In a Kondo lattice, the spin exchange coupling between a local spin and the conduction electrons acquires nonlocal contributions due to conduction electron scattering from surrounding local spins and the subsequent RKKY interaction. It leads to a hitherto unrecognized interference of Kondo screening and the RKKY interaction beyond the Doniach scenario. We develop a renormalization group theory for the RKKY-modified Kondo vertex. The Kondo temperature T_{K}(y) is suppressed in a universal way, controlled by the dimensionless RKKY coupling parameter y. Complete spin screening ceases to exist beyond a critical RKKY strength y_{c} even in the absence of magnetic ordering. At this breakdown point, T_{K}(y) remains nonzero and is not defined for larger RKKY couplings y>y_{c}. The results are in quantitative agreement with STM spectroscopy experiments on tunable two-impurity Kondo systems. The possible implications for quantum critical scenarios in heavy-fermion systems are discussed.

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Dedicated to Ulrich Eckern on the occasion of his 60th birthday.A three-level system with partially broken SU(3) symmetry immersed in a metal, comprised of a unique noninteracting ground state and two-fold degenerate excited states, exhibits a stable two-channel Kondo fixed point within a wide range of parameters, as has been shown in previous work. Such systems can, for instance, be realized by protons dissolved in a metal and bound in the interstitial space of the host lattice, where the degeneracy of excited rotational states is guaranteed by the space inversion symmetry of the lattice. We analyze the robustness of the 2CK fixed point with respect to a level splitting of the excited states and discuss how this may explain the behavior of the well-known dI/dV spectra measured by Ralph and Buhrman on ultrasmall quantum point contacts in a magnetic field.

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