RKKY interaction and local density of states for a triangular triple quantum dot system

Abstract

By means of the numerical renormalization group technique, we study the local density of states (LDOS) for a triangular triple quantum dot system, with two dots connected in parallel to the conduction leads. We find the location of the Ruderman–Kittel–Kasuya–Yosida (RKKY) peak identified in the LDOS could be illustrated as JRKKY=aΓ2/U+bt22/U, with U being the on-site Coulomb repulsion, Γ the dot-lead coupling, and t2 the hopping between the connected dots and the side dot. When the hopping between two connected dots t1 turns on, the spectrum weight of the RKKY peaks decreases due to the competition between the direct and the RKKY interactions. As t1 increases beyond a critical point t1c, two connected dots form a spin singlet, and decouple from both the side dot and the conduction leads, thus the Kondo and RKKY peaks could not be found. For t1<t1c, the conductance reaches to the unitary limit, while for t1≥t1c, it drops to zero.