele链中耗散导致节点环分裂为两个例外环，揭示了拓扑结构的物理图像，并提出了一种低维系统中测量拓扑不变量的方法。
摘要：
Weyl例外节点线通常出现在三维拓扑半金属中，但也出现在一维系统的参数空间中。在本工作中，我们研究了在三维拓扑半金属中耗散对节点环的影响。我们发现，在存在耗散的情况下，能量谱变得完全复数，原来的节点环被分裂成两个例外环。我们引入了一个由谱生成的动量空间中的涡流场，以表征例外环的拓扑性质。这提供了拓扑结构的清晰物理图像。这两个例外环作为自由涡流中的两个相反旋向的涡流线。在此背景下，三维拓扑半金属是两个由例外环配置确定的量子相之间的边界。我们还提出了一种一维模型，其在参数空间中具有相同的拓扑特征。它提供了一种在低维系统中测量拓扑不变量的简便方法。数值模拟表明，拓扑不变量在系统参数的随机扰动下是稳健的。
英文摘要：
The Weyl exceptional nodal lines usually occur in 3D topological semimetals, but also emerge in the parameter space of 1D systems. In this work, we study the impact of dissipation on the nodal ring in a 3D topological semimetal. We find that the energy spectrum becomes fully complex in the presence of dissipation, and the original nodal ring is split into two exceptional rings. We introduce a vortex field in the momentum space, which is generated from the spectrum, to characterize the topology of the exceptional rings. This provides a clear physical picture of the topological structure. The two exceptional rings act as two vortex filaments of a free vortex flow with opposite circulations. In this context, the 3D topological semimetal is the boundary separating two quantum phases identified by two configurations of exceptional rings. We also propose a 1D model that has the same topological feature in the parameter space. It provides a simple way to measure the topological invariant in a low-dimensional system. Numerical simulations indicate that the topological invariant is robust under the random perturbations of the system parameters.
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