Hole doping and electronic correlations in Cr substituted BaFe2As2

We thank the referee for their comments and suggestions. Following are our answers:

1 - Case of hole doping
**** Clearer presentation of the data
Figure 1 in the manuscript has been changed.
*** The dxy hole pocket
We have elaborated further on the subject of the assignment of the orbital character of the bands and the mixed character of the dxy and dzy bands in the case of the 8.5%Cr sample (see below).
Indeed, the blue band in GM-LH direction is not the same as the GX-LH. Rather it is the same as the green one in GM-LV. It is noteworthy that the polarization and measurement-geometry selection rules for the GM direction primarily affect the dxy-derived band (see BFA and Cr3.5%). This also indicates mixed orbital character induced by the increasing Cr content, with the weight of the dxy outer hole pocket reduced in this direction and transferred to the GX direction. Previously, we discussed this effect only in the context of the dxy bands in GX. Following the requested change 2 (see below), we modified Figure 1 and the respective discussion to clarify these aspects.
*** No hole doping in Cr-substituted CsFe2As2
In Ref. [44] the authors report an increase in the Sommerfeld coefficient as a function of Cr content in Cr-substituted CsFe2As2. The result is associated with increasing electronic correlations in this system caused by the Cr introduction. The authors also report ARPES data, focusing on the hole pockets around the Gamma point. Unexpectedly, the hole pocket size barely changes with Cr content, a situation that is reminiscent of the much-debated case of Mn-substituted BaFe2As2. Therefore, from the standpoint of the size of the hole pockets, Cr is not doping holes in CsFe2As2.

2 - MDC analysis
*** Abstract and dyz band
The abstract was changed to make it clear that only the spectral features related to the dyz were extracted from experiments. We called attention to this fact later in the text (introduction and conclusion) as well.
We also would like to assert that the analysis of the spectral features of the dyz is a very robust procedure. This is because for measurements along GX and LV polarization, only one hole band is observed close to the Gamma point (see Fig 1). In the other cases, the spectral analysis is indeed “tentative” and thus was not included in the present version of the paper.

In Figure 4 of the ArXiv V01 of this work (https://arxiv.org/pdf/2312.09014v1) this was included. For reference, the Figure 4 is attached. Panels (a) and (b) show this analysis for the BFA sample. In panel (b), two crossing bands are analyzed for GammaM-LH configuration, and the results are satisfactory. In panel (e) we show some details of the fitting for a selected MDC (two bands = four Lorentzians).
But for Cr8.5%, whereas the results for one band are satisfactory (panel (c)), results for two bands (panel (d)) fail to describe some parts of the spectra. In panel (f) this is explicitly shown in the example. We thus excluded this analysis from the present version of the manuscript to focus only on the spectral analysis of the dyz band, which is a trustworthy and robust analysis for all samples.

Regarding the requested changes:

1 - This is now clarified in the main text. On pages 4-5, the discussion was rewritten for clarity and a new paragraph was included to discuss this point further. This discussion is now as below:

“The Cr hole doping effect on the bands forming the hole pockets around $\Gamma$ is visible from direct inspection of the data. Indeed, the hole pocket Fermi vectors, $k_{F}$, are increasing with Cr introduction, in line with the expectation of hole-doping by Cr substitution. Even for the highest Cr doping level in this work ($8.5\%$Cr), a total of three hole pockets are still visible around $\Gamma$, being mainly observed in pairs because of the polarization selection rules.
Closer inspection in the case of the $8.5\%$Cr sample, reveals a change in the polarization selection rules at this substitution level. In the upper left panel of Fig. 1(c), the spectral weight of the outer hole pocket is seen crossing the Fermi surface in an experimental configuration ($\Gamma X$, LH polarization) for which one expects to observe only bands with $d_{xz/yz}$ main orbital character. This is evidence that the main orbital character of the $d_{xy}$ derived bands and their hybridization are significantly affected by Cr, as observed for Co substitution [57]. In addition, comparing the upper and bottom right panels of Fig. 1(c), one observes a relatively weak polarization dependence. The green band in the upper right panel appears where we would expect, based on the other samples, to observe the outer hole pocket. Instead, this band seems related to the band at the bottom panel and thus is of main $d_{yz}$ orbital character. This also evidences the underlying change in the hybridization of the bands with main $d_{xz/yz}$ orbital characters.”

