Dual topological nodal line and nonsymmorphic Dirac semimetal in three dimensions

There are two types of previously known three-dimensional Dirac semimetals (DSs) - topological DSs and nonsymmorphic DSs. Here, we present a three-dimensional DS that exhibits features of both topological and nonsymmorphic DSs. We introduce a minimal tight-binding model for the space group 100 that describes a layered crystal made of two-dimensional planes in the p4g wallpaper group. Using this model, we demonstrate that double glide mirrors allow a noncentrosymmetric three-dimensional DS that hosts both symmetry-enforced Dirac points at time-reversal invariant momenta and twofold-degenerate Weyl nodal lines on a glide-mirror-invariant plane in momentum space. The proposed DS allows for rich topological physics manifested in both topological surface states and topological phase diagrams, which we discuss in detail. We also perform first-principles calculations to predict that the proposed DS is realized in a set of existing materials BaLaXBY5, where X=Cu or Au, and Y=O, S, or Se.