Kondo Effect in Artificial and Real Molecules

In this Thesis we develop a novel direction in the theory of nano-objects, i.e., structures of nanometer size in a tunnel contact with macroscopic electron reservoirs (metallic leads). This theory arose and was developed rapidly during the two recent decades as a response to challenging achievements of modern nanotechnology and experimental techniques. Evolution of this technology enabled the fabrication of various low-dimensional systems from semiconductor heterostructures to quantum wires and constrictions, quantum dots, molecular bridges and artificial structures constructed from large molecules. This impressive experimental progress initiated the development of a new direction in quantum physics, namely, the physics of artificial nano-objects. We focus in this work on a theoretical investigation of the Kondo physics in quantum dots and molecules with strong correlations. An exciting series of recent experiments on mesoscopic and nanoscale systems has enabled a thorough and controlled study of basic physical problems dealing with a local moment interacting with a Fermi sea of conduction electrons. Scanning tunnel microscopy and quantum–dot devices have provided new tools for studying the Kondo effect in many new perspectives and with unprecedented control. As experimental and theoretical investigations of tunneling phenomena continue, it turns out that the physics of tunneling spectroscopy of large molecules and complex quantum dots have much in common. In particular we elucidate the Kondo effect predicted in tunneling through triple quantum dots and sandwich-type molecules adsorbed on metallic substrate, which are referred to as trimers. The unusual dynamical symmetry of nano-objects is one of the most intriguing problems, which arise in the theory of these systems. We demonstrate that trimers possess dynamical symmetries whose realization in Kondo tunneling is experimentally tangible. Such experimental tuning of dynamical symmetries is not possible in conventional Kondo scattering. We develop the general approach to the problem of dynamical symmetries in Kondo tunneling through nano-objects and illustrate it by numerous examples of trimers in various configurations, in parallel, in series and in ring geometries. In the first part of this Thesis, the evenly occupied trimer in a parallel geometry is studied. We show that Kondo tunneling through the trimer is controlled by a family of SO(n) dynamical symmetries. The most striking feature of this result is that the value of the group index n = 3, 4, 5, 7 can be changed experimentally by tuning the gate voltage applied to the trimer. Following the construction of the corresponding on algebras, the scaling equations are derived and the Kondo temperatures are calculated. In the second part, the Kondo physics of trimer with both even and odd electron occupation in a series geometry is discussed. We derive and solve the scaling equations for the evenly occupied trimer in the cases of the P ×SO(4)×SO(4), SO(5), SO(7) and P × SO(3)× SO(3) dynamical symmetries. The dynamical-symmetry phase diagram is displayed and the experimental consequences are drawn. The map of Kondo temperature as a function of gate voltages is constructed. In addition, the influence of magnetic field on the dynamical symmetry and its role in the Kondo tunneling through the trimer are studied. It is shown that the anisotropic Kondo effect can be induced in the trimer by an external magnetic field. The corresponding symmetry group is SU(3). In the case of odd electron occupation, the effective spin Hamiltonian of the trimer manifests a two-channel Kondo problem albeit only in the weak coupling regime (due to unavoidable anisotropy). In the third part, the point symmetry C3v of an artificial trimer in a ring geometry and its interplay with the spin rotation symmetry SU(2) are studied. This nano-object is a quantum dot analog of the Coqblin-Schrieffer model in which the Kondo physics is governed by a subtle interplay between spin and orbital degrees of freedom. The orbital degeneracy is tuned by a magnetic field, which affects the electron phases thereby leading to a peculiar Aharonov-Bohm effect. The following novel results were obtained in the course of this research: • It is found that evenly occupied trimer manifests a new type of Kondo effect that was not observed in conventional spin 1/2 quantum dots. The dynamical SO(n) symmetries of Kondo tunneling through evenly occupied trimer both in parallel and series geometry are unravelled. These symmetries can be experimentally realized and the specific value of n = 3, 4, 5, 7 can be controlled by gate voltage and/or tunneling strength. The Kondo temperature explicitly depends on the index n and this dependence may be traced experimentally by means of measuring the variation of tunnel conductance as a function of gate voltages. The hidden dynamical symmetry manifests itself, firstly in the very existence of the Kondo effect in trimer with even occupation, secondly in non-universal behavior of the Kondo temperature TK . In a singlet spin state the anisotropic Kondo effect can be induced in the trimer by an external magnetic field. • It is shown that the effective spin Hamiltonian of a trimer with odd electron occupation weakly connected in series with left (l) and right (r) metal leads is composed of two-channel exchange and co-tunneling terms. Renormalization group equations for the corresponding three exchange constants Jl, Jr and Jlr are solved in a weak coupling limit (single loop approximation). Since Jlr is relevant, the system is mapped