Unified formulations for RKKY interaction, side Kondo behavior, and Fano antiresonance in a hybrid tripartite quantum dot device with filtered density of states

Hybrid quantum dot structures are potential building blocks for spintronic devices and quantum logic gates, within which the understanding of many-body correlations is a prerequisite for implementing quantum information processing and generating controlled entanglement. Herein, we consider a hybrid tripartite quantum dot device, one of which is embedded directly between the source and drain electrodes, while the other two dots are side coupled to the first one. Modeling the system using the three-impurity Anderson model, we concentrate on the Ruderman-Kittel-Kasuya-Yosida interaction, the suppression of the Kondo behavior in the side dots, the destructive quantum interference, the gate-controlled quantum phase transitions, the Dicke effect, the ferromagnetic Kondo effect, and the thermodynamical properties in various parameter regimes using the numerical renormalization group method. Unified formulations are established, which are associated with the effective width of the zero-energy peak of the central dot without side dots, the central-side exchange coupling, as well the on-site electron-electron repulsion. We demonstrate that these formulas are well suitable for the non-, weak-, and strong-interacting cases.