Novel family of topological semimetals with butterflylike nodal lines

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 ${\mathrm{Al}}₂{\mathrm{Y}}₃$.