Scaling theories, most notably of the power law form, characterize a diverse array of naturally occurring phenomena. Seemingly unrelated systems with widely differing microscopic details can be described by relations with identical scaling exponents when the underlying dynamics are similar. This property, known as universality, is relevant when considering systems driven out of equilibrium by some perturbation. In a system with an emergent characteristic energy scale, examining the system response as a function of the perturbation scaled relative to that energy can reveal such universality. The many-body Kondo state in quantum dots, as observed in a variety of microscopic implementations[1, 2, 3, 4, 5, 6], is an example of such a system. In these devices itinerant electrons in source and drain leads are coupled via tunneling barriers to a single magnetic impurity. At zero source-drain bias (V ), below an emergent Kondo energy scale, kBTK, the local moment of the impurity is screened by the conduction electrons. As a result of the screening process the (zero-bias) conductance, G, is enhanced at low temperatures (T 0) drives the system into the nonequilibrium Kondo regime.[10, 11, 12] G(T,V ) exhibits a resonance peak centered at V = 0. Theoretical treatments of idealized quantum dots have argued that G(T,V ) in the single channel Kondo state may be described by an analogous function in bias voltage and temperature. However, there is discussion regarding the energy scales and order to which this scaling will hold as well as the number of system specific coefficients required, their expected values, and the universality of these coefficients.[13, 14, 15, 16, 17, 18] Recent experiments by Grobis et al.[19] have shown that G(T,V ) measured in a single channel GaAs quantum dot (TK � 0.3 K) in the nonequilibrium regime is well described by a universal scaling function with two scaling parameters. In this Letter we test the universality of these results, applying the analogous analytical approach to 29 molecule-based devices with Kondo temperatures ranging from 35 K to 155 K. We find that the conductances of SMTs containing either C60[6, 20, 21] or a transition metal complex[22] are accurately described by the same scaled parameters as the GaAs dot[19]. We confirm the quadratic voltage and temperature dependence of G in the low energy limit. The values of the extracted scaling coefficients are quite consistent throughout the ensemble. We discuss possible explanations for the systematic differences between our coefficients and those inferred from previous experiments[19] and theoretical model predictions.
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Open Access
Apr 24, 2009
Luis G G V Dias Da Silva + 4