We also changed the color of the band on Fig 1(c) GM-LH panel from blue to green. Since these bands are broad and overlapping, EDC second derivatives were used to extract some of the points, however, this method is not reliable close to the FS, due to the convolution of the lineshape and Fermi-Dirac distribution. Therefore, we removed the questionable points extracted from EDC second derivative from the green (formerly blue) band, since it misrepresents the actual band dispersion. We claim in the new version of the manuscript, as seen above, that these bands are of dyz character, and the dxy contribution that should be expected for GM-LH is present in the form of a new orbital hybridization.

2 - The range of the binding energy was slightly modified to allow a better visualization of the bands, the fitted band points are plotted smaller for clarity.

3 and 4 - Following the referee’s suggestions, accordingly also with ref 2, we moved the VCA and no VCA comparison to the appendix. The dz² band discussion, which relates directly to the approximation limitation, was also moved. The theory left in the main text of the manuscript is only necessary to address the main experimental results discussions directly, namely, the hole pocket sizes and spectral band analysis.

In this regard, Fig 3 presents data analysis that is motivated by the theoretical results presented in Fig 2. We feel that presenting first all data analysis and then the theoretical results would somehow break this interplay between theory/experiment that was indeed part of our process. We rounded the text, making it shorter and more appealing. We invite the referee for a critical reassessment of the text. We hope that the referee will find that the text now reads smoothly.

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We thank the referee for their comments and suggestions. About the requested changes, we answer in turn:

1 and 2 - regarding the manuscript length and DFT+DMFT calculation details, we followed the referee’s suggestions (also pointed out by ref 3) and moved the VCA and no VCA comparison to the appendix. The dz² band discussion, which relates directly to the approximation limitation, was also moved.

3 - According to the referee’s suggestion, we decided to focus on the aspects that are directly related to our data. Indeed, we do not show a breakdown of low-energy effective models but rather of a particular prediction of the model: i.e. that the magnetism in doped BFA should be connected with the changes in the FS caused by doping. We believe that it is well supported by our experiments that in the case of Cr and Mn-substituted BFA this connection is broken. But it could be indeed the case that a higher order theory can capture the minimal physics.

We have removed the sentence:
“It is thus suggested that low-energy effective models are not adequate to understand the evolution of magnetism for these substitutions.”

We had also rewritten the final paragraph:
“The absence of SC in Cr- and Mn-substituted BaFe$_2$As$_2$ remains a topic of discussion despite intensive research in the past years. In the case of MnBFA, recent experimental work proposes that electronic correlations and the disordered scattering of the Fe-derived magnetic excitations should be part of any minimal model addressing this problem [29, 30]. In the case of CrBFA, the present paper shows that what distinguishes Cr from another hole-doped material, as K-substituted BFA, is indeed the underlying competition between the Cr- and Fe-derived magnetism. This finding suggests that the magnetic scattering of the Fe-derived excitation by Cr suppresses SC in CrBFA.”

We thank Dr. Huiqian Luo for his report.
From the DFT+DMFT calculations, we can extract the quasiparticle weight (Z) as a function of orbital, directly from the Self-energy, without having to consider parabolic band dispersion approximation. The weight ranges between ~0.3-0.5, indicating a correlated regime, having the tendency to decrease as a function of doping. This is shown in the attached figure for our calculations with VCA as dashed lines. By parabolic band fitting, we can extract the effective mass m* which, in this limited approximation, is inversely proportional to Z. By taking Z = 1/m* (valid for the Fermi liquid regime), we can compare the calculated with experimental Z (solid lines). We can see that the experiments show a considerably heavier band close to the Fermi surface for the outer hole pocket of dxy character. The calculation, although capturing the pocket size trend, did not bring much in terms of orbital dependency results. The main conclusion is related to localization as a function of doping, which we had already seen from the ARPES spectral function analysis. Since the parabolic band dispersion approximation is not so precise, we prefer not to bring this comparison to the manuscript.

To mention these results, we include the following paragraph on the manuscript pg 8:

“Electronic correlations can also be examined by extracting the quasiparticle weight, or renormalization factor, (Z). From our calculations, Z can be extracted from the self-energy without using the parabolic band dispersion approximation. These calculations show Z values between $0.3-0.5$, with Z decreasing (more correlated) with doping. From experiments, the mass renormalization ($m^*$) can be obtained by parabolic fittings of the band dispersions. We observed that near the Fermi surface the outer hole pocket, of $d_{xy}$ orbital character, is much heavier ($m^*/m_e$ = 15) than predicted by theory ($m^*/m_e$ = 2.7) and that the orbital dependence of the renormalization factors is stronger. These results, however, may only indicate that accessing correlations by the parabolic approximation is not the best strategy in the case of Hund’s metal [64].”

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