The energy band attraction (EBA) caused by the nonorthogonal eigenvectors is a unique phenomenon in the non-Hermitian (NH) system. However, restricted by the required tight-binding approximation and meticulously engineered complex potentials, such an effect has never been experimentally demonstrated before. Here by a suitable design of all-dielectric Mie resonators in a parallel-plate transmission line, we for the first time verify the photonic analog of the EBA effects both theoretically and experimentally. The evolution of the EBA effect in a two-level NH system from gapped bands to gapless bands to flat bands is observed by precisely tuning the loss of the Mie resonators. The transmission spectra can be theoretically connected to the eigenvalues and eigenvectors of the NH Hamiltonian. Furthermore we extend our methods to a graphenelike two-dimensional NH system. Our works show a metamaterial approach toward NH topological photonics and foster a deeper understanding of band theory in open systems.

中文翻译：

---

非Hermitian系统中的能带吸引效应

由非正交特征向量引起的能带吸引（EBA）是非Hermitian（NH）系统中的一种独特现象。然而，受所需的紧密结合近似和精心设计的复杂电势的限制，这种效果以前从未在实验上得到证明。在这里，通过对平行板传输线中全电介质Mie谐振器的适当设计，我们首次在理论上和实验上验证了EBA效应的光子模拟。通过精确调节Mie谐振器的损耗，可以观察到两级NH系统中EBA效应从带隙带到无隙带到平坦带的演变。透射光谱在理论上可以与NH哈密顿量的特征值和特征向量相连。此外，我们将方法扩展到类似石墨烯的二维NH系统。我们的工作展示了一种用于NH拓扑光子学的超材料方法，并增进了对开放系统中能带理论的更深入的了解。