Two-Carrier Description of Cuprate Superconductors from NMR

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This manuscript presents an exciting detective story on the nature of the HTSC in cuprates seen through the NMR data. They discover a universal relation, eq. (2), and explain the results by a two-component model, one due to the hybridized Cu-O orbital, and the other due to an isotropic component just on Cu. They have similar, but different, temperature dependences. The planar part is universal, but the isotropic one is composition dependent. They suspect that the latter may involve Cu 4s orbital. This is the beginning of a new pathway to solve this age-old mystery. It is well-written and should be published almost as is.

The scaling by eq. (2) and Fig. 3 is really impressive, and tells an important story. Here the shift, delta, depends on composition through the maximum Tc.  It will be useful to add a plot of delta vs. T_c,max, or the distance between Cu and apical oxygen, to support the story in the text. 

A minor point; in Figs. 3 and 4 the sample description needs a small explanation; OV92 must mean overdoped with Tc = 92K, etc.

 

Author Response

Comment 1: It will be useful to add a plot of delta vs. T_c,max, or the distance between Cu

and apical oxygen, to support the story in the text.

Response 1: Thank you for pointing this out. We agree that a plot showing a family dependence might be helpful. A new figure relating to this comment can be now found in the revised version of the manuscript. Since Tc,max is not directly applicable for each material in question, we have used the oxygen hole content, n_p, which is known to scale with Tc,max and readily available from NMR (see Rybicki et al. 2016). Note that we show S*chi_IC vs. n_p rather than the offset delta, as we believe it is the more informative relation with respect to cuprate superconductivity.

Comment 2: A minor point; in Figs. 3 and 4 the sample description needs a small explanation; OV92 must mean overdoped with Tc = 92K, etc

Response 2: Your interpretation of the notation is indeed correct. Since it may not be obvious to a reader who is not familiar with this notation, we have added a key to the notation in the figure legends wherever it is used.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

NMR spectroscopy is a powerful experimental technique which was intensively applied to study high-T_c superconductivity in cuprates starting from their discovery. Early on, many researchers concluded that the properties of cuprates could be described within a single-electronic-fluid picture. However, a number of experimental observations cannot be satisfactorily explained within this simplified scenario.

In this manuscript, Bandur et al. present an interesting investigation and analysis of planar copper and oxygen NMR data from essentially all hole doped cuprates with a particular emphasis on NMR spin shifts. By doing this analysis, the authors discovered a remarkable scaling between the planar Cu axial shift and any planar O shift in essentially all cuprates. Authors propose a phenomenological explanation of this scaling within the two-component spin susceptibility framework. Implications of the obtained results for the physics of cuprates is discussed in detail.

This work demonstrates a deep knowledge of both the experimental literature and the longstanding conceptual challenges in cuprates NMR. It resolves the long-standing NMR shift conundrum, i.e. the missing scaling between the bare copper and oxygen shifts. Obtained results are important to get further insight into the microscopic physics governing the properties of the cuprate high-T_c superconductors. The manuscript fits very well within the scope of the journal Condensed Matter and will be of significant interest to researchers working on high-Tc superconductivity and NMR spectroscopy.

I have following remarks concerning the text of the manuscript:

1. The physical origin of the temperature-independent offset δ remains somewhat unclear. May be authors can provide more clear discussion about its possible origin.
2. Authors discuss the correlation between the two susceptibilities and superconducting properties of cuprates. However, it is difficult to follow this discussion without any figures in the manuscript illustrating such correlations. If possible, it would be very helpful to plot the variation of the two susceptibilities as a function of doping and across different cuprate families. This would improve readability of the manuscript, which is quite dense and difficult to follow in the discussion and conclusion section.

To summarize, the manuscript presents a significant progress in the understanding of cuprate superconductors based on NMR data. The results are interesting and the conclusions are largely well supported. After addressing the minor clarifications suggested above, the paper will be well suited for publication in the journal Condensed Matter.

Comments for author File: Comments.pdf

Author Response

Comment 1: The physical origin of the temperature-independent offset δ remains somewhat unclear. May be authors can provide more clear discussion about its possible origin.

Response 1: δ is a temperature independent shift contribution on planar copper which appears mainly in K_parallel. Indeed, the origin of the family-dependent offset remains unclear, and we have currently no rigorous explanation for it. We have modified the text discussing delta to make clear that it is, in fact, of as-yet undetermined origin, and state that this is an open research question. As a side note: a previous attempt in explaining family- dependent orbital shift contributions on planar copper was proposed by Zheng et al. 1996 Physica C. We currently do not know whether this scenario is realistic for the cuprates.

Comment 2: Authors discuss the correlation between the two susceptibilities and superconducting properties of cuprates. However, it is difficult to follow this discussion without any figures in the manuscript illustrating such correlations. If possible, it would be very helpful to plot the variation of the two susceptibilities as a function of doping and across different cuprate families. This would improve readability of the manuscript, which is quite dense and difficult to follow in the discussion and conclusion section.

