The Ancient Romans’ Route to Charge Density Waves in Cuprates
Round 1
Reviewer 1 Report
The paper "The ancient romans' route to charge density waves in cuprates" by S. Caprara provides an excellent review of the complex evolution of scientific research in the field of polarons and charge density in high temperature superconductors. However, the paper could be improved in a revised version taking into account the following points:
1] in the title and the text (line 35 pag.2) the author could consider to change the French wording "romans' route" into the English wording "roman road.
2] line 1 of the abstract replace "Rome group" with "Rome Groups" since in these last 30 years several groups have been working in the field of theory of high temperature superconductors (HTS) in Rome.
3] at the end of 6th session, after line 218 in pag.7, the author could add few lines to remind the important scenario proposed by other authors in Rome. The author could remind that following the appearance of photo-induced x-ray diffraction satellites in cuprates at low temperature below 150K, in A, B, C references it has been shown the predicted self-organization of anisotropic polarons into striped puddles:
A) Campi, G., Castro, D. D., Bianconi, G., Agrestini, S., Saini, N. L., Oyanagi, H., & Bianconi, A. Photo-Induced phase transition to a striped polaron crystal in cuprates. Phase Transitions 2002, 75(7-8), 927-933.
B) Campi, G., Ricci, A., Poccia, N., Fratini, M., & Bianconi, A. X-Rays Writing/Reading of charge density waves in the CuO2 plane of a simple cuprate superconductor. Condensed Matter 2017, 2(3), 26.
C) Kusmartsev, F. V., Di Castro, D., Bianconi, G., & Bianconi, A. Transformation of strings into an inhomogeneous phase of stripes and itinerant carriers. Physics Letters A 2000, 275(1-2), 118-123.
The data analysis has shown that photoinduced polarons have an anisotropic shape with a finite size of about 1 nm; it has been inferred that they are in the intermediate coupling regime and coexist with itinerant carriers in the doping range between 0.06 and 0.21 holes per Cu site. From these experimental results Campi et al. have deduced that the intermediate polarons show internal fluctuations which generate an anisotropic polaron-polaron van Der Waals attraction giving a fluid-like behavior exhibiting a complex phase separation. They have proposed a phase diagram formally similar to the gas-to-liquid-liquid transition in supercooled water, where the anisotropy interaction generates a novel intermediate liquid phase between the standard gas and liquid phases.
D) Campi, G., & Bianconi, A. A Case of Complex Matter: Coexistence of Multiple Phase Separations in Cuprates, in Symmetry and Heterogeneity in High Temperature Superconductors 2006, pp. 147-156, Springer, Dordrecht.
E) Innocenti, D., Ricci, A., Poccia, N., Campi, G., Fratini, M., & Bianconi, A. A model for liquid-striped liquid phase separation in liquids of anisotropic polarons. Journal of superconductivity and novel magnetism 2009, 22(6), 529-533.
F) Campi, G., Innocenti, D., & Bianconi, A. CDW and similarity of the Mott insulator-to-metal transition in cuprates with the gas-to-liquid-liquid transition in supercooled water. Journal of Superconductivity and Novel Magnetism 2015, 28(4), 1355-1363
4] This intermediate phase has been identified with the 1/8 polaronic generalized Wigner CDW phase. In this scenario, it was proposed that the superconducting phase is determined by the complex filamentary network of interface pathways which could be mapped by an hyperbolic geometry:
G) Campi, G., & Bianconi, A. High-Temperature superconductivity in a hyperbolic geometry of complex matter from nanoscale to mesoscopic scale. Journal of Superconductivity and Novel Magnetism 2016, 29(3), 627-631.
Finally, the paper is worth of publication in the Condensed matter special issue but the author has to consider the suggested improvements, submitting a revised manuscript
Author Response
I thank the referee for her/his constructive criticism, that really helped me to improve the quality of my presentation. I have definitely been too hasty, it is evident that a work covering three decades of research activities should include many more references. I definitely agree to add those that the referees suggest (and even few more), although I feel that the list will never be really complete.
Now I come to the response point by point:
1] in the title and the text (line 35 pag.2) the author could consider to change the French wording "romans' route" into the English wording "roman road.
