# Topological Dirac Nodal-net Fermions in AlB$_2$-type TiB$_2$ and ZrB$_2$

## TL;DR

This paper predicts a topological Dirac nodal-net semimetal state in TiB₂ and ZrB₂ using first-principles calculations, revealing unique topological features and surface states protected by symmetries.

## Contribution

It identifies a novel Dirac nodal-net semimetal state in TiB₂ and ZrB₂, with detailed analysis of topological excitations and surface Dirac points, expanding understanding of topological semimetals.

## Key findings

- Nodal-net state in TiB₂ and ZrB₂ identified without SOC
- Presence of triple point, nexus, and nodal link topological excitations
- Surface Dirac points analogous to graphene on TiB₂ surfaces

## Abstract

Based on first-principles calculations and effective model analysis, a Dirac nodal-net semimetal state is recognized in AlB$_2$-type TiB$_2$ and ZrB$_2$ when spin-orbit coupling (SOC) is ignored. Taking TiB$_2$ as an example, there are several topological excitations in this nodal-net structure including triple point, nexus, and nodal link, which are protected by coexistence of spatial-inversion symmetry and time reversal symmetry. This nodal-net state is remarkably different from that of IrF$_4$, which requires sublattice chiral symmetry. In addition, linearly and quadratically dispersed two-dimensional surface Dirac points are identified as having emerged on the B-terminated and Ti-terminated (001) surfaces of TiB$_2$ respectively, which are analogous to those of monolayer and bilayer graphene.