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Concept
Kondo effect
Summary
In physics, the Kondo effect describes the scattering of conduction electrons in a metal due to magnetic impurities, resulting in a characteristic change i.e. a minimum in electrical resistivity with temperature.
The cause of the effect was first explained by Jun Kondo, who applied third-order perturbation theory to the problem to account for scattering of s-orbital conduction electrons off d-orbital electrons localized at impurities (Kondo model). Kondo's calculation predicted that the scattering rate and the resulting part of the resistivity should increase logarithmically as the temperature approaches 0 K. Experiments in the 1960s by Myriam Sarachik at Bell Laboratories provided the first data that confirmed the Kondo effect. Extended to a lattice of magnetic impurities, the Kondo effect likely explains the formation of heavy fermions and Kondo insulators in intermetallic compounds, especially those involving rare earth elements such as cerium, praseodymium, and ytterbium, and actinide elements such as uranium. The Kondo effect has also been observed in quantum dot systems.
The dependence of the resistivity on temperature , including the Kondo effect, is written as
where is the residual resistivity, the term shows the contribution from the Fermi liquid properties, and the term is from the lattice vibrations: , , and are constants independent of temperature. Jun Kondo derived the third term with logarithmic dependence on temperature and the experimentally observed concentration dependence.
Kondo's solution was derived using perturbation theory resulting in a divergence as the temperature approaches 0 K, but later methods used non-perturbative techniques to refine his result. These improvements produced a finite resistivity but retained the feature of a resistance minimum at a non-zero temperature. One defines the Kondo temperature as the energy scale limiting the validity of the Kondo results. The Anderson impurity model and accompanying Wilsonian renormalization theory were an important contribution to understanding the underlying physics of the problem.
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