Glide Symmetry Protected Higher-Order Topological Insulators from Semimetals with butterfly-like Nodal Lines

We propose a new family of topological semimetals (TSMs) which harbors an unprecedented nodal line (NL) landscape consisting of a pair of concentric intersecting coplanar ellipses (CICE). We identify the generic criteria for the existence of the CICE in a time reversal invariant spinless fermion system with negligible spin-orbital coupling (SOC). Consequently, 9 out of 230 space groups (SGs) are feasible for hosting CICE whose location centers in the Brillouin zone (BZ) are identified. We provide a simplest model with SG Pbam which exhibits CICE, and the exotic intertwined drumhead surface states. Then, we unveil the intrinsic link between this exotic class of nodal-line semimetals (NLSMs) and a Z4 = 2 topological crystalline insulator (TCI), by including substantial SOC. This TCI supports in turn a double-hourglass fermion on the (001) surface protected by two glide mirror symmetries, which originates from the intertwined drumhead surface states (DSSs) of the CICE NLs. The higher order topology is further demonstrated for the first time by the emergence of one-dimensional (1D) helical hinge states protected by a glide symmetry.

Zhou, X. et al. arXiv:2005.04360 (2020).
Zhou, X. et al. arXiv:2005.06071 (2020).