  The breakdown of the lattice Kondo effect in local-moment metals can lead to
non-trivial forms of quantum criticality and a variety of non-Fermi-liquid
phases. Given indications that Kondo-breakdown transitions involve criticality
not only in the spin but also in the charge sector, we investigate the
interplay of Kondo breakdown and strong valence fluctuations in generalized
Anderson lattice models. We employ a parton mean-field theory to describe the
transitions between deconfined fractionalized Fermi liquids and various
confined phases. We find that rapid valence changes near Kondo breakdown can
render the quantum transition first order. This leads to phase-separation
tendencies which, upon inclusion of longer-range Coulomb interactions, will
produce intrinsically inhomogeneous states near Kondo-breakdown transitions. We
connect our findings to unsolved aspects of experimental data.
