Universality and the temperature-dependent zero-bias conductance of nanodevices
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Abstract
Late in the 1980's, theoretical analyses came to the conclusion that the Anderson model for dilute magnetic alloys should describe the low-temperature transport properties of nanodevices. A decade later, the development of the 'single-electron transistor', a quantum dot bridging two otherwise independent two-dimensional electron gases, ractified those predictions. In particular, the universal curve $g_univ(T)$ for the thermal dependence of the impurity contribution to the resistivity of a dilute magnetic alloy was shown to reproduce quantitatively the measured conductances through the quantum dot. More recently, a more complex nanostructure known as the 'T-shaped' or 'side-coupled' device, which couples a quantum dot to a quantum wire and the latter to two leads, was developed. When the current through the device was measured as a function of the gate voltage applied to the dot, instead of the flat plateaus observed in single-electron transistors, Fano antiresonances
emerged, showing that (i) the currents through the wire and through the dot interfere; and (ii) the thermal dependence of the conductance is qualitatively different from $g_univ(T)$. Our work focuses the side-coupled device. We will show that, even under conditions that maximize interference, the thermal dependence of the conductance can always be mapped onto $g_univ(T)$. The mapping is linear, with coefficients that depend on the low-temperature phase shift $\delta$ introduced in the quantum wire by the coupling to the dot. In the realm of the Anderson model, one of the coefficients is determined by a simple expression involving the phase-shift $\delta$ and the Fano parameter $q$, which measures the amplitude for conduction through the dot relative to the amplitude for conduction through the wire. The second coefficient, by contrast, is constant. As an illustration, we will report a numerical renormalization-group computation of the temperature-dependent conductance for the Anderson model of the side-coupled device for various ratios between the currents through the dot and the wire (i.~e., various $q$'s) and show that, in all cases, our expression maps the resulting conductances onto $g_univ(T)$. In addition, we will show that the mapping provides a straightforward procedure simplifying the interpretation of experimental curves. Applied to the measurements recently published by Sato et al. Phys. Rev. Lett. 95, 066801 (2005), that procedure yields conductance curves in excellent agreement with the experimental results and provides first-principle justification for the authors' phenomenological interpretation of their data. Work supported by the FAPESP, CNPq, and IBEM (Brazil).