Transport properties of strongly correlated electrons in quantum dots using a simple circuit model

Abstract

Numerical calculations are shown to reproduce the main results of recent experiments involving nonlocal spin control in nanostructures (N. J. Craig et al., Science 304, 565 (2004)). In particular, the splitting of the zerobias-peak discovered experimentally is clearly observed in our studies. To understand these results, a simple "circuit model" is introduced and shown to provide a good qualitative description of the experiments. The main idea is that the splitting originates in a Fano anti-resonance, which is caused by having one quantum dot sideconnected in relation to the current's path. This scenario provides an explanation of Craig et al.'s results that is alternative to the RKKY proposal, which is here also addressed.Keywords: Kondo effect; Nanoscopic systems; Correlated electrons In this Letter, numerical simulations in good agreement with the experiments reported by Craig et al. [1] are presented. The central conclusion of this work is that Fano antiresonance ideas are essential to explain this experimental results. Although the study of transport properties including current noise [6] of a microscopic quantum model is the most common way to understand nanoscopic transport, we will instead explain the experiments using a a very simple "circuit model", where one of the elements is a T-connected QD that has an intrinsic reduction of conductance with varying biases. ments [1] with the labeling used in this Letter. Figure 1b is a schematic representation of the system, introducing two different tunneling parameters (hopping matrix elements t and t ) and the Coulomb repulsion U in each QD (assumed the same for simplicity). To model this system, the Anderson impurity Hamiltonian is used for both QDs. To calculate the conductance G, using the Keldysh formalism [2], a cluster containing the interacting dots and a few sites of the leads is solved exactly [3], the Green functions are calculated, and the leads are incorporated through a Dyson Equation embedding procedure. Details of the embedding have been extensively discussed before [4]. All the results shown were obtained for U = 0.5, t = 0.2, zero-bias, and zero temperature. In Fig. 2, results for the conductance across QD1 and for the occupancy per spin orientation n 2 of QD2 are presented. In Fig. 2a, t = 0.2 and V g2 varies from −2.0 to −0.3. For V g2 = −2.0, QD2 is occupied by two electrons ( n 2 = 1) and the conductance of QD1 displays the characteristic Kondo behavior reported before [5]. For V g2 = −0.35 the average value of n 2 decreases to ≈ 0.7 (≈ 1.4 electrons in QD2) and n 2