Real-space numerical renormalization-group computation of transport properties in the side-coupled geometry

TL;DR

This paper introduces a real-space NRG method for computing transport properties in side-coupled quantum dot systems, demonstrating its accuracy and applicability to experimental data, especially in the Kondo regime.

Contribution

The paper presents a new real-space formulation of NRG, called eNRG, which simplifies calculations and improves the description of quantum dot coupling in transport studies.

Findings

eNRG provides accurate transport property calculations consistent with analytical universal functions.

The method effectively describes the Kondo regime and related thermoelectric properties.

Application to experimental thermopower data shows the method's practical relevance.

Abstract

The equilibrium transport properties of an elementary nanostructured device with side-coupled geometry are computed and related to universal functions. The computation relies on a real-space formulation of the numerical renormalization-group (NRG) procedure. The real-space construction, dubbed eNRG, is more straightforward than the NRG discretization and allows more faithful description of the coupling between quantum dots and conduction states. The procedure is applied to an Anderson-model description of a quantum wire side-coupled to a single quantum dot. A gate potential controls the dot occupation. In the Kondo regime, the electrical conductance through this device is known to map linearly onto a universal function of the temperature scaled by the Kondo temperature. Here, the energy moments from which the Seebeck coefficient and the thermal conductance can be computed are shown to map linearly onto universal functions also. The moments and transport properties computed by the eNRG procedure are shown to agree very well with these analytical developments. Algorithms facilitating comparison with experimental results are discussed. As an illustration, one of the algorithms is applied to thermal dependence of the thermopower measured by K\"{o}hler [PhD Thesis, TUD, Dresden, 2007] in Lu$_{0.9}$Yb$_{0.1}$Rh$_{2}$Si$_{2}$.