old reviewer A (Hewson)
I think the entry of Dr Kondo could be improved:
1) I think it needs more of a context explaining why a resistance minimum is unusual, and why it was a longstanding puzzle until Kondo's calculation provided an explanation.
2) The calculation of Kondo is described well, but I think the later work could be explained more clearly. Particularly, I think it would help to bring in the idea of the narrow resonance that develops in the electron density of states at low temperatures (Kondo resonance), which provides an explanation of the low temperature behaviour in terms of the fully-dressed or quasi-particles of Fermi liquid theory. I think it would also be of interest to mention the direct experimental observation of this resonance in recent experiments in quantum dots ----- the development of this resonance at low temperatures permits electron transmission through the low temperatures, which otherwise would not be possible.
3) Some clear figures would help to illustrate some of the ideas
4) The English reads rather awkwardly at points, and needs some editing.
Note of the editor: Dr. Hewson (reviewer A) accepted the invitation of becoming a co-author of the article, hence he resigned from his task of reviewer.
The whole article is a very readable and enlightening review of the Kondo Effect. But sometimes I felt that sections separating subtopics might be helpful to the reader. Another request is to put in figures in appropriate places; in particular I feel like to have the figure showing the excellent agreement between the theoretical and experimental resitance curves. Another is for the curves of resistance versus T for La<1-x>Ce<x>Cu<6> with various values of x.
Next I mention minor points which might be of help for the author to correct misprints or to know what the reader may want to know.
1) In lines 17-18, p. 1, ﾒresistivity arising from lattice scattering and that arising from Kondo effect and proportional to logT.ﾓ This might be rewritten more explanatorily as ﾒresistivity arising from lattice scattering which decreases and that arising from Kondo effect which increases with decreasing temperature proportionally to -logT.ﾓ 2) After eq. (4) in line 10 in p. 4, it might be helpful to have a comment such as ﾒThis equation is valid also in the case where the electron spin is flipped in the scattering process.ﾓ This might be concisely combined with the sentence before the equation. 3) In line 14, p. 5, ﾒJrho is of the order of ﾐ0.1ﾓ may be more explanatory in such a way as ﾒJrho takes a negative value of about ﾐ0.1ﾓ 4) In line 4, p. 6, ﾒas the temperature approaches T<K> defined byﾓ might be written as ﾒas the temperature approaches the so-called Kondo temperature T<K> defined byﾓ . 5) In line 10, p. 13, ﾒseveral ten thousandsﾓ may be corrected to ﾒseveral tens of thousandsﾓ. 6) In lines 12-13, p. 13, ﾒhave foundﾓ may be ﾒhave been foundﾓ .
Something might be wrong but I wish my comments would be useful to the author.
new reviewer A
The present article on Kondo effect is clearly written so that it should be accepted without any major change.
The referee has some minor suggestions, however.
(1) This article starts from a short definition of the Kondo effect. The statement is certainly correct, but it seems to me that the definition is too narrow. Many researchers now use the word "Kondo effect" in a slightly broader sense including not only the log T dependence of resistivity but also anomalous temperature dependence in general caused by many-body effects due to localized magnetic moments in metals. As an example, I should like to propose the following definition:
The Kondo effect is, in the narrow sense, an unusual scattering mechanism of conduction electrons in a metal due to magnetic impurities, which contributes a term to the electrical resistivity that increases logarithmically with temperature as the temperature T is lowered (as Log(T)). Nowadays the Kondo effect means, in a broader sense, anomalous temperature dependence of physical quantities, which originates from many-body processes caused by quantum-mechanical nature of localized magnetic moments in a metal. Thus the Kondo effect has become a key concept to understand various problems in condensed matter physics.
(2) A minor misprint is present in eq.(6). epsilon_k should be replaced by epsilon_F.
(3) It would be helpful for readers to mention briefly that J<0 comes from the mixing of wave functions between the localized state and conduction electrons, as descibed in the original paper by Jun Kondo.
(4) In the Section of "The Kondo Problem" the contribution of Nozieres is mentioned together with his paper in LT conference. It seems more appropriate however to cite his original paper (J. Low. Temp. Phys. 17, 31 (1974)) rather than his paper in conference proceedings.
(5) The source of Fig. 6 (A. Sumiyama et al.: J. Phys. Soc. Jpn. 55, 1294 (1986)) should be mentioned in the Figure Caption.
(6) In Fig. 7 \(CeCy_2Si_2\) is not correct. It is actually \(CeCu_2Si_2\). This should be pointed out in the Figure Caption.