Universality and the thermal dependence of the conductance of nanodevices

The conductance of a quantum wire side-coupled to a quantum dot will be discussed. In this device, plots of the conductance $G$ vs.\ the gate voltage $V_g$ applied to the dot display Fano antiresonances due to the interference between the current traversing the~wire and the flux of electrons that hop to the dot to bypass the adjacent section of the wire; at fixed $V_g$'s, the interference accounts for a variety of thermal dependences $G(T)$. Analytical renormalization-group arguments will be presented that map $G(T)$ to the universal curve $g(T/T_K)$ for the conductance of the spin-degenerate Anderson impurity Hamiltonian, with temperatures normalized by the Kondo temperature $T_K$. This linear, universal mapping will be shown to (i) generate curves in excellent agreement with the measurements of Sato~et al.~[Phys.\ Rev.\ Lett.\ {\bf 95}, 066801 (2005)] and justify those authors' phenomenological description of their data; (ii) fit novel numerical renormalization-group data for the conductance of the side-coupled device; and (iii) link $G(T)$ to the conductance of the single-electron transistor.