Kondo effect in systems with dynamical symmetries

Abstract

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 $|S_i{M}_i>$. Under certain conditions (to be explained below) some of the lowest energy levels $E_{S_i}$ 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 ${\mathbf{R}}_n$ are needed (in order to fully determine its quantum states), which have non-zero matrix elements between states of different spin multiplets $<S_i{M}_i|{\mathbf{R}}_n|S_j{M}_j>\ne 0$. 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 $\mathbf{s}$ with the operators of the dot then contains new exchange terms, $J_n\mathbf{s}\cdot {\mathbf{R}}_n$ beside the ubiquitous ones $J_i\mathbf{s}\cdot {\mathbf{S}}_i$. The operators ${\mathbf{S}}_i$ and ${\mathbf{R}}_n$ 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 ${\mathbf{R}}_n$ 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.

24 two-column pages

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Cited by in corpus (16)

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• Kondo-Dicke resonances in electronic transport through triple quantum dots
• Tunneling through triple quantum dots with mirror symmetry
• Orbital Kondo effect in double quantum dots
• Dicke-like effect in spin-polarized transport through coupled quantum dots
• Quantum Phase Transition and Dynamically Enhanced Symmetry in Quadruple Quantum Dot System
• Semi-fermionic representation for spin systems under equilibrium and non-equilibrium conditions
• Temperature-dependent gap equations and their solutions in the SU(4) model of high-temperature superconductivity
• SU(12) Kondo Effect in Carbon Nanotube Quantum Dot
• Dynamical and point symmetry of the Kondo effect in triangular quantum dot
• Decoherence and Dephasing in Kondo Tunneling through Double Quantum Dots
• Fluctuation-exchange approximation theory of the non-equilibrium singlet-triplet transition
• Two channel orbital Kondo effect in quantum dot with SO(n) symmetry
• Non-equilibrium transport theory of the singlet-triplet transition: perturbative approach
• Magnetic field induced two-channel Kondo effect in multiple quantum dots
• Kondo Effect in Artificial and Real Molecules