We all know one of the most widely studied phenomena in condensed-matter physics is Kondo effect.
Very briefly the milestones are as follows: This field began in 1933 when Wander Johannes de Haas and co-authors reported an unexpected rise in the resistivity of some gold samples at low temperature [1]. First, Phil Anderson formulated a microscopic model of how local moments form in metals with magnetic impurities. Anderson showed that Coulomb interactions are the reason the magnetic impurity behaves like a local moment [2]. Jun Kondo calculated the scattering rate of conduction electrons from local moments to second order and was able to reproduce the low temperature upturn and the depth of the resistivity minimum [3]. In Kondo's solution the calculated logarithmic divergence cannot physically persist to zero temperature. The zero-temperature limit remained unsolved. The calculated logarithmic divergence cannot physically persist to zero temperature. Renormalization group was required to solve this so-called Kondo problem [4]. It has been the subject of numerous reviews since the 1970s. Up to date, various approximate solutions have been introduced.
While Kondo's calculations were able to reproduce the resistivity upturn, There is a dramatic decrease in resistance in the superconductivity phase. What is the relationship between Kondo effect and superconductivity? Does anybody know about the latest work on this issue? Particulary, Is there anyone who is aware of a study about the solution of Kondo problem with DMFT (Dynamical Mean-Field Theory)?
[1] W.J. de Haas, J. de Boer, and G.J. van den Berg, Physica 1, 1115 (1933)
[2] P. W. Anderson, Phys. Rev. 124 41 (1961)
[3] J. Kondo, Prog. Theo. Phys. 32 37 (1964)
[4] K. Wilson, Rev. Mod. Phys. 47 773 (1975)
Kondo effect and superconductivity are two distinct phenomena. Kondo effect is a resonance phenomenon (in presence of magnetic impurities) that dominates as temperature is decreased towards zero, and superconductivity is a paring phenomenon (this is certainly the case in at least conventional superconductors) that is signified by a U(1) gauge symmetry breaking and the attendant Meissner effect. The minimum in the resistivity as function of temperature in Kondo systems is not a precursor of zero resistivity and thus superconductivity -- the Kondo problem is not this minimum on it own, but that resistivity increases on further decreasing the temperature, instead of saturating towards a value consistent with the expected impurity scattering.
For references concerning the application of the Dynamical Mean-Field Theory (DMFT) to Kondo systems, consult the following review articles by
Georges et al. (1996)
Article Dynamical Mean-Field Theory of Strongly Correlated Fermion S...
and Kotliar et al. (2006)
Article Electronic structure calculations with dynamical mean-field theory
Kondo effect and superconductivity are two distinct phenomena. Kondo effect is a resonance phenomenon (in presence of magnetic impurities) that dominates as temperature is decreased towards zero, and superconductivity is a paring phenomenon (this is certainly the case in at least conventional superconductors) that is signified by a U(1) gauge symmetry breaking and the attendant Meissner effect. The minimum in the resistivity as function of temperature in Kondo systems is not a precursor of zero resistivity and thus superconductivity -- the Kondo problem is not this minimum on it own, but that resistivity increases on further decreasing the temperature, instead of saturating towards a value consistent with the expected impurity scattering.
For references concerning the application of the Dynamical Mean-Field Theory (DMFT) to Kondo systems, consult the following review articles by
Georges et al. (1996)
Article Dynamical Mean-Field Theory of Strongly Correlated Fermion S...
and Kotliar et al. (2006)
Article Electronic structure calculations with dynamical mean-field theory
Dear Bahadir,
The Kondo effect describes one state of a magnetic impurity and the electric conductivity. The physical model which explains this effect is pseudogap Anderson's model employed for heavy fermions too and quantum critical transition phases. Broadly speaking, the main feature is that below 10K the resistivity increase instead to decrease as in usual metals happens.
Curiously, the dynamics of the magnetic moments induced in d-wave superconductor ,as the cuprates are doped with non-magnetic impurities, can be described as a psedogap Kondo model.
A very good review where Kondo effect and d-superconductivity appears well related is
Rev. Mod. Phys. 79, 1015 (2007)
arXiv:cond-mat/0606317v3
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