Spin-Orbit Interaction Effects in the Electronic Structure of B20-type CoSi: First-Principles Density Functional Study

We have performed fully relativistic first-principles density functional calculations for non-magnetic B20-type CoSi. The spin-orbit interaction has crucial effects on the electronic structures of a chiral crystal. The calculated band structure around the Fermi energy shows Bloch vector $k$-linear dispersion expressed by a $real$-$spin$ Weyl Hamiltonian, i.e., a mass-less Dirac Hamiltonian. We found the hedgehog-like spin texture in Bloch $\mathit{k}$-vector space (momentum space) on the isoenergy surface around the $\mathrm{\Gamma }$ point. The Fermi velocity for $k$-linear dispersion is about 0.22$v_F^g$, where $v_F^g$ is the Fermi velocity of graphene.