Thermal dependence of the zero-bias conductance through a nanostructure

We show that the conductance of a quantum wire side-coupled to a quantum dot, with a gate potential favoring the formation of a dot magnetic moment, is a universal function of the temperature. Universality prevails even if the currents through the dot and the wire interfere. We apply this result to the experimental data of Sato et al. [Phys. Rev. Lett. 95, 066801 (2005)]. Nanodevices owe much of their development to the theory of many-body phenomena. Consider, e. g., the single electron transistor (SET), a quantum dot bridging two otherwise independent two-dimensional electron gases [1,2]. The competition between the Coulomb blockade, which bars transport through the dot, and the Kondo screening of the dot magnetic moment by the electron gases [3], which favors low-temperature conduction, was discussed on blackboards [4] a decade before it surfaced in the laboratory [1]. By the time the first device was developed, quantitatively accurate theoretical results were available. Chiefly important was the universal conductance curve GSET (T ) for the symmetric Anderson model [5, 6], which was shown to match the temperature dependence of the zero-bias conductances in SETs and analogous devices. More recently, experiment has leaped ahead of theory. The development of complex structures, such as the sidecoupled device [7–12], has motivated only qualitative predictions. As Fig. 1 shows, the current in the side-coupled device is carried by electrons that can either traverse the quantum wire or hop to a quantum dot to skip the central section [12]. A Fano parameter q [13], defined below, measures the amplitude for the latter process relative to that for the former. The limit q → ∞ emulates a SET. For smaller q’s, the wire bypasses the Coulomb blockade and Figure 1: Side-coupled device. The gate potential Vg controls the energy εd of the quantum-dot level cd. The open circle depicts the Wannier orbital f0. allows high-temperature conduction. Below the Kondo temperature TK , the screening of the magnetic moment enhances the electronic flux through the dot and allows interference with the flow along the central portion of the wire [14, 15]. Attentive to the diversity of experimental findings, we have applied numerical renormalization-group (NRG) tools to an Anderson Hamiltonian modeling the sidecoupled device. The resulting essentially exact numerical data for the temperature-dependent conductance Gq(T ) will be detailed elsewhere [16]. Here, we focus the relation between Gq(T ) and the universal curve G S SET (T ). Our central result covers the Kondo domain, the set of dot energies and dot-wire couplings that favor the formation of