Fingerprints of multifold fermions in optics: linear and nonlinear optical responses of CoSi and RhSi

The 230 space groups, of which only 65 are chiral, describe all possible combinations of non-magnetic crystal symmetries in nature. Materials described by some of these groups host band degeneracies near the Fermi level protected by the corresponding crystal symmetries. A remarkable example of materials exhibiting this type of degeneracies are the topological semimetals RhSi and CoSi. The low-energy quasiparticles emerging near the protected band degeneracies, referred to as multifold fermions, have no counterpart as elementary fermionic particles. We present in this talk the linear optical conductivity of all chiral multifold fermions[1] and show that it provides an experimental fingerprint for each type of multifold fermion. We use a tight-binding model for space group 198, where RhSi and CoSi crystallize, revealing that the location of the chemical potential is crucial to understand the optical response seen in experiments[2,3], determined at low energies by the threefold fermion at the Γ point in both materials, and providing signatures of the existence of a spin-3/2 fourfold fermion in CoSi. Finally, we study the second-harmonic generation of RhSi. We analyze the experimental results using a second-order k·p Hamiltonian and compare our results with density functional theory calculations to provide a comprehensive description of the origin of the different features in the second-harmonic response and their relation to the topological character of the bands in RhSi.