# Topological semimetal phases manifested in transition metal dichalcogenides intercalated with 3d metals

## TL;DR

This study identifies stable topological semimetal phases in 3d metal-intercalated transition metal dichalcogenides through ab initio calculations, revealing Weyl semimetals with unique electronic properties suitable for condensed matter research.

## Contribution

It introduces a new class of topological semimetals in 3d metal-intercalated TMDs, characterized by twelve Weyl nodes and distinct magnetic and nonmagnetic phases, expanding the material platform for topological physics.

## Key findings

- Identified Weyl semimetals with twelve Weyl nodes in 3dI-TMDCs.
- VNb3S6 is half-metallic with two bands crossing at the Fermi level.
- MnNb3S6 exhibits a quasi-nodal-line degeneracy with minimal gap.

## Abstract

In the search for stable topological semimetals with clean band profiles, we have screened all the 3$d$ metal-intercalated transition-metal dichalcogenides (3dI-TMDCs) by performing hybrid-functional-based ab initio calculations. Two classes of topological materials featuring twelve Weyl nodes in the $k_z=0$ plane (without spin-orbit interactions) are identified: (a) time-reversal-breaking Weyl semimetals VT$_3$X$_6$ (ferromagnetic) and (b) spinless Weyl semimetals MnT$_3$X$_6$ (nonmagnetic), where T=Nb, Ta; X=S, Se. VNb$_3$S$_6$, prototypical of class (a), is half-metallic with only two bands crossing at the Fermi level to form Weyl nodes. MnNb$_3$S$_6$ in the nonmagnetic phase is essentially a spinless version of VNb$_3$S$_6$ featuring an equally clean and simple band profile. Although the space group symmetry (P6$_3$22) implies that the degeneracy between the two bands is lifted for $k$ away from the Weyl nodes, the gap remains extremely small ($\ll$ 0.1 meV) along a loop connecting the Weyl nodes. This quasi-nodal-line degeneracy is explained in terms of the quasi-mirror symmetry of the lattice, induced by the in-plane twofold rotation axes, and the specific orbital nature of the bands. 3dI-TMDCs are chemically and thermally stable stoichiometric compounds containing no toxic elements and are a viable platform for the study of topological condensed-matter physics.