# Crossing-Line-Node Semimetals: General Theory and Application to Rare-Earth Trihydrides

## TL;DR

This paper develops a theoretical framework for classifying crossing-line-node semimetals with mirror symmetry, including effects of spin-orbit interaction, and applies it to rare-earth trihydrides to identify their topological phases.

## Contribution

It introduces a general classification scheme for crossing-line-node semimetals considering symmetry and spin-orbit effects, aiding material identification.

## Key findings

- Identifies crossing-line-node Dirac semimetal in rare-earth trihydrides
- Classifies topological phase transitions induced by spin-orbit interaction
- Provides a method to predict semimetal behavior from band structures without detailed calculations

## Abstract

Multiple line nodes in energy-band gaps are found in semimetals preserving mirror-reflection symmetry. We classify possible configurations of multiple line nodes with crossing points (crossing line nodes) under point-group symmetry. Taking the spin-orbit interaction (SOI) into account, we also classify topological phase transitions from crossing-line-node Dirac semimetals to other topological phases, e.g., topological insulators and point-node semimetals. This study enables one to find crossing-line-node semimetal materials and their behavior in the presence of SOI from the band structure in the absence of SOI without detailed calculations. As an example, the theory applies to hexagonal rare-earth trihydrides with the HoD3 structure and clarifies that it is a crossing-line-node Dirac semimetal hosting three line nodes.