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Using first-principles calculations, we report that ZrO is a topologicalmaterial with the coexistence of three pairs of type-II triply degenerate nodalpoints (TNPs) and three nodal rings (NRs), when spin-orbit coupling (SOC) isignored. Noticeably, the TNPs reside around Fermi energy with large linearenergy range along tilt direction (> 1 eV) and the NRs are formed by threestrongly entangled bands. Under symmetry-preserving strain, each NR wouldevolve into four droplet-shaped NRs before fading away, producing distinctevolution compared with that in usual two-band NR. When SOC is included, TNPswould transform into type-II Dirac points while all the NRs have gaped.Remarkably, the type-II Dirac points inherit the advantages of TNPs: residingaround Fermi energy and exhibiting large linear energy range. Both featuresfacilitate the observation of interesting phenomena induced by type-IIdispersion. The symmetry protections and low-energy Hamiltonian for thenontrivial band crossings are discussed.

From Type-II Triply Degenerate Nodal Points and Three-Band Nodal Rings to Type-II Dirac Points in Centrosymmetric Zirconium Oxide