Finite-Size Effects in Conductance Measurements on Quantum Dots

The observation of the Kondo effect in quantum dots has provided new opportunites to finally observe the controversial Kondo screening cloud. Here we study the conductance of a quantum dot embedded in a finite length quantum wire, predicting a change in behavior when the length of the wire is comparable to the size of the screening cloud.

Figure 1

Schematic representation of the device under consideration. ${ϵ}_D$ and ${ϵ}_W$ control, respectively, the dot and wire gate voltage.

Figure 2

On-resonance conductance as a function of temperature (assuming ${ϵ}_W$ is on resonance) for both cases ${\Delta }_n\ll T_{K,1}^0$ (right blue curve) and ${\Delta }_n\gg {\delta }_n\gg T_{K,2}^0$ (left red curve). The curves in plain style correspond to the perturbative calculations plus the Fermi liquid result for the first case only. We have schematically extrapolated these curves (dotted lines) where neither the perturbative nor the Fermi liquid theory applies. The inset represents $T_K=f(T_K^0)$ in a log-log scale for ${ϵ}_W$ on resonance (plain curve which becomes almost flat at low $T_K^0\ll {\delta }_n$), and ${ϵ}_W$ off-resonance (dashed curve which drops sharply at low $T_K^0$). Both curves coincide at $T_K^0>{\Delta }_n$.