Universal functions for the transport properties through nanostructured devices

A renormalization-group analysis of the temperature-dependent transport properties of a nanostructured device will be presented. To be specific, the single-electron transistor geometry, in which a quantum dot bridges two otherwise independent electron gases, will be considered. The renormalization-group analysis will consider the equilibrium electrical and thermal conductances and the thermopower in the Kondo regime and will be based on the spin-degenerate Anderson model for the device. The three properties can be related to the three lowest energy moments $\mathcal{L}_j$ ($j=0,1,2$) of the temperature-dependent spectral density of the dot level. We will rigorously show that each moment $\mathcal{L}_j$ maps linearly onto a universal function $L_{j}$ of the temperature scaled by the Kondo temperature $T_K$, with linear coefficients determined by the ground-state occupation of the quantum dot. Essentially exact numerical renormalization-group results for each of the three universal functions will be presented, showing that they can be related to each other at relatively high temperatures, $T>T_K$. The results will be compared to previous theoretical studies of the transport properties, and the implications concerning the interpretation of experimental data will be discussed.