Topological Dirac nodal-net fermions in AlB2-type TiB2 and ZrB2

Based on first-principles calculations and effective model analysis, a Dirac nodal-net semimetal state is recognized in AlB2-type TiB2 and ZrB2 when spin-orbit coupling (SOC) is ignored. Taking TiB2 as an example, several topological novel states have been found in this nodal-net structure including triple point, nexus, and nodal link, which are protected by the coexistence of spatial-inversion symmetry and time-reversal symmetry. In addition, linearly and quadratically dispersed two-dimensional surface Dirac points have been identified as getting on the B-terminated and Ti-terminated (001) surfaces of TiB2, respectively, which are analogous to those of monolayer and bilayer graphene.