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Topological semimetals can be classified by the connectivity anddimensionality of the band cross- ing in momentum space. The band crossings ofa Dirac, Weyl, or an unconventional fermion semimet- al are 0D points, whereasthe band crossings of a nodal-line semimetal are 1D closed loops. Here wepropose that the presence of perpendicular crystalline mirror planes canprotect 3D band crossings characterized by nontrivial links such as a Hopf linkor a coupled-chain, giving rise to a variety of new types of topologicalsemimetals. We show that the nontrivial winding number protects topolog- icalsurface states distinct from those in previously known topological semimetalswith a vanishing spin-orbit interaction. We also show that these nontriviallinks can be engineered by tuning the mirror eigenvalues associated with theperpendicular mirror planes. Using first-principles band structurecalculations, we predict the ferromagnetic full Heusler compound Co2MnGa as acandidate. Both Hopf link and chain-like bulk band crossings and unconventionaltopological surface states are identified.

Topological Hopf and chain link semimetal states and their application to Co2MnGa (Theory and Materials Prediction)