Linear and nolinear optical responses of chiral multifold semimetals

The chiral topological semimetals RhSi and CoSi exhibit band degeneracies near the Fermi level enforced by the crystal symmetries. The low-energy quasiparticles emerging near these band degeneracies, referred to as multifold fermions, have no counterpart as elementary fermionic particles. We calculate 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 [4]. 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.