The English dictionary includes the word “route” with two meanings:
1. a way or course taken in getting from a starting point to a destination;
2. a method or process leading to a specified result.
That is the reason why I preferred the word “route”, and I would like to keep it. But if the referee really feels that this usage might be misleading, than I am ready to accept the referee’s suggestion.
2] line 1 of the abstract replace "Rome group" with "Rome Groups" since in these last 30 years several groups have been working in the field of theory of high temperature superconductors (HTS) in Rome.
Yes, of course, I apologize for my sloppiness. Now I specify “the research group in Rome, to which the author belongs” and then, in the body of the paper, I also add a sentence “It must be emphasized that, over more than three decades, several groups in Rome have been working in the field of high-Tc cuprates. Their role and relevance is witnessed by the many references cited in this piece of work.”
3] at the end of 6th session, after line 218 in pag.7, the author could add few lines to remind the important scenario proposed by other authors in Rome. The author could remind that following the appearance of photo-induced x-ray diffraction satellites in cuprates at low temperature below 150K, in A, B, C references it has been shown the predicted self-organization of anisotropic polarons into striped puddles:
A) Campi, G., Castro, D. D., Bianconi, G., Agrestini, S., Saini, N. L., Oyanagi, H., & Bianconi, A. Photo-Induced phase transition to a striped polaron crystal in cuprates. Phase Transitions 2002, 75(7-8), 927-933.
B) Campi, G., Ricci, A., Poccia, N., Fratini, M., & Bianconi, A. X-Rays Writing/Reading of charge density waves in the CuO2 plane of a simple cuprate superconductor. Condensed Matter 2017, 2(3), 26.
C) Kusmartsev, F. V., Di Castro, D., Bianconi, G., & Bianconi, A. Transformation of strings into an inhomogeneous phase of stripes and itinerant carriers. Physics Letters A 2000, 275(1-2), 118-123.
The data analysis has shown that photoinduced polarons have an anisotropic shape with a finite size of about 1 nm; it has been inferred that they are in the intermediate coupling regime and coexist with itinerant carriers in the doping range between 0.06 and 0.21 holes per Cu site. From these experimental results Campi et al. have deduced that the intermediate polarons show internal fluctuations which generate an anisotropic polaron-polaron van Der Waals attraction giving a fluid-like behavior exhibiting a complex phase separation. They have proposed a phase diagram formally similar to the gas-to-liquid-liquid transition in supercooled water, where the anisotropy interaction generates a novel intermediate liquid phase between the standard gas and liquid phases.
D) Campi, G., & Bianconi, A. A Case of Complex Matter: Coexistence of Multiple Phase Separations in Cuprates, in Symmetry and Heterogeneity in High Temperature Superconductors 2006, pp. 147-156, Springer, Dordrecht.
E) Innocenti, D., Ricci, A., Poccia, N., Campi, G., Fratini, M., & Bianconi, A. A model for liquid-striped liquid phase separation in liquids of anisotropic polarons. Journal of superconductivity and novel magnetism 2009, 22(6), 529-533.
F) Campi, G., Innocenti, D., & Bianconi, A. CDW and similarity of the Mott insulator-to-metal transition in cuprates with the gas-to-liquid-liquid transition in supercooled water. Journal of Superconductivity and Novel Magnetism 2015, 28(4), 1355-1363
Thank you for these suggestions, text and reference list have been modified accordingly.
4] This intermediate phase has been identified with the 1/8 polaronic generalized Wigner CDW phase. In this scenario, it was proposed that the superconducting phase is determined by the complex filamentary network of interface pathways which could be mapped by an hyperbolic geometry:
G) Campi, G., & Bianconi, A. High-Temperature superconductivity in a hyperbolic geometry of complex matter from nanoscale to mesoscopic scale. Journal of Superconductivity and Novel Magnetism 2016, 29(3), 627-631.
Thank you for this suggestion, text and reference list have been modified accordingly.
I have carefully considered all the remarks and suggestions of the referee, and changed the manuscript accordingly. I hope that the manuscript may now be accepted for publication.
