# Dual topological nodal line and nonsymmorphic Dirac semimetal in three dimensions

## TL;DR

This paper introduces a new three-dimensional Dirac semimetal that combines topological and nonsymmorphic features, demonstrated through a minimal model and first-principles calculations, revealing rich topological phenomena.

## Contribution

The study presents a novel 3D Dirac semimetal with combined topological and nonsymmorphic properties, supported by a minimal tight-binding model and material predictions.

## Key findings

- Discovery of a 3D Dirac semimetal with both features
- Identification of symmetry-enforced Dirac points and Weyl nodal lines
- Prediction of real materials exhibiting this semimetal

## Abstract

Previously known three-dimensional Dirac semimetals (DSs) occur in two types -- topological DSs and nonsymmorphic DSs. Here we present a novel three-dimensional DS that exhibits both features of the 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 BaLa$X$B$Y_5$, where $X$ = Cu or Au, and $Y$ = O, S, or Se.