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Chinese Physics B

Voltage-controlled Kosterlitz–Thouless transitions and various kinds of Kondo behaviors in a triple dot device

Yong‐Chen Xiong, Zhang Jun, Wang-Huai Zhou, A. Laref

Published Aug 1, 2017• 1 citation
Publisher

Abstract

The transport property and phase transition for a parallel triple dot device are studied by adopting Wilson's numerical renormalization group technique, focusing on the effects of level spacings between neighboring dot sites. By keeping dot 2 at the half-filled level and tuning the level differences, it is demonstrated that the system transits from local spin quadruplet to triplet and doublet sequently, and three kinds of Kondo peaks at the Fermi surface could be found, which are separated by two Kosterlitz–Thouless type quantum phase transitions and correspond to spin–3/2, spin–1, and spin–1/2 Kondo effect, respectively. To obtain a detailed understanding of these problems, the charge occupation, the spin—spin correlation, the transmission coefficient, and the temperature-dependent magnetic moment are shown, and necessary physical arguments are given.

DOI
10.1088/1674-1056/26/9/097102

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The transport property and phase transition for a parallel triple dot device are studied by adopting Wilson's numerical renormalization group technique, focusing on the effects of level spacings between neighboring dot sites. By keeping dot 2 at the half-filled level and tuning the level differences, it is demonstrated that the system transits from local spin quadruplet to triplet and doublet sequently, and three kinds of Kondo peaks at the Fermi surface could be found, which are separated by two Kosterlitz–Thouless type quantum phase transitions and correspond to spin–3/2, spin–1, and spin–1/2 Kondo effect, respectively. To obtain a detailed understanding of these problems, the charge occupation, the spin—spin correlation, the transmission coefficient, and the temperature-dependent magnetic moment are shown, and necessary physical arguments are given.
By means of the numerical renormalization group method, we study the phase transition, the spectral property, and the temperature-dependent magnetic moment for a parallel double dot system with level difference, where the dot energies are kept symmetric to the half-filled level. A Kosterlitz–Thouless (KT) transition between local spin triplet and singlet is found. In the triplet regime, the local spin is partially screened by the conduction leads and spin–1 Kondo effect is realized. While for the singlet, the Kondo peak is strongly suppressed and the magnetic moment decreases to 0 at a definite low temperature. We attribute this KT transition to the breaking of the reflection symmetry, resulting from the difference of the charge occupations of the two dots. To understand this KT transition and related critical phenomena, detailed scenarios are given in the transmission coefficient and the magnetic moment, and an effective Kondo model refers to the Rayleigh-Schrödinger perturbation theory is used.
Semiconductor quantum dot structure provides a promising basis for quantum information processing, within which to reveal the quantum phase and charge transport is one of the most important issues. In this paper, by means of the numerical renormalization group technique, we study the quantum phase transition and the charge transport for a parallel triple dot device in the strongly correlated limit, focusing on the effect of inter-dot hopping t beyond the Kondo regime. We find the quantum behaviors depend closely on the initial electron number on the dots, and the present model may map to single, double, and side-coupled impurity models in different parameter spaces. An orbital spin-1/2 Kondo effect between the conduction leads and the bonding orbital, and several magnetic-frustration phases are demonstrated when t is adjusted to different regimes. To understand these phenomena, a canonical transformation of the energy levels is given, and important physical quantities with respect to increasing t and necessary theoretical discussions are shown.
By means of the numerical renormalization group method, I study the Kondo effect and quantum phase transitions in a double quantum dot system with on-site repulsion UUU, interdot repulsion V,V,V, and magnetic field BBB. At zero temperature and B=0B=0B=0, there is a local spin triplet-singlet transition of the Kosterlitz-Thouless type when VVV increases to a critical value ${V}_{c}\ensuremath{\approx}U$. With increasing BBB, a singlet-triplet transition of the second order occurs at a critical magnetic field ${B}_{c}\ensuremath{\approx}V\ensuremath{-}U$. The magnetic susceptibility and the first derivatives of the spin correlation and double occupation are expected to diverge at Bc{B}_{c}Bc​ and to have different critical exponents, which are universal for different parameters. An appropriate magnetic field can restore the Kondo effect.
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 ttt, 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 ttt, 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 Sdot=3∕2{S}_{\mathit{\text{dot}}}=3∕2Sdot​=3∕2, 1∕21∕21∕2, and 0 on the dots. At low temperature, the local spin Sdot=3∕2{S}_{\mathit{\text{dot}}}=3∕2Sdot​=3∕2 is partially screened to a residual spin S=1S=1S=1, while the local spin Sdot=1∕2{S}_{\mathit{\text{dot}}}=1∕2Sdot​=1∕2 is totally screened. In both local quadruplet and doublet states, the Kondo resonance accompanied with a conductance of the unitary limit 2e2∕h2{e}^{2}∕h2e2∕h is observed, while no Kondo effect is found in the local spin-singlet state.
The numerical renormalization group is employed to study a double quantum (DQD) dot system consisting of two equivalent single-level dots, each coupled to its own lead and with a mutual capacitive coupling embodied in an interdot interaction U', in addition to the intradot Coulomb interaction U. We focus on the regime with two electrons on the DQD, and the evolution of the system on increasing U'/U. The spin-Kondo effect arising for U'=0 (SU(2) x SU(2)) is found to persist robustly with increasing U'/U, before a rapid but continuous crossover to (a) the SU(4) point U'=U where charge and spin degrees of freedom are entangled and the Kondo scale strongly enhanced; and then (b) a charge-Kondo state, in which a charge-pseudospin is quenched on coupling to the leads/conduction channels. A quantum phase transition of Kosterlitz-Thouless type then occurs from this Fermi liquid, strong coupling (SC) phase, to a broken symmetry, non-Fermi liquid charge ordered (CO) phase at a critical U'_c. Our emphasis in this paper is on the structure, stability and flows between the underlying RG fixed points, on the overall phase diagram in the (U,U')-plane and evolution of the characteristic low-energy Kondo scale inherent to the SC phase; and on static physical properties such as spin- and charge-susceptibilities (staggered and uniform), including universality and scaling behaviour in the strongly correlated regime. Some exact results for associated Wilson ratios are also obtained.
We study correlated two-level quantum dots, coupled in effective one-channel fashion to metallic leads, with electron interactions including on-level and interlevel Coulomb repulsions, as well as the interorbital Hund's rule exchange favoring the spin-1 state in the relevant sector of the free dot. For arbitrary dot occupancy, the underlying phases, quantum phase transitions (QPTs), thermodynamics, single-particle dynamics, and electronic transport properties are considered, and direct comparison is made to conductance experiments on lateral quantum dots. Two distinct phases arise generically, one characterized by a normal Fermi liquid fixed point (FP) and the other by an underscreened (USC) spin-1 FP. Associated QPTs, which occur in general in a mixed valent regime of nonintegral dot charge, are found to consist of continuous lines of Kosterlitz-Thouless transitions, separated by first-order level-crossing transitions at high symmetry points. A ``Friedel-Luttinger sum rule'' is derived and, together with a deduced generalization of Luttinger's theorem to the USC phase (a singular Fermi liquid), is used to obtain a general result for the T=0T=0T=0 zero-bias conductance, expressed solely in terms of the dot occupancy and applicable to both phases. Relatedly, dynamical signatures of the QPT show two broad classes of behavior, corresponding to the collapse of either a Kondo resonance, or antiresonance, as the transition is approached from the Fermi liquid phase, the latter behavior being apparent in experimental differential conductance maps. The problem is studied using the numerical renormalization group method, combined with analytical arguments.