Reviewer 2 Report
In this paper the author describe the charge density wave scenario of high temperature cuprate superconductors (HTC). After a brief but exhaustive introduction the author describe the evolution of the theory and then compares the output with different experiments spanning decades.
This paper represents a nice review which brings the reader to have an account of the "historycal" evolution of the CDW scenario put forward by the group of rome over several decades. In parallel it is described some evolution which occurred in the experimental techniques and how experimental results compares with the theory.
An issue which should be clarified better in the present paper is the relevance of the proposed charge fluctuation scenario vs its theoretical competitors such as the spin mediated attraction.
It is clear that many other scenarios have been proposed to explain some features of the HTC and the present paper focused on only one of that, however it would be of benefit to the reader to have comparison with such other scenarios.
This could be of relevance especially discussing the experiments. (sect. 4,5,6).
Here follows some detailed comments to the manuscript.
Eq. (1) the "potential" shown here is a complex variable depending on q and \omega. The author should better clarify the physical meaning of (1) also in relation with diagrams presented in Fig. 1
line 90
"Since this wave vector is the result of the form of Vee and Π, as functions of q, the
instability wave vector qc is unrelated to the periodicity"
this seems in contraddiction with line 96 statement
"The details of the band structure of cuprates, determining Π, and of the effective interaction Vee"
Figure 1. u is unclear to me what means the dotted line enetring the vertex u? From the unnumbered equation before Fig. 1 is not clear to me that u should be an interaction among dynamical CDW as stated il line 99. Could the author better specify the meaning of u?
Fig. 2 This as far as I understand is a sketch of a possible phase diagram. But in the caption is written "TC0DW below which charge density waves should occur in the random phase approximation" this would prompt the reader to a quantitative calculation. If this is the case the author should mention the calculation explicitly. It is however quite difficult to understand to which extent details of this phase diagram are related to actual calculation. In particular is unclear whether Tc(p) line has been drawn according some calculation on a definite model.
line 132 omit or at least comment some results.
section 4.
Other bosonic mediators may have properties detected in ARPES similar to CDW, it would of benefit to comment the peculiarities of CDW mediator.
section 5.
Same as section 4.
lines 157-162 Do analysis cited here means that the proposed scenario has a limited validity i.e. is valid only in the overdoped regime? If so this point should be more emphasized.
section 6.
lines 208-212 It is not clear to me why the resiliency of superconducitivity have necessarily the same origin in the overdoped and in the underdoped region of phase diagram. Again spin fluctuations should be dominant in the latter. Could the author better clarify this point?
206 Tc(x)? should be Tc(p)
Author Response
I thank the referee for her/his constructive criticism, that really helped me to improve the quality of my presentation.
Now I come to the response point by point:
1] An issue which should be clarified better in the present paper is the relevance of the proposed charge fluctuation scenario vs its theoretical competitors such as the spin mediated attraction.It is clear that many other scenarios have been proposed to explain some features of the HTC and the present paper focused on only one of that, however it would be of benefit to the reader to have comparison with such other scenarios. This could be of relevance especially discussing the experiments. (sect. 4,5,6).
Yes, of course. I am aware of the fact that that there are several scenarios. My intention was to focus on a single scenario, because the scope of this piece of work is to tell the story of how such a specific scenario emerged, given for granted that along the years, other scenarios, based on other assumptions and experimental facts, have been developed. However, I also understand the point of view of the referee, so I modify the introductory section accordingly.
2] Eq. (1) the "potential" shown here is a complex variable depending on q and \omega. The author should better clarify the physical meaning of (1) also in relation with diagrams presented in Fig. 1.
Actually, in Fig. 1 I did not represent the diagram corresponding to Eq. (1), which is the standard Random-Phase-Approximation expression of a screened electron-electron interaction. This can become complex (contrary to the bare - i.e., unscreened - electron-electron interaction, that is real) because the polarization bubble Π is a complex function, including damping effects resulting from the decay process involving electron-hole pairs. I tried to make this point clearer. Furthermore, it seems a good suggestion to add to Fig. 1 also the diagrams leading to Eq. (1) (more precisely, the closely related Eq. (3)].
