In recent years, the exotic properties of topological semimetals (TSMs) have attracted great attention and significant efforts have been made in seeking new topological phases and material realization. In this work, we propose a family of TSMs which harbors an unprecedented nodal line (NL) landscape consisting of a pair of concentric intersecting coplanar ellipses (CICEs) at half-filling. Meanwhile, the CICE at half-filling guarantees the presence of a second pair of CICEs beyond half-filling. Both CICEs are linked at fourfold degenerate points at zone boundaries. In addition, we identify the generic criteria for the existence of the CICE in a time-reversal-invariant spinless fermion system or a spinful system with negligible spin-orbital coupling. Consequently, 9 out of 230 space groups (SGs) are feasible for hosting CICEs whose location centers in the first Brillouin zone (BZ) are identified. We provide a simple model with SG $Pbam$ (No. 55) which exhibits CICEs, and the exotic intertwined drumhead surface states, induced by double band inversions. Finally, we propose a series of material candidates that host butterflylike CICE NLs, such as $\text{Zr}{X}_2$ ($X=\text{P}$, As), ${\mathrm{Tl}}_2{\mathrm{GeTe}}_5, {\mathrm{CYB}}_2$, and ${\mathrm{Al}}_2{\mathrm{Y}}_3$.

中文翻译：

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具有蝴蝶状节点线的新型拓扑半金属族

近年来，拓扑半金属（TSMs）的奇异性质引起了人们的极大关注，并在寻求新的拓扑相和材料实现方面做出了重大努力。在这项工作中，我们提出了一个 TSM 家族，它包含一个前所未有的节点线 (NL) 景观，由一对半填充的同心相交共面椭圆 (CICE) 组成。同时，半填充时的 CICE 保证了半填充后的第二对 CICE 的存在。两个 CICE 都在区域边界的四重退化点连接。此外，我们确定了在时间反转不变的无旋转中 CICE 存在的通用标准费米子系统或自旋轨道耦合可忽略不计的自旋系统。因此，230 个空间组 (SG) 中有 9 个可用于托管其位置中心位于第一个布里渊区 (BZ) 的 CICE。我们提供了一个带有 SG 的简单模型$磷乙\mathrm{一种}米$(No. 55) 展示了 CICE，以及​​由双带反转引起的奇异的交织鼓面表面状态。最后，我们提出了一系列承载类似蝴蝶的 CICE NL 的候选材料，例如$\text{锆}{X}_2$ ($X=\text{磷}$， 作为）， ${\mathrm{时间}}_2{\mathrm{格特}}_5, {\mathrm{中青}}_2$， 和 ${铝}_2{\mathrm{是}}_3$.