Evolution and universality of two-stage Kondo effect in single manganese phthalocyanine molecule transistors

The Kondo effect offers an important paradigm to understand strongly correlated many-body physics. Although under intensive study, some of the important properties of the Kondo effect, in systems where both itinerant coupling and localized coupling play significant roles, are still elusive. Here we report the evolution and universality of the two-stage Kondo effect, the simplest form where both couplings are important using single molecule transistor devices incorporating Manganese phthalocyanine molecules. The Kondo temperature T* of the two-stage Kondo effect evolves linearly against effective interaction of involved two spins. Observed Kondo resonance shows universal quadratic dependence with all adjustable parameters: temperature, magnetic field and biased voltages. The difference in nonequilibrium conductance of two-stage Kondo effect to spin 1/2 Kondo effect is also identified. Messages learned in this study fill in directive experimental evidence of the evolution of two-stage Kondo resonance near a quantum phase transition point, and help in understanding sophisticated molecular electron spectroscopy in a strong correlation regime.