Two-state behaviour of Kondo trimers

Abstract

The electronic properties and spectroscopic features of a magnetic trimer with a Kondo-like coupling to a non-magnetic metallic substrate are analyzed at zero temperature. The substrate density of states is depressed in the trimer neighbourhood, being exactly zero at the substrate chemical potential. The size of the resonance strongly depends on the magnetic state of the trimer, and exhibits a two-state behavior. The geometrical dependence of these results agree qualitatively with recent experiments and could be reproduced in a triangular quantum dot arrangement. Keywords:The combination of the Scanning Tunneling Microscope (STM), which can be used as a "tool" to build and characterize atomically-precise structures, and the availability of high-quality clean metallic surfaces has provided a unique opportunity to investigate the chemical and physical properties of deposited atoms, molecules, and clusters with unprecedented resolution. It has been natural then that much of the research concentrates on one of the old paradigms of condensed-matter physics: the behavior of magnetic impurities immersed in an otherwise non-magnetic matrix. Ground-breaking experiments have been reported on the properties of magnetic monomers[1] and dimers[2], quantum-confinement of surface two-dimensional electron gases by a "corral" of STM-positioned magnetic atoms [3], and "molecule cascade" devices[4], with potential for quantum computing. In most of these examples, it has become evident that at low-temperatures the physics of magnetic impurities on the metallic surface is dominated by the so-called Kondo effect. Historically, the Kondo effect was introduced more than forty years ago to explain the resistivity minimum for decreasing temperatures observed in metallic matrices with a minute fraction of magnetic impurities. [5] Additional interest in the Kondo effect arose recently from the semiconductor nano-oriented community, after realization[7, 8] that a quantum dot with two attached conducting leads behaves in many aspects as a magnetic atom in a metal. [9,10] The aim of this work is the theoretical study of a magnetic trimer in contact with a metallic substrate. The trimer geometry is very interesting, due to the fact that it is the simplest geometrical arrangement (including monomers and dimers) which displays magnetic frustration among the three magnetic moments for the case of antiferromagnetic interactions [11]. The main result from our work is that as a consequence of the interplay between the trimer-metal Kondo interaction which tries to stabilize the trimer in a high-spin state, and the intratrimer antiferromagnetic interactions which try of stabilize a low-spin trimer state, the whole system exhibits -2 -1 0 1 2 t' t 3 2 1 J J J J 1 J 2 J 2 FIG. 1: Schematic diagram of the system considered: an AF spin trimer Kondo-coupled to a non-interacting chaina two-state spectroscopic behavior that depends on the geometrical arrangement of the triangle (whether it is an equilateral or isosceles triangle) and on the interaction parame...

Conductance through an array of quantum dots

“…An example of this system is a trimer coupled to one site of a conducting lead. 45 In this case, the model is mapped to an effective site side coupled to a conducting lead, 11,13,18,19 instead of embedded in the lead.…”

Numerical renormalization group study of two-channel three-impurity triangular clusters

“…In contrast to simpler models, however, the three-impurity model allows to study crossovers between various non-trivial fixed points. Spurred on by a number of experimental achievements 42,43,44,45,46,47,48,49 , the interest in the transport properties of three-impurity models recently intensified 50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66 . We thus also study the conductance through a system of three coupled quantum dots described by a related model featuring three Anderson-model-like impurity electron levels interconnected by tunneling coupling and connected to conduction bands by hybridization.…”

Fermi-liquid theory for the persistent current past a side-coupled quantum dot

“…The screening of the impurity spin by the conduction electrons is, in some circumstances, associated with the formation of a "screening cloud" of size ξ K = v F /T K surrounding the impurity. 10,11,12,13,14,15,16 Here v F is the Fermi velocity and T K the Kondo temperature.…”