Kondo Physics in Artificial Molecules

There are numerous models in the literature of condensed matter theory, whose significance for achieving progress in our understanding of nature goes far beyond the original aim of explaining specific experimental observations. One may mention in this context the Bardeen-Cooper-Schrieffer’s explanation of the nature of electron pairing in superconductors, the Ginzburg-Landau equation intended for describing critical uctuations, the concept of selflocalization of excitations in a perfect crystal formulated by Deigen, Pekar and Toyozawa and various other seminal ideas. The explanation offered by J. Kondo for the puzzling shallow minimum in the temperature dependent resistivity of metals doped by magnetic impurities [1] is one of the most salient examples of this kind of scenario. To explain it, consider first Kondo’s original idea, which was formulated within the framework of a well-established Hamiltonian describing exchange interaction between an impurity spin S_r located on a given site r and the spin density s_r pertaining to a Fermi sea of conduction electrons at this site. The latter is defined by the Fourier transform of the itinerant spin$$s_{kk'} = c_{k\sigma }^\dag \hat \tau c_{k'\sigma '} $$ projected on the impurity site r, namely$$s_r = \sum\nolimits_{kk'} {s_{kk'} } {\text{ exp[i(}}k - k'{\text{)}} \cdot r{\text{]}}$$.