3] line 90
"Since this wave vector is the result of the form of Vee and Π, as functions of q, the
instability wave vector qc is unrelated to the periodicity"
this seems in contraddiction with line 96 statement
"The details of the band structure of cuprates, determining Π, and of the effective interaction Vee"
It is not a contradiction, but I understand the referee’s concern. The detail of the band structure are, of course, important, but since the point in q space where Vee and -1/Π meet (q=qc, the instability characteristic wave vector) is not fixed by the lattice periodicity, it describes an incommensurate charge density wave. I tried to improve the discussion about this relevant issue.
4] Figure 1. u is unclear to me what means the dotted line entering the vertex u? From the unnumbered equation before Fig. 1 is not clear to me that u should be an interaction among dynamical CDW as stated il line 99. Could the author better specify the meaning of u?
Actually the line is dashed, so it represents a charge density wave. In a solid, elementary excitations are usually described like particles (they are called quasiparticles). Quasiparticles interact the same way electrons do (although with a different form of the interaction, depending on the specific excitation). In the Feynman diagram language Fig. 1 (b) [former (a)] represents two incoming charge density waves that scatter and give rise to two outgoing charge density waves. The interaction is “mediated” by electrons in the medium (the solid circle describes a virtual electron that propagates), in low-energy processes, this effective interaction is a constant, here called u. As a result of this interaction, parameters defining the charge density waves are corrected with respect to their value in the absence of interaction, by terms proportional to u in perturbation theory. This holds, e.g., for m0 which is corrected into m=m0+u\delta m, where the term u\delta m represents the correction proportional to u. I tried to make this point clearer
5] Fig. 2 This as far as I understand is a sketch of a possible phase diagram. But in the caption is written "TC0DW below which charge density waves should occur in the random phase approximation" this would prompt the reader to a quantitative calculation. If this is the case the author should mention the calculation explicitly. It is however quite difficult to understand to which extent details of this phase diagram are related to actual calculation. In particular is unclear whether Tc(p) line has been drawn according some calculation on a definite model.
The details of the calculations might be found in the original papers. Here, my scope is only to provide an idea. However, I agree with the referee that the idea can be conveyed in a more meaningful way, so I tried to modify this discussion in the revised version. The Tc(p) line is the experimental one.
6] line 132 omit or at least comment some results.
Comments have been added.
7] section 4.
Other bosonic mediators may have properties detected in ARPES similar to CDW, it would of benefit to comment the peculiarities of CDW mediator.
Yes, and indeed some features of the ARPES spectra are captured by spin fluctuations, with similar structure, but different values of the parameters (for instance, a different qc). I expanded this part in the revised version.
8] section 5.
Same as section 4.
lines 157-162 Do analysis cited here means that the proposed scenario has a limited validity i.e. is valid only in the overdoped regime? If so this point should be more emphasized.
No, it is valid at all dopings where the anomalous peak is observed. The spin fluctuations do contribute to Raman spectra, but since their quantum critical point is at much lower doping, they cannot produce an anomalous peak in the Raman spectra in the region of dopings where it is observed. I tried to make this point clearer.
9] section 6.
lines 208-212 It is not clear to me why the resiliency of superconducitivity have necessarily the same origin in the overdoped and in the underdoped region of phase diagram. Again spin fluctuations should be dominant in the latter. Could the author better clarify this point?
The reason is because the quantum critical point for spin fluctuations is outside the
superconducting dome and not underneath it. So, although spin fluctuations will indeed contribute to pairing, the quantum critical fluctuations boosting Tc must be associated with the quantum critical point(s) underneath the superconducting dome, associated to charge density waves. I made this point clearer in the revised text.
10] 206 Tc(x)? should be Tc(p)
Yes, thank you for spotting the typo.
I have carefully considered all the remarks and suggestions of the referee, and changed the manuscript accordingly. I hope that the manuscript may now be accepted for publication.
Round 2
Reviewer 1 Report
The author has addressed my main criticisms. The manuscript is now well suited to be published in condensed matter.
Reviewer 2 Report
I recognize that the author has taken into account my suggestions and consequently modify the manuscript notably in the introduction as well as in the presentation of the results.
The new version of the paper is more clearer for a wider audience and I think it can be published as it is.
I notice a typo on line 261 (perhaps a {} missing in the latex code)
