广义本征值方程的能带结构与圆锥曲线
Band structures of generalized eigenvalue equation and conic section
AI总结：
本文利用辅助本征值从几何角度解释广义本征值方程能带的实-复转变，揭示其与电子系统Lifshitz转变及两类Dirac锥费米面的对应关系，并阐明光子系统中EP由材料参数频率依赖性诱导。
摘要：
若干超材料的能带结构由广义本征值方程描述，即使涉及的矩阵为厄米矩阵，也会出现复能带。本文对能带结构的实-复转变提供了一种几何理解。具体而言，我们基于辅助本征值的分析阐明了广义本征值方程的实-复转变与电子系统中Lifshitz转变之间的对应关系。此外，我们阐明，当介电常数$\varepsilon$和磁导率$μ$与频率无关时，光子系统的实（复）能带对应于电子系统中第二类（第一类）Dirac锥的费米面。另外，我们的分析阐明，在我们的光子系统中，EP是由介电常数$\varepsilon$和磁导率$μ$的频率依赖性所诱导的。
英文摘要：
Band structures of several metamaterials are described by generalized eigenvalue equations where complex bands emerge even if the involved matrices are Hermitian. In this paper, we provide a geometrical understanding of the real-complex transition of the band structures. Specifically, our analysis, based on auxiliary eigenvalues, elucidates the correspondence between the real-complex transition of the generalized eigenvalue equations and Lifshitz transition in electron systems. Furthermore, we elucidate that real (complex) bands of a photonic system correspond to the Fermi surfaces of type-II (type-I) Dirac cones in electron systems when the permittivity $\varepsilon$ and the permeability $μ$ are independent of frequency. In addition, our analysis elucidates that EPs are induced by the frequency dependence of the permittivity $\varepsilon$ and the permeability $μ$ in our photonic system.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
