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Physical Review B

Spectral properties and quantum phase transitions in parallel triple quantum dots

Weizhong Wang

Published Sep 14, 2007• 40 citations
Publisher

Abstract

The spectral properties and the quantum phase transitions in parallel triple quantum dot systems are investigated using the numerical renormalization-group method. For small interdot hopping $t$, the Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interaction between the dots is identified in the spectra and is consistent with that obtained by the perturbation theory. With increasing $t$, due to the competition between the RKKY exchange and the direct exchange between dots, there exist two first-order quantum phase transitions between the phases with the local spin ${S}_{\mathit{\text{dot}}}=3∕2$, $1∕2$, and 0 on the dots. At low temperature, the local spin ${S}_{\mathit{\text{dot}}}=3∕2$ is partially screened to a residual spin $S=1$, while the local spin ${S}_{\mathit{\text{dot}}}=1∕2$ is totally screened. In both local quadruplet and doublet states, the Kondo resonance accompanied with a conductance of the unitary limit $2{e}^{2}∕h$ is observed, while no Kondo effect is found in the local spin-singlet state.

DOI
10.1103/physrevb.76.115114

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The system of several (N)(N)(N) quantum dots coupled in parallel to the same single-mode conduction channel can be modeled as a single-channel NNN-impurity Anderson model. Using the generalized Schrieffer-Wolff transformation we show that near the particle-hole symmetric point, the effective Hamiltonian in the local moment regime is the NNN-impurity S=1∕2S=1∕2S=1∕2 Kondo model. The conduction-band-mediated RKKY exchange interaction between the dots is ferromagnetic and at intermediate temperatures locks the moments into a maximal spin S=N∕2S=N∕2S=N∕2 ground state. We provide an analytical estimate for the RKKY interaction. At low temperatures the spin is partially screened by the conduction electrons to $N∕2\ensuremath{-}1∕2$ due to the Kondo effect. By comparing accurate numerical renormalization group results for magnetic susceptibility of the NNN-impurity Anderson model to the exact Bethe ansatz results of a S=N∕2S=N∕2S=N∕2 SU(2) Kondo system we show that at low-temperature the quantum dots can be described by the effective S=N∕2S=N∕2S=N∕2 Kondo model. Moreover, the Kondo temperature is independent of the number of impurities NNN. We demonstrate the robustness of the spin N∕2N∕2N∕2 ground state as well as of the associated S=N∕2S=N∕2S=N∕2 Kondo effect by studying the stability of the system with respect to various experimentally relevant perturbations. We finally explore various quantum phase transitions driven by these perturbations.
We investigate electronic transport through a parallel double quantum dot (DQD) system with strong on-site Coulomb interaction and capacitive interdot coupling. By applying the numerical renormalization group (NRG) method, the ground state of the system and the transmission probability at zero temperature have been obtained. For a system of quantum dots with degenerate energy levels and small interdot tunnel coupling, the spin correlations between the DQDs is ferromagnetic and the ground state of the system is a spin-1 triplet state. The linear conductance will reach the unitary limit (2e(2)/h) due to the underscreened Kondo effect at low temperature. As the interdot tunnel coupling increases, there is a quantum phase transition from ferromagnetic to antiferromagnetic spin correlation in DQDs and the linear conductance is strongly suppressed.
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