# From Nodal Chain Semimetal To Weyl Semimetal in HfC

## TL;DR

This paper predicts that HfC can transition from a nodal chain semimetal to a Weyl semimetal with 30 pairs of Weyl points upon including spin-orbit coupling, supported by first-principles calculations and surface state analysis.

## Contribution

It demonstrates a new material, HfC, hosting a nodal chain that evolves into Weyl points due to spin-orbit coupling, differing from previous materials like IrF4.

## Key findings

- HfC hosts a nodal chain semimetal state without SOC.
- SOC induces 30 pairs of Weyl points in HfC.
- Surface states and Fermi arcs are characterized for experimental verification.

## Abstract

Based on first-principles calculations and effective model analysis, we propose that the WC-type HfC, in the absence of spin-orbit coupling (SOC), can host a three-dimensional nodal chain semimetal state. Distinguished from the previous material IrF4 [T. Bzdusek et al., Nature 538, 75 (2016)], the nodal chain here is protected by mirror reflection symmetries of a simple space group, while in IrF4 the nonsymmorphic space group with a glide plane is a necessity. Moreover, in the presence of SOC, the nodal chain in WC type HfC evolves into Weyl points. In the Brillouin zone, a total of 30 pairs of Weyl points in three types are obtained through the first-principles calculations. Besides, the surface states and the pattern of the surface Fermi arcs connecting these Weyl points are studied, which may be measured by future experiments.