Kondo effect

In

systems.

Theory

The dependence of the resistivity ${\displaystyle \rho }$ on temperature ${\displaystyle T}$, including the Kondo effect, is written as

${\displaystyle \rho (T)=\rho _{0}+aT^{2}+c_{m}\ln {\frac {\mu }{T}}+bT^{5},}$

where ${\displaystyle \rho _{0}}$ is the residual resistivity, the term ${\displaystyle aT^{2}}$ shows the contribution from the

Fermi liquid

properties, and the term ${\displaystyle bT^{5}}$ is from the lattice vibrations: ${\displaystyle a}$, ${\displaystyle b}$, ${\displaystyle c_{m}}$ and ${\displaystyle \mu }$ are constants independent of temperature. Jun Kondo derived the third term with logarithmic dependence on temperature and the experimentally observed concentration dependence.

Background

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.^[4] Based on the Schrieffer–Wolff transformation, it was shown that the Kondo model lies in the strong coupling regime of the Anderson impurity model. The Schrieffer–Wolff transformation^[5] projects out the high energy charge excitations in the Anderson impurity model, obtaining the Kondo model as an effective Hamiltonian.

The Kondo effect can be considered as an example of asymptotic freedom, i.e. a situation where the coupling becomes non-perturbatively strong at low temperatures and low energies. In the Kondo problem, the coupling refers to the interaction between the localized magnetic impurities and the itinerant electrons.

Examples

Extended to a lattice of magnetic ions, the Kondo effect likely explains the formation of

The Kondo effect has been observed in quantum dot systems.^[6][7] In such systems, a quantum dot with at least one unpaired electron behaves as a magnetic impurity, and when the dot is coupled to a metallic conduction band, the conduction electrons can scatter off the dot. This is completely analogous to the more traditional case of a magnetic impurity in a metal.

Band-structure hybridization and flat band topology in Kondo insulators have been imaged in angle-resolved photoemission spectroscopy experiments.^[8][9][10]

In 2012, Beri and Cooper proposed a topological Kondo effect could be found with Majorana fermions,^[11] while it has been shown that quantum simulations with ultracold atoms may also demonstrate the effect.^[12]

In 2017, teams from the Vienna University of Technology and Rice University conducted experiments into the development of new materials made from the metals cerium, bismuth and palladium in specific combinations and theoretical work experimenting with models of such structures, respectively. The results of the experiments were published in December 2017