Dynamical Symmetries in Kondo Tunneling through Complex Quantum Dots

Kuzmenko, Tetyana; Kikoin, K.; Avishai, Y.

doi:10.1103/physrevlett.89.156602

Cited by 29 publications

(62 citation statements)

References 19 publications

(37 reference statements)

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“…In the first experimental realization of TQD [33] the former option was chosen, whereas the first theoretical study [50] was devoted to to the second possibility.…”

Section: >>mentioning

confidence: 99%

“…1,a,b [50]. To demonstrate these features let us consider TQD with in lateral geometry in more details.…”

Section: >>mentioning

confidence: 99%

“…2) and change the singlet-triplet splitting, so that the spin states are classified as S l r , and T l r , . The relative positions of energy levels in spin multiplets evolve as a function of model parameters and various types of level crossings occur (see [50] for detailed calculations). Similar situation arises for vertical configuration of Fig.…”

Section: >>mentioning

confidence: 99%

“…The corresponding wave functions are vector sums of states composed of a «pas-sive» electron sitting in the central and dot singlet/triplet (S/T) two-electron states in the l r , dots. Then using certain Young tableaux [50], one concludes that the spin dynamics of such TQD is repre- (4) SO (5) SO (7) SO(3) SO (4) SO (5) SO (3) SO (7) P SO (4) …”

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confidence: 99%

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Tunneling and magnetic properties of triple quantum dots

Kikoin

2007

Low Temperature Physics

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“…In the first experimental realization of TQD [33] the former option was chosen, whereas the first theoretical study [50] was devoted to to the second possibility.…”

Section: >>mentioning

confidence: 99%

“…1,a,b [50]. To demonstrate these features let us consider TQD with in lateral geometry in more details.…”

Section: >>mentioning

confidence: 99%

Section: >>mentioning

confidence: 99%

Section: >>mentioning

confidence: 99%

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Tunneling and magnetic properties of triple quantum dots

Kikoin

2007

Low Temperature Physics

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“…Within this framework, our earlier results 14 fit into an elegant pattern of classification of dynamical symmetry groups, which is expanded here in a somewhat more complete and rigorous formalism. The main lesson to be learned is that Kondo physics in CQD suggests a novel and in some sense rather appealing aspect of low-dimensional physics of interacting electrons.…”

Section: Introductionmentioning

confidence: 95%

Kondo effect in systems with dynamical symmetries

2004

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This paper is devoted to a systematic exposure of the Kondo physics in quantum dots for which the low energy spin excitations consist of a few different spin multiplets |SiMi . Under certain conditions (to be explained below) some of the lowest energy levels ES i are nearly degenerate. The dot in its ground state cannot then be regarded as a simple quantum top in the sense that beside its spin operator other dot (vector) operators Rn are needed (in order to fully determine its quantum states), which have non-zero matrix elements between states of different spin multiplets SiMi|Rn|Sj Mj = 0. These "Runge-Lenz" operators do not appear in the isolated dot-Hamiltonian (so in some sense they are "hidden"). Yet, they are exposed when tunneling between dot and leads is switched on. The effective spin Hamiltonian which couples the metallic electron spin s with the operators of the dot then contains new exchange terms, Jns · Rn beside the ubiquitous ones Jis · Si. The operators Si and Rn generate a dynamical group (usually SO(n)). Remarkably, the value of n can be controlled by gate voltages, indicating that abstract concepts such as dynamical symmetry groups are experimentally realizable. Moreover, when an external magnetic field is applied then, under favorable circumstances, the exchange interaction involves solely the Runge-Lenz operators Rn and the corresponding dynamical symmetry group is SU (n). For example, the celebrated group SU (3) is realized in triple quantum dot with four electrons.

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Explicit and Hidden Symmetries in Quantum Dots and Quantum Ladders

Kikoin

Avishai

Kiselev

2004

Molecular Nanowires and Other Quantum Objects

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The concept of dynamical hidden symmetries in the physics of electron tunneling through composite quantum dots (CQD) and quantum ladders (QL) is developed and elucidated. Quite generally, dynamical symmetries are realizable in the space of low energy excited states in a given charge sector of nanoobjects, which involve spin variables and/or electron-hole pairs. While spin multiplets in an individual rung of a QL or in an isolated CQD form a representation space of the usual rotation group, this SU (2) symmetry is broken due to spin transfer (in QL) electron cotunneling through CQD. Dynamical symmetries in the space of spin multiplets are then unravelled in these processes. The corresponding symmetry groups are described by SO(n) or SU (n) depending on the origin of rotation group symmetry breaking. The effective spin Hamiltonians of QL and CQD are derived and expressed in terms of the pertinent group generators. We employ fermionization procedure for analyzing the physical content of these dynamical symmetries, including Kondo tunneling through CQD and Haldane gap formation in QL.

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Dynamical Symmetries in Kondo Tunneling through Complex Quantum Dots

Cited by 29 publications

References 19 publications

Tunneling and magnetic properties of triple quantum dots

Tunneling and magnetic properties of triple quantum dots

Kondo effect in systems with dynamical symmetries

Explicit and Hidden Symmetries in Quantum Dots and Quantum Ladders

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