MnGa

Topological semimetals can be classified by the connectivity and dimensionality of the band crossing in momentum space. The band crossings of a Dirac, Weyl, or an unconventional fermion semimetal are 0D points, whereas the band crossings of a nodal-line semimetal are 1D closed loops. Here we propose that the presence of perpendicular crystalline mirror planes can protect 3D band crossings characterized by nontrivial links such as a Hopf link or a coupled-chain, giving rise to a variety of new types of topological semimetals. We show that the nontrivial winding number protects topological surface states distinct from those in previously known topological semimetals. We also show that these nontrivial links can be engineered by tuning the mirror eigenvalues associated with the perpendicular mirror planes. Using first-principles band structure calculations, we predict the ferromagnetic full Heusler compound Co₂MnGa as a candidate. Both Hopf link and chain-like bulk band crossings and unconventional topological surface states are identified.