Quenching of overcompensated Kondo impurities via channel asymmetry

We consider a spin-1/2 impurity interacting with conduction electrons in two different orbital channels via an isotropic spin exchange. The exchange is the same for both channels, but a crystalline field breaks the symmetry between the orbital channels. This corresponds to a splitting of the conduction electron Γ₈ into two doublets in the quadrupolar Kondo effect and to the application of an external magnetic field in the electron assisted tunneling of an atom in a double-well potential. We study the ground-state properties of the impurity as a function of the magnetic and crystalline fields. The crystalline field quenches the critical behavior of the overcompensated fixed point: The impurity ground state is a singlet.