Identifying an effective model for the two-stage-Kondo regime: Numerical renormalization group results

TL;DR

This paper uses numerical renormalization group methods to identify the parameter regime where the two-stage Kondo effect occurs in a double quantum dot system, providing a practical way to distinguish it from other regimes.

Contribution

It introduces a method to accurately identify the two-stage Kondo regime in a double quantum dot system using effective parameters and susceptibility analysis.

Findings

The TSK regime occurs within a specific parameter range of inter-dot and lead couplings.

An effective single impurity Anderson model can describe the second Kondo stage.

Universal behavior in spin correlations characterizes the TSK regime.

Abstract

A composite impurity in a metal can explore different configurations, where its net magnetic moment may be screened by the host electrons. An example is the two-stage Kondo (TSK) system, where screening occurs at successively smaller energy scales. Alternatively, impurities may prefer a local singlet disconnected from the metal. This competition is influenced by the system's couplings. A double quantum dot T-shape geometry, where a "hanging" dot is connected to current leads only via another dot, allows experimental exploration of these regimes. Differentiating the two regimes has been challenging. This study provides a method to identify the TSK regime in such a geometry. The TSK regime requires a balance between the inter-dot coupling ($t_{01}$) and the coupling of the quantum dot connected to the Fermi sea ($\Gamma_0$). Above a certain ratio, the system transitions to a molecular regime, forming a local singlet with no Kondo screening. The study identifies a region in the $t_{01}$--$\Gamma_0$ parameter space where a pure TSK regime occurs. Here, the second Kondo stage properties can be described by a single impurity Anderson model with effective parameters. By examining the magnetic susceptibility of the hanging quantum dot, a single parameter, $\Gamma_{\rm eff}$, can simulate this susceptibility accurately. This effective model also provides the hanging quantum dot's spectral function accurately within a limited parameter range, defining the true TSK regime. Additionally, spin correlations between the quantum dots show universal behavior in this parameter range. These findings can guide experimental groups in selecting parameter values to place the system in either the TSK regime or the crossover to the molecular regime.