  Local quantum phase transitions driven by Kondo correlations have been
theoretically proposed in several magnetic nanosystems; however, clear
experimental signatures are scant. Modeling a nickelocene molecule on a Cu(100)
substrate as a two-orbital Anderson impurity with single-ion easy-plane
anisotropy coupled to two conduction bands, we find that recent scanning
tunneling spectra measured at different microscope tip heights reveal the
existence of a topological quantum phase transition from the usual local Fermi
liquid with high zero-bias conductance to a non-Landau Fermi liquid,
characterized by a non-trivial quantized Luttinger integral, with a small
conductance. The effects of intermediate valence, finite temperature, and
structural relaxation of the molecule position allow us to explain the
different observed behaviors.
