论文标题
具有非富米边界条件的散装 - 热系统中的广义拓扑散装对应关系
Generalized topological bulk-edge correspondence in bulk-Hermitian continuous systems with non-Hermitian boundary conditions
论文作者
论文摘要
散装对应（BEC）是拓扑系统的标志。在具有无界波向量的连续（非局部）冬宫系统中，最近显示了Chern绝缘子的BEC。在非炎症系统中，如何进一步影响损失和/或收获？在这项工作中，我们通过研究具有非热边界条件的散装热系统，迈出了这一方向的第一步。在这种情况下，我们发现边缘模式在散射矩阵的根部出现，而不是在遗传下的情况下，它们在其杆子（或更准确地说，是根和杆的融合）上出现的。这需要对相对列文森定理进行非平凡的修改。然后，我们证明拓扑结构与赫尔米尔人的情况保持不变，并且普遍的BEC持有，前提是一个人在波形平面中采用了适当修改的轮廓，以便散射矩阵相绕组正确计数边缘模式。在存在奇特粘度的情况下，我们使用在浅海或活性系统中的波浪模型以及带有HALL粘度的2D电子气体来体现所有这些。我们利用这个机会来检查较大的奇数粘度的情况，在此散射矩阵变为$ 2 \ times2 $，这在先前关于Hermitian广义BEC的作品中尚未讨论。
The bulk-edge correspondence (BEC) is the hallmark of topological systems. In continuous (nonlattice) Hermitian systems with an unbounded wave vector, it was recently shown that the BEC of Chern insulators is modified. How would it be further affected in non-Hermitian systems, experiencing loss and/or gain? In this work, we take the first step in this direction, by studying a bulk-Hermitian continuous system with non-Hermitian boundary conditions. We find in this case that edge modes emerge at the roots of the scattering matrix, as opposed to the Hermitian case, where they emerge at its poles (or, more accurately, coalescence of roots and poles). This entails a nontrivial modification to the relative Levinson's theorem. We then show that the topological structure remains the same as in the Hermitian case, and the generalized BEC holds, provided one employs appropriately modified contours in the wave-vector plane so that the scattering matrix phase winding counts the edge modes correctly. We exemplify all this using a paradigmatic model of waves in a shallow ocean or active systems in the presence of odd viscosity, as well as 2D electron gas with Hall viscosity. We use this opportunity to examine the case of large odd viscosity, where the scattering matrix becomes $2\times2$, which has not been discussed in previous works on the Hermitian generalized BEC.
