# Prediction of three-fold fermions in a nearly-ideal Dirac semimetal BaAgAs

## TL;DR

This paper predicts and analyzes a silver-based Dirac semimetal, BaAgAs, which hosts three-fold fermions and can transition between different topological phases, providing a platform for exploring novel fermionic excitations.

## Contribution

The study demonstrates how BaAgAs realizes three-fold fermions and transitions into a nearly-ideal Dirac semimetal, revealing tunable topological phases through first-principles calculations and symmetry analysis.

## Key findings

- BaAgAs hosts triply-degenerate nodal points protected by crystal symmetry.
- Turning on spin-orbit coupling creates a nearly-ideal Dirac semimetal with Dirac nodes.
- Breaking inversion symmetry in BaAgAs$_{1-x}$P$_x$ yields a tunable three-fold fermion semimetal.

## Abstract

Materials with triply-degenerate nodal points in their low-energy electronic spectrum produce crystalline-symmetry-enforced three-fold fermions, which conceptually lie between the two-fold Weyl and four-fold Dirac fermions. Here we show how a silver-based Dirac semimetal BaAgAs realizes three-fold fermions through our first-principles calculations combined with a low-energy effective $\mathbf{k.p}$ model Hamiltonian analysis. BaAgAs is shown to harbor triply-degenerate nodal points, which lie on its $C_{3}$ rotation axis, and are protected by the $C_{6v}$($C_2\otimes C_{3v}$) point-group symmetry in the absence of spin-orbit coupling (SOC) effects. When the SOC is turned on, BaAgAs transitions into a nearly-ideal Dirac semimetal state with a pair of Dirac nodes lying on the $C_{3}$ rotation axis. We show that breaking inversion symmetry in the BaAgAs$_{1-x}$P$_x$ alloy yields a clean and tunable three-fold fermion semimetal. Systematic relaxation of other symmetries in BaAgAs generates a series of other topological phases. BaAgAs materials thus provide an ideal platform for exploring tunable topological properties associated with a variety of different fermionic excitations.