Conductance through an array of quantum dots

Abstract

We propose a simple approach to study the conductance through an array of $N$ interacting quantum dots, weakly coupled to metallic leads. Using a mapping to an effective site which describes the low-lying excitations and a slave-boson representation in the saddle-point approximation, we calculated the conductance through the system. Explicit results are presented for $N=1$ and $N=3$: a linear array and an isosceles triangle. For $N=1$ in the Kondo limit, the results are in very good agreement with previous results obtained with numerical renormalization group. In the case of the linear trimer for odd $N$, when the parameters are such that electron-hole symmetry is induced, we obtain perfect conductance ${G}_{0}=2{e}^{2}∕h$. The validity of the approach is discussed in detail.