Mechanism of High-Temperature Superconductivity in Correlated-Electron Systems
Round 1
Reviewer 1 Report
Manuscript number: condensedmatter-502569 Condenssed Matter MDPI (Article)
TITLE: Mechanism of high-temperature superconductivity in many-electron systems
AUTHORS: Takashi Yanagisawa
The manuscript entitled “Mechanism of high-temperature superconductivity in many-electron systems” by T. Yanagisawa is devoted to theoretical investigation of high-temperature superconductivity in a model system (Hubbard model, d-p model) by means of variational Monte Carlo. The paper is written in a good English and is readable easily by a reader. Nevertheless, before the publication the Author should consider some improvements concerning the points listed below. In my opinion, it should be published after major revisions.
The study of superconductivity in cuprates is a very current topic, in particular in the context its mechanism. It is still unsolved problem about the microscopic origin of high-temperature superconductors, in particular in cuprates (which are considered here) and iron-based pnictides. The results look correct, but obviously I was not able to recalculate them in such short time.
In my opinion the manuscript should be published after major revisions (may be accepted in future for publication with corrections mentioned below).
1. The following is a general comment. Namely, I had a problem with distinguishing what is new results included in the manuscript and what is a review of previous results. The balance between these two as for an original article is not standard. If I properly understood, only in parts 7, 8, and 9 (and 10 as a conclusions) the new results are included. Moreover, the Author cites 42 his works, which is 25% of all bibliography. I understand that the Author is well-known scientist, but could the Author, at least, justify such proportions? Maybe the manuscript should be submitted rather as a review not as a regular article?
2. In section 2 the Author discuss the BCS theory of superconductivity, however, He does not cite original works of Bardeen, Cooper and Schrieffer. In my opinion proper credit, at least to Phys. Rev. 104, 1189 (1956), Phys. Rev. 106, 162 (1957) and Phys. Rev. 108, 1175 (1957), should be included. The similar remark applies to the part devoted to McMilan formula, where the important references, e.g. G.M. Eliashberg, Sov. Phys. JETP 11, 696 (1960), J.P. Carbotte, Rev. Mod. Phys. 62, 1027 (1990) should be cited, because the formula (5) is, in fact derived, in the framework of the Eliashberg formalism.
3. In section 3 the Author wrote: “In the case of half-filling, the Mott transition occurs when U(> 0) is large and the ground state is an insulator.” What does it mean large? For the Bethe lattice U/D (D – half-bandwidth) is about 3 for Mott metal-insulator transition. Is it big? Moreover, for large U the insulator is described by t-J model [originally derived in, e.g., J. Phys. C 10 (1977) L271, Phys. Rev. B 18 (1978) 3453] and the Heisenberg model is the limit of Hubbard model only for U going to infinity (and for half-filing). I suggest to rewrite the text in the neighborhood of Eq. (7) to be more precise.
4. Later in Section 3 it is written that “The mechanism of superconductivity is certainly non-phonon mechanism.” After that there is not any references supporting such statement. In my opinion, apart from the arguments described in the manuscript text (near Eq. (8)), the other reason supporting that statement is also small size of Cooper pair in cuprates [compare also so-called theories of local pairs, e.g., Rev. Mod. Phys. 62, 113 (1990), Physica C 210, 61 (1993), J. Phys. Condens. Matter 24, 215601 (2012), and references therein] . Nevertheless, some references to existing literature, even in the existing text, should be included.
5. There is no origin of data in Table 1 given. It should be improved.
6. In Fig. 6 the “on-site attractive region” is indicated. Is it a region of superconducting phase existence or not? Please clarify.
7. I cannot seen the ticks on the horizontal axis in Figs. 6, 7, and 8 – they should be above/before the color filling of the graphs or outside the graph (they should be simply visible). Such improvement would be very useful for a reader for proper identification of the parameters.
8. In captions of Fig. 3, 4, 5 it should be clearly indicated that the results are obtained for Hubbard model or for d-p model. Please, add the proper text.
9. From the caption of Fig. 8 one can conclude that the Section 9 is devoted only for the Hubbard model, but in the main text I do not see any information. Such information should be added. I regret that similar analysis has not been performed for d-p model from Section 5.
10. At the beginning of Section 8.2 the Author wrote: “In general, in the three-band d-p model, the AF correlation is very strong and the AF state is more stable than in the single-band Hubbard model”. Is it any general rule or theorem somewhere proven? Next, the Author wrote: “It is necessary to find the region where the AF correlation is weak.” I guess that this is due to the fact that the superconductivity is of the Author interest, but it could be clearly indicated.