Response 2: Thanks for pointing this out. We agree that an additional figure improves the readability of the manuscript. Such a figure has now been added in order to highlight family- dependent differences of the interplanar component and provide a visual representation of what is discussed in the text.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

In the present paper, on the basis of analysis of comprehensive NMR data on the cuprate superconductors in the literature, the authors propose a new universal scaling of the temperature, doping, field-direction, and family dependences of the ⁶³Cu and ¹⁷O NMR line Knight shifts. It has been demonstrated that the ¹⁷O shifts can be understood as an isotropic one component while that the ⁶³Cu shifts have two components. The first component is isotropic and family-independent, reflecting the two-dimensional character of the CuO₂ plane, while the other is more three-dimensional, and family-dependent, eventually leading to the different T_c,max’s of different families. The data analysis is impressively extensive, and the deduced scaling is new and highly suggestive. The new scaling is important and will have significant impact on the high-T_c research. Therefore, I would like to support the publication of the paper in Condensed Matter. Prior to the publication, the authors may improve the paper by taking into account the following points, most of them are minor:

1. It is stated that the additional shift at planar Cu is isotropic for most materials except La_2-xSr_xCuO₄. Does this suggest the involvement of the axial orbitals (Cu 3d_z2-r2, Cu 4s, apical p_z), which are important only in LSCO (Ref. 7: Pavarini et al., PRL)? The authors can discuss this point in relation to the x-ray absorption study of LSCO single crystals by C. T. Chen et al., PRL 68, 2543 (1992).
2. The second component is concluded to be three-dimensional due to its doping dependent DOS at EF. Why does this doping dependence suggest the three-dimensionality?
3. “La0201” in Fig. 2 seems to represent La_2-xSr_xCuO₄ but is not very common. It may be replaced by “La214”.
4. The dark green and orange markers in Fig. 2(d) have no corresponding data in Fig. 2(a)-(c). Why?
5. The numbers for the ⁶³K_|| and ⁶³K_⊥ axes are inconsistent between Fig. 2(b) and Fig. 2(d).
6. It is mentioned that d is temperature-independent, but it should also be mentioned whether d is family-dependent or family-independent.
7. Line 171: Should “Fig. 2(b, d)” read “Fig. 2(c, d)”?
8. Definition of Δχ^IC is necessary since Δχ^PC is explicitly defined.

Author Response

Comment 1: It is stated that the additional shift at planar Cu is isotropic for most materials except La2-xSrxCuO4. Does this suggest the involvement of the axial orbitals (Cu 3dz2-r2, Cu 4s, apical pz), which are important only in LSCO (Ref. 7: Pavarini et al., PRL)? The authors can discuss this point in relation to the x-ray absorption study of LSCO single crystals by C. T. Chen et al., PRL 68, 2543

(1992).

Response 1:
Yes, you are exactly correct, that we believe this additional shift is related to the axial orbitals which have a significant weight near the Fermi level in LSCO, unlike other cuprates. We have expanded on this a bit in the text to clarify. Thank you as well for the additional reference; it fits well into our manuscript and we have added it to the discussion of LSCO.

Comment 2: The second component is concluded to be three-dimensional due to its doping dependent DOS at EF. Why does this doping dependence suggest the three-dimensionality?

Response 2:

We have removed this statement, as it was intended to be more of a side-note than a reason for our conclusions; the reason the second component is described as more three-dimensional is due to the s-like nature, which is not so two-dimensionally confined to the CuO2 planes as the dx2-y2/p_sigma hybridized orbitals are.

Comment 3: “La0201” in Fig. 2 seems to represent La2-xSrxCuO4 but is not very common. It may be replaced by “La214”.

1

Response 3:

Thank you for pointing this out. We have changed the notation accordingly to make it more accessible.

Comment 4: The dark green and orange markers in Fig. 2(d) have no corresponding data in Fig. 2(a)-(c). Why?

Response 4:

The panels of Fig. 2 are intended to be a survey of a few representative datasets rather than the totality of the available data; It was our intention here to just give a brief overview, and refer the reader who wants to see the full data sets to the paper cited in the caption, among others. Additionally, in terms of the oxygen data, not all materials have been measured in all orientations with respect to the magnetic field.

Comment 5: The numbers for the 63K|| and 63K⊥ axes are inconsistent between Fig. 2(b) and Fig. 2(d).

Response 5:

Yes, it is mentioned in the caption that in (b), the temperature-independent shift contributions have been removed. We have changed the axis labels on this figure to add the superscript S to indicate more clearly that this is only the spin part of the shift.

Comment 6:

Response 6:

Thank you for pointing out that this was unclear. We have added explicitly where we introduce delta that it is indeed family dependent.

Comment 7: Line 171: Should “Fig. 2(b, d)” read “Fig. 2(c, d)”?

Response 7:

It was actually meant as-is. However, upon reflecting, we decided to only refer to Fig. 2(d) since it is more directly visually relevant here.

Comment 8: Definition of ΔχIC is necessary since ΔχPC is explicitly defined.

Response 8:

Thank you for pointing this out. We have added an explicit definition of χIC.

 

 

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

The paper under consideration presents a systematic study of NMR frequency shifts in cuprate superconductors, offering a valuable synthesis of a large extent of experimental data. The authors have organized these results, allowing for a clear comparison that successfully highlights common trends across the cuprates families. This comparison is highly useful for researchers in the field.

To account for the observed trends, the authors propose an explanation based on the presence of two distinct susceptibilities related to the planar and inter-planar nature of the spin components. This approach is convincing and provides a physical basis for the experimental observations. The interpretation offered is not only plausible but also aligns with a physical scenario consisting in a two-band electronic structure and the presence of striped phases in the cuprates.

The work is of high scientific quality, combining data analysis with a conceptual model. The findings contribute significantly to the understanding of these materials, and the manuscript is written very clearly.

Hence, I recommend that the article be accepted for publication in its current form.

with regards, 

the reviewer

Author Response

Dear Reviewer,

Thank you very much for taking the time to read and review our manuscript. We are very appreciative of your feedback and broad-scope view of the cuprates.

Yours Sincerely, The authors

Author Response File: Author Response.pdf