Frustration-controlled quantum phase transition between multiple singular two-stage Kondo behaviors in a tetrahedral quadruple quantum dot structure

Abstract

Semiconductor quantum dots are considered to be promising candidates for the hardware of quantum information technology and optoelectronic devices. Herein, motivated by a tetrahedrally shaped colloidal quadruple quantum dot structure made from In-based III--V semiconductors, which has been synthesized very recently by Leemans et al. [J. Am. Chem. Soc., 143, 4290 (2021)], we provide timely insight into the electronic transport and the quantum phase transition (QPT) for such an architecture. When the interdot hopping between different side dots (${t}_{2}$) is absent, a singular two-stage Kondo effect is revealed for small central-side coupling ${t}_{1}$. The two screening processes are separated by an energy scale of the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, and the fitting parameters deviate from the regular ones of the side-coupled double dot system. The RKKY interaction and temperature are well illustrated by functions of ${t}_{1}^{4}/(U{T}_{K1}^{2})$, where $U$ and ${T}_{K1}$ are the on-site electron-electron repulsion and the first Kondo temperature, respectively. When ${t}_{2}$ turns on, the ground state of the side dots transits from a spin quadruplet to a magnetic frustration phase, and then to a singlet, through two first-order QPTs. In the frustration phase, another new two-stage Kondo effect is demonstrated, which includes the process of screening the local spin on the central dot firstly, and then that on the neighborless side dot is screened at a lower temperature. Both the Kondo temperatures are found to be rather sensitive to ${t}_{2}$. When ${t}_{2}$ is large enough, the reappearance of the regular Kondo effect is found. With fixed ${t}_{2}=0$, charging the central dot triggers a transition from an antiferromagnetic correlation among the side dots to a ferromagnetic one, accompanied by a Kondo behavior in the central dot. We adopt the state-of-the-art numerical renormalization group method to implement the above behaviors, combined with analytical arguments.