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arXiv:cond-mat/0308413 · Physical Review B

Conductance dip in the Kondo regime of linear arrays of quantum dots

C. A. Büsser, Adriana Moreo, Elbio R. Dagotto

Published Jul 7, 2004• 35 citations
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Abstract

Using exact diagonalization of small clusters and Dyson equation embedding techniques, the conductance $G$ of linear arrays of quantum dots is investigated. The Hubbard interaction induces Kondo peaks at low temperatures for an odd number of dots $N$ and a filling of one particle per dot. Remarkably, for $N=3,5,\dots{}$ the Kondo peak is split in half by a deep minimum, and the conductance vanishes at the gate voltage that induces particle-hole symmetry in the system. Tentative explanations for this unusual effect are proposed, including an interference process between two channels contributing to $G$, with one more and one less particle than the exactly solved cluster ground state. The Hubbard interaction and fermionic statistics of electrons also appear to be important to understand this phenomenon. Although most of the calculations used a particle-hole symmetric Hamiltonian and formalism, results also presented here show that the conductance dip exists even when this symmetry is broken. The conductance cancellation effect obtained using numerical techniques is potentially interesting, and other many-body techniques should be used to confirm its existence.

DOI
10.1103/physrevb.70.035402

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Using exact diagonalization of small clusters and Dyson equation embedding techniques, the conductance GGG of linear arrays of quantum dots is investigated. The Hubbard interaction induces Kondo peaks at low temperatures for an odd number of dots NNN and a filling of one particle per dot. Remarkably, for N=3,5,…N=3,5,\dots{}N=3,5,… the Kondo peak is split in half by a deep minimum, and the conductance vanishes at the gate voltage that induces particle-hole symmetry in the system. Tentative explanations for this unusual effect are proposed, including an interference process between two channels contributing to GGG, with one more and one less particle than the exactly solved cluster ground state. The Hubbard interaction and fermionic statistics of electrons also appear to be important to understand this phenomenon. Although most of the calculations used a particle-hole symmetric Hamiltonian and formalism, results also presented here show that the conductance dip exists even when this symmetry is broken. The conductance cancellation effect obtained using numerical techniques is potentially interesting, and other many-body techniques should be used to confirm its existence.
The ground-state properties of quartet quantum-dot arrays are studied using the numerical renormalization group (NRG) method with a four-site Hubbard model connected to two noninteracting leads. Specifically, we calculate the conductance and local charge in the dots from the many-body phase shifts, which can be deduced from the fixed-point eigenvalues of NRG. As a function of the on-site energy ϵd{ϵ}_{d}ϵd​ which corresponds to the gate voltage, the conductance shows alternatively wide peaks and valleys. Simultaneously, the total number of electrons Nel{N}_{\mathrm{el}}Nel​ in the four dots shows a quantized staircase behavior due to a large Coulomb interaction UUU. The conductance plateaus of the unitary limit emerging for odd Nel{N}_{\mathrm{el}}Nel​ are caused by the Kondo effect. The valleys of the conductance emerge for even Nel{N}_{\mathrm{el}}Nel​, and their width becomes substantially large at half-filling. It can be regarded as a kind of the Mott-Hubbard insulating behavior manifesting in a small system. These structures of the plateaus and valleys become weak for large values of the hybridization strength $\ensuremath{\Gamma}$ between the chain and leads. We also discuss the parallel conductance for the array connected to four leads.
We study the ground‐state properties of a triple quantum dot based on a three‐site Hubbard model connected to two non‐interacting leads. Using the numerical renormalization group (NRG), the many‐body phase shifts and dc conductance are calculated away from half‐filling as a function of the onsite energy εd, which corresponds to the gate voltage. The results for conductance g show the typical Kondo plateaus of the Unitary limit g ≈ 2e2/h at some finite ranges of the gate‐voltage corresponding to odd Nel (≈ 1, 3 and 5), where Nel is the total number of electrons in the triple dot. The conductance shows broad minima for even Nel(≈ 2 and 4). The local charge Nel shows a staircase behavior as a function of εd.
The transport properties of a linear structure of three quantum dots, with the central one connected to leads, are studied using the logarithmic discretization embedded cluster approximation. It is shown that the side dot spins can be ferromagnetically (F) or antiferromagnetically (AF) correlated between them, depending on the charge at the central dot. The system possesses a regime of coexistence of a two stage Kondo effect and the F phase. Ferromagnetism destroys the Kondo ground state when the system is driven to the molecular regime by increasing the interdot interaction above the largest Kondo temperature. Instead, an AF ground state does not compete with the Kondo regime. This remarkable behavior indicates that the measurement of the conductance can be an efficient readout procedure when the system operates as a quantum gate.
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 describe a formulation to deduce the phase shifts, which determine the ground-state properties of interacting quantum-dot systems with the inversion symmetry, from the fixed-point eigenvalues of the numerical renormalization group (NRG). Our approach does not assume the specific form of the Hamiltonian nor the electron-hole symmetry, and it is applicable to a wide class of quantum impurities connected to noninteracting leads. We apply the method to a triple dot which is described by a three-site Hubbard chain connected to two noninteracting leads, and calculate the dc conductance away from half-filling. The conductance shows the typical Kondo plateaus of Unitary limit in some regions of the gate voltages, at which the total number of electrons N_el in the three dots is odd, i.e., N_el =1, 3 and 5. In contrast, the conductance shows a wide minimum in the gate voltages corresponding to even number of electrons, N_el = 2 and 4. We also discuss the parallel conductance of the triple dot connected transversely to four leads, and show that it can be deduced from the two phase shifts defined in the two-lead case.
The Kondo effect and the Fano–Kondo effect are important phenomena that have been observed in quantum dots (QDs). We theoretically investigate the transport properties of a coupled QD system in order to study the possibility of detecting a qubit state from the modulation of the conductance peak in the Kondo effect and the dip in the Fano–Kondo effect. We show that the peak and dip of the conductance are both shifted depending on the qubit state. In particular, we find that we can estimate the optimal point and tunneling coupling between the |0> and |1> states of the qubit by measuring the shift of the positions of the conductance peak and dip, as functions of the applied gate voltage on the qubit and the distance between the qubit and the detector.