Kondo effect under arbitrary spin-momentum locking

The Kondo effect originates from the spin exchange scattering of itinerant electrons with a localized magnetic impurity. Here, we consider generalization of Weyl-type electrons with their spin locked on a spherical Fermi surface in an arbitrary way and study how such spin-momentum locking affects the Kondo effect. After introducing a suitable model Hamiltonian, a simple formula for the Kondo temperature is derived with the second-order perturbation theory, which proves to depend only on the spin averaged over the Fermi surface. In particular, the Kondo temperature is unaffected as long as the average spin vanishes, but decreases as the average spin increases in its magnitude, and eventually vanishes when the spin is completely polarized on the Fermi surface, illuminating the role of spin-momentum locking in the Kondo effect.