Conductance through an array of quantum dots

TL;DR

This paper introduces a simplified method to analyze electrical conductance in arrays of interacting quantum dots connected to metallic leads, using a mapping to an effective site and slave-boson techniques, with results matching established methods.

Contribution

It presents a novel, simplified approach for calculating conductance in quantum dot arrays, extending analysis to N=1 and N=3 configurations with good agreement to known results.

Findings

Good agreement with NRG for N=1 in the Kondo limit

Perfect conductance in symmetric linear trimer for odd N

Method applicable to various quantum dot arrangements

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 (NRG). 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 $G_0=2e^2/h$. The validity of the approach is discussed in detail.