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

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 (t2) is absent, a singular two-stage Kondo effect is revealed for small central-side coupling t1. 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 t14 /(UTK21), where U and TK1 are the on-site electron-electron repulsion and the first Kondo temperature, respectively. When t2 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 t2. When t2 is large enough, the reappearance of the regular Kondo effect is found. With fixed t2 = 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.