11. In Section 9 the mutual stability between there different phases is discussed. The phases are AFI (antiferromagnet), AFSC (the coexistence of antiferromagnetism and superconductivity) and SC (superconducting). In Figure 8 there is also presented condensation energy as a function of doping. As I understood the condensation energy is a difference between the state with Delta=0 and with Deltamin, which correspond the state with minimal energy (obtained by variation of trial function). We have for region: x<0.06 - only AFI solution found, 0.06<x<xA – only AFSC solution found, xA<x<xB – both AFSC and SC solutions found, and x>xB – only SC solution found. From the figure one can see that if SC state exists (it appears for xA=0.07) it has always lower energy that AFSC state. I also understood that in the region xA<x<xB two solutions exist (AFSC and SC). Thus the AFSC-SC transition is not for x corresponding to vanishing of AFSC state (which is xB=0.09), but this corresponding to the appearance of SC phase [I cannot see the value precisely due to absence of ticks on horizontal axis]. Am I correct? In my opinion the statement “In the underdoped region, approximately 0.06 < x < 0.9 in this figure, there is the coexistent state of antiferromagnetism and superconductivity” is misleading. Moreover, what type of coexistence occurs in AFSC state – is it microscopic coexistence (mixed phase) or phase separation (macroscopic coexistence)?
12. What is the phase separation inside AFI region, for which the criterion is determined from Eq. (31)? Is it a macroscopic separation and is Eq. (31) equivalent with Maxwell’s construction [cf. eg., 1991 Phys. Rev. B 44 7455 (1991); J. Phys. Condens. Matter 24, 215601 (2012)]? Or is the mentioned phase separation is something different (e.g. Phys. Rev. B 70 224516 (2004)) ? It is not clear. Please, explain.
13. The title of the article suggest that the mechanism of high-temperature superconductivity in many-electrons system will be presented. But in conclusions, I do not see any explicit statement what is the mechanism. Could the Author indicated what is the mechanism? In addition I would like to put attention that superconductivity always occur in many-electron system [it is collective state of Cooper pairs consisting of two electrons]. Maybe, some reformulation of the title should be considered.
After these issues will be resolved, I believe this paper might become suitable for publication in “Condensed Matter” MDPI journal. It can be quite important contribution to the existing literature.
Author Response
Manuscript number: condensedmatter-502569
Responses to Reviewer 1
We have revised the manuscript following comments and suggestions by the reviewer. Our responses are as follows.
1. The Manuscript has two parts. In Part I, we give a brief review on mechanisms of superconductivity. In Part II, we discuss the mechanism of high temperature cuprates. We think that the manuscript is regarded as a review.
2. We included references of the BCS theory and the McMillan formula following suggestions.
3. In the manuscript, ‘large’ means as large as the bandwidth. We say that U is large when U/D is about 3. When U is of the order of the bandwidth, U is not large enough to perform the mapping to the t-J model. We do not consider such a region where the t-J model description is relevant.
4. We added references suggested by the reviewer.
5. We added references for Table 1. The value of transfer t has been estimated for cuprate superconductors, iron based superconductors and others.
6. It is not clear whether the ground state is superconducting or forms a charge-density wave in the “on-site attractive region”. We expect that there is the possibility that an s-wave superconductivity occurs in this region.
7. Figures 6, 7 and 8 are modified so that the ticks are clearly shown.
8. The captions of Figs. 3, 4 and 5 are revised to show that the results are obtained for the Hubbard model.
9. The description of Sec. 9 is modified. A similar study for the d-p model is under study now.
10. In OVMC calculations for the d-p model, the AF state becomes very stable compared to the single-band Hubbard model. This is the empirical result and there is no theorem about this.
11. As the reviewer pointed out, the AFSC-SC transition is not for corresponding to vanishing of AFSC state. The transition is at x=xc where 0.06<xc<0.09. The exact value of xc has not been determined.
12. The phase separation inside AFI region is equivalent with Maxwell’s construction. We cited references following suggestion.
13. We think that the mechanism of high-temperature superconductivity is the electron pairing due to the strong correlation. We modified the title of the paper a little bit.
We believe that the manuscript has been improved and thank the reviewer for useful comments.
Reviewer 2 Report
The manuscript by Yanagisawa discusses high temperature superconductivity for correlated electron systems. It provides rather extensive, and useful, introduction, to the various theories of different superconductivity mechanisms. Then it proceeds to describe the variational Monte carlo method, and presents original results for certain parametrization on the antiferromagnetic and the superconducting states, with rather specific predictions of doping level suggested for very high temperature superconductivity in cuprates.
