Kondo effect in "bad metals"

We study the low-temperature properties of a Kondo lattice using the large-N formalism. For a singular density of conduction states (DOS), we generalize the single-impurity result of Withoff and Fradkin: the strong-coupling fixed point becomes irrelevant if the DOS vanishes at the Fermi level E_F. However, for E_F close enough to the singularity, and close to half-filling, the Kondo temperature, $T_K$, can become much smaller than the characteristic Fermi liquid scale. At T=0, a meta-magnetic transition occurs at the critical magnetic field H_c ~ (k_B/mu_B) T_K. Our results provide a qualitative explanation for the behavior of the YbInCu_4 compound below the valence-change transition.