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The paradigm of Landau's Fermi liquid theory has been challenged with thefinding of a strongly interacting Fermi liquid that cannot be adiabaticallyconnected to a non-interacting system. A spin-1 two-channel Kondo impurity withanisotropy D has a quantum phase transition between two topologically differentFermi liquids with a peak (dip) in the Fermi level for D < Dc (D > Dc).Extending this theory to general multi-orbital problems with finite magneticfield, we reinterpret in a unified and consistent fashion several experimentalstudies of iron phthalocyanine molecules on Au(111) that were previouslydescribed in disconnected and conflicting ways. The differential conductanceshows a zero-bias dip that widens when the molecule is lifted from the surface(reducing the Kondo couplings) and is transformed continuously into a peakunder an applied magnetic field. We reproduce all features and propose anexperiment to induce the topological transition.

Iron phthalocyanine on Au(111) is a "non-Landau" Fermi liquid