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

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 $k.p$ 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.

6 pages, 4 figures; Published in Phys. Rev. Materials (R)