The mechanism of superconductivity in cuprates has been a very long standing and extremely important theoretical challenge, so any contribution is welcome to this topic - which is perfectly suited to the journal Condensed Matter.
The quality of the presentation is very good, there are only a few typoes here and there.
Author Response
Manuscript number: condensedmatter-502569
Responses to Reviewer 2
Thank you for your comments on the manuscript. We thank the reviewer for appreciating our paper.
Reviewer 3 Report
1st review of "Mechanism of high-temperature superconductivity in many-electron systems" by Takashi Yanagisawa
Articles concerns very important field of physics : high temperature (HTC) superconductors (SC). In my opinion article has form of review paper and I'm how should be evaluated. If as a regular article, then author should shown what elements described in paper are new. It is important in context of 162 references. Unfortunately I can't find this information exactly in introduction or summary.
In my opinion paper is little chaotic. I can not accept paper in this form.
Please, indicate new elements in paper.
Section 2: described e.g. superconductivity in context BCS theory, where el-ph interaction is main source s-wave symmetry. Why in relation to HTC SC this is important ? As we know in HTC SC we observe d-wave superconductivity. Additionaly in realtion to the conventional SC the HTC materials are mult-atomic (which autor should exact described in 5 Sec.).
Large negative site of paper is absence references to experimental papers (e.g. in Sec. 4 , where author described efective mass in different materials). Maybe some of ref from table 2 can be helpfully.
In references can be added few new / more recent papers about HTC SC : e.g. D. Rybicki et al., Nat. Commun. 7, 11413 (2016)
Fig. 5 - plots shown AF order parameter : how defined ? this quantity is not defined in text.
Fig. 8 - why boundary between AF and AF-SC in for const x ?
If author shown only results from OVMC (see last paragraph of Introduction) maybe sec 2-4 are not necessary?
Author Response
Manuscript number: condensedmatter-502569
Responses to the reviewer 3
We have revised the manuscript following comments by the reviewer. Our responses are as follows.
1. We divided the manuscript into two parts. The first part, Part I, gives a brief review on mechanisms of superconductivity, and we discuss the mechanism of high-temperature cuprates in the second part, Part II. New results are shown in Part II.
2. We added references for experimental results. We also added the paper by D. Rybicki et al. following suggestion.
3. We amended the figure caption of Fig. 5 where the vertical axis indicates the condensation energy of AF state.
4. We added a description on Fig. 8. The transition from AF-SC to AFI occurs at some value of x=xA, and for x<xA the ground state becomes an insulator. The transition occurs because the second derivative of E becomes negative at x=xA.
We believe that the manuscript has been improved and thank the reviewer for useful comments.
Author Response File: 
Author Response.pdf
Round 2
Reviewer 1 Report
I really acknowledge the Author’s efforts to improve the manuscript. Going through the replies for all Referees’ comments I am satisfied with the introduced modifications. Thus, I could recommend the manuscript for publication.
However, in my opinion, the manuscript is too long and has too much references (203) for regular article and should be considered rather as a review. Nevertheless, I think that the paper could be interesting contribution in the field and it should be published in Condensed Matter MDPI journal.
Author Response
I thank the reviewer for valuable comments. I think that it is better to publish the paper as a review.
I thank the reviewer for comments again.
Reviewer 3 Report
2nd review "Mechanism of high-temperature superconductivity in correlated-electron systems" by T. Yanagisawa
I appreciate the effort put in improving the manuscript, however I still can not accept this manuscript -- some corrections confused me:
(line 213) "From this view point the on-site Coulomb interaction can be the candidate of the origin of high temperature superconductivity." -- this can be inncorect understanding, because in typical situation on site interaction is source of s-wave SC. Please explain this sentence or correct it.
Moreover, still few typos can be corrected (e.g. Ref. 141: J. Phys. COndes. Matter should be J. Phys. Condes. Matter; Ref. 188 is Phys. Rev. 2007, B76, 180504 should be Phys. Rev. B 2007, 76, 180504 - similar in Ref.192, 184 etc)
Author Response
I thank the reviewer for useful comments. The paper was amended as follows.
1. The sentence was modified as
“From this view point, the repulsive Coulomb interaction can be a candidate of the
origin of high temperature superconductivity.”
The repulsive interaction usually does not become a source of s-wave
superconductivity, except the cases where it may induce anisotropic s-wave
superconductivity. The on-site attractive interaction of course may induce s-wave
superconductivity.
2. We corrected some typos in the manuscript.
We thank the referee for useful comments again.
