Analysis of Dirac exceptional points and their isospectral Hermitian counterparts
Analysis of Dirac exceptional points and their isospectral Hermitian counterparts
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DOI：
10.1103/physrevb.107.104106
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发表时间：
2023-03
影响因子：
3.7
通讯作者：
J. H. Rivero;Liang Feng;L. Ge
中科院分区：
文献类型：
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作者：
J. H. Rivero;Liang Feng;L. Ge
最近，在非厄米系统中报道了狄拉克例外点（EP）。与埃尔米特系统中的狄拉克点不同，该狄拉克 EP 除了简并能量之外还合并了本征态。与典型的 EP 不同的是，该狄拉克 EP 处连接的两个能级在其附近保持真实，并显示线性而不是平方根色散，在混合空间中形成倾斜的狄拉克锥，该混合空间由动量维度和非厄米性强度的合成维度组成。在本报告中，我们首先提出了带有狄拉克 EP 的简单三带和两带矩阵模型，其中可以解析地表达倾斜狄拉克锥体的线性色散。重要的是，我们的分析还表明存在埃尔米特和非埃尔米特系统，它们在整个参数空间中具有相同的（实值）能谱，除了前者中的一个或多个简并被后者中的狄拉克 EP 取代。最后，我们证明存在一个假想的狄拉克锥，其中心有一个 EP。
Recently, a Dirac exceptional point (EP) was reported in a non-Hermitian system. Unlike a Dirac point in Hermitian systems, this Dirac EP has coalesced eigenstates in addition to the degenerate energy. Also different from a typical EP, the two energy levels connected at this Dirac EP remain real in its vicinity and display a linear instead of square root dispersion, forming a tilted Dirac cone in the hybrid space consisting of a momentum dimension and a synthetic dimension for the strength of non-Hermiticity. In this report, we first present simple three-band and two-band matrix models with a Dirac EP, where the linear dispersion of the tilted Dirac cone can be expressed analytically. Importantly, our analysis also reveals that there exist Hermitian and non-Hermitian systems that have the same (real-valued) energy spectrum in their entire parameter space, with the exception that one or more degeneracies in the former are replaced by Dirac EPs in the later. Finally, we show the existence of an imaginary Dirac cone with an EP at its center.