Weyl points (WPs), nodal degenerate points in three-dimensional (3D) momentum space, are said to be ‘ideal’ if they are symmetry-related and well-separated, and reside at the same energy and far from nontopological bands. Although type-II WPs have unique spectral characteristics compared with type-I counterparts, ideal type-II WPs have not yet been reported because of a lack of an experimental platform with enough flexibility to produce strongly tilted dispersion bands. Here, we experimentally realize a topological circuit that hosts only topological bands with a minimal number of four ideal type-II WPs. By stacking two-dimensional (2D) layers of inductor-capacitor (LC) resonator dimers with the broken parity inversion symmetry (P), we achieve a strongly tilted band structure with two group velocities in the same direction, and topological surface states in an incomplete bandgap. Our results establish an ideal system for the further study of Weyl physics and other exotic topological phenomena.

中文翻译：

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拓扑电路中的理想 II 型韦尔点


外尔点 (WP) 是三维 (3D) 动量空间中的节点简并点，如果它们对称相关且分离良好，且处于相同能量且远离非拓扑能带，则称其为“理想”点。尽管与I型WP相比，II型WP具有独特的光谱特性，但由于缺乏足够灵活的实验平台来产生强烈倾斜的色散带，理想的II型WP尚未见报道。在这里，我们通过实验实现了一个拓扑电路，该电路仅承载具有最少数量的四个理想 II 型 WP 的拓扑带。通过堆叠具有破缺奇偶校验反转对称性 ( P ) 的电感电容 ( LC ) 谐振器二聚体的二维 (2D) 层，我们实现了强倾斜能带结构，其中两个群速度方向相同，并且拓扑表面态处于带隙不完整。我们的结果为进一步研究外尔物理和其他奇异的拓扑现象建立了一个理想的系统。