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

TL;DR

This study predicts ZrO as a topological material hosting coexisting type-II triply degenerate nodal points and nodal rings, which evolve under strain and spin-orbit coupling, leading to observable phenomena related to type-II Dirac points.

Contribution

It reveals the topological features of ZrO, including the evolution of nodal rings into Dirac points under SOC and strain, providing new insights into topological semimetals.

Findings

ZrO hosts three pairs of type-II triply degenerate nodal points and nodal rings.

Strain causes nodal rings to evolve into droplet-shaped rings.

Including SOC transforms TNPs into type-II Dirac points with gapped NRs.

Abstract

Using first-principles calculations, we report that ZrO is a topological material with the coexistence of three pairs of type-II triply degenerate nodal points (TNPs) and three nodal rings (NRs), when spin-orbit coupling (SOC) is ignored. Noticeably, the TNPs reside around Fermi energy with large linear energy range along tilt direction (> 1 eV) and the NRs are formed by three strongly entangled bands. Under symmetry-preserving strain, each NR would evolve into four droplet-shaped NRs before fading away, producing distinct evolution compared with that in usual two-band NR. When SOC is included, TNPs would transform into type-II Dirac points while all the NRs have gaped. Remarkably, the type-II Dirac points inherit the advantages of TNPs: residing around Fermi energy and exhibiting large linear energy range. Both features facilitate the observation of interesting phenomena induced by type-II dispersion. The symmetry protections and low-energy Hamiltonian for the nontrivial band crossings are discussed.