Weyl-Dirac nodal line phonons with type-selective surface states

TL;DR

This paper introduces a group theory-based scheme to identify Weyl-Dirac nodal line phonons in select space groups, revealing unique surface states and topological features in specific materials, advancing the understanding of complex topological phononic systems.

Contribution

It presents a rapid identification method for Weyl-Dirac nodal lines in bosonic systems and uncovers their unique surface state properties and material realizations.

Findings

Only 5 of 230 space groups host these nodal lines.

Weyl and Dirac nodal lines form a composite network with distinct surface states.

Materials NdRhO₃ and ZnSe₂O₅ are identified as candidates with these features.

Abstract

The band complex formed by multiple topological states has attracted extensive attention for the emergent properties produced by the interplay among the constituent states. Here, based on group theory analysis, we present a scheme for rapidly identifying the Weyl-Dirac nodal lines (a complex of Weyl and Dirac nodal lines) in bosonic systems. We find only 5 of the 230 space groups host Weyl-Dirac nodal line phonons. Notably, the Dirac nodal line resides along the high-symmetry line, whereas the Weyl nodal line is distributed on the high-symmetry plane and is interconnected with the Dirac nodal line, jointly forming a composite nodal network structure. Unlike traditional nodal nets, this nodal network exhibits markedly distinct surface states on different surfaces, which can be attributed to the fundamental differences in the topological properties between the Weyl and Dirac nodal lines. This unique property thus allows the material to present distinct surface states in a termination-selective manner. Furthermore, by first-principles calculations, we identify the materials NdRhO$_{3}$ and ZnSe$_{2}$O$_{5}$ as candidate examples to elaborate the Weyl-Dirac nodal line and their related topological features. Our work provides an insight for exploring and leveraging topological properties in systems with coexisting multiple topological states.