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 |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.

Tunneling through triple quantum dots with mirror symmetry

“…4,8,13 The novelty of the present scenario is that it is manifested in quantum dots with odd occupation where the absence of the Kondo effect occurs due to ferromagnetic exchange coupling with the localized spin doublet. The nonuniversality of T K occurs as this ferromagnetic exchange competes with two antiferromagnetic exchange interactions ͑with doublet and quartet localized moments͒, so that, in some sense, one deals with a "three-stage" Kondo effect.…”

“…6,7 A more complicated model of the asymmetric triple quantum dot ͑TQD͒ with a small dot sandwiched between two large dots was considered in Ref. 8 for odd and even occupations N =3,4. It was shown that the Kondo regime is accessible in both cases.…”

Charge-switchable molecular magnet and spin blockade of tunneling

“…Such situations were also considered in the context of exotic Kondo effects involving dynamical symmetries in multiple quantum-dot systems. 38,39 Finally, similar models with two types of electron orbitals have been studied for the description of the neutral-ionic transition 40 in organic crystals, in the context of ferroelectrics and superconductivity in transition metal oxides. 41…”

Single Electron Tunneling in Small Molecules

“…We can eliminate the charge degrees of freedom on the metal-ion sites by a Schrieffer-Wolff transformation [26] and obtain an effective 4-site model H M eff = − jk σ t /2 c † jσ c kσ + H l . Similar "ionic" or "double-shell" models have been studied in other contexts [10,[27][28][29]. When neglecting the hopping t , the charging energies u > v > w dictate that the first electron reduces one of the four ligands, say j = 1.…”

“…We focus here on the situation where the molecule is weakly coupled to the external controlled reservoirs (electrodes and light-sources [8]) and external dissipative environments (mechanical or electromagnetic). Strong coupling phenomena such as Kondo-tunneling are discussed in [9,10] and the references therein. We consider here only stationary non-equilibrium states resulting from time-independent external